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profile/blog/posts/guest-students-laplace/index_files/libs/quarto-html/quarto.js create mode 100644 profile/blog/posts/guest-students-laplace/index_files/libs/quarto-html/tippy.css create mode 100644 profile/blog/posts/guest-students-laplace/index_files/libs/quarto-html/tippy.umd.min.js diff --git a/profile/bib.bib b/profile/bib.bib index 88f7b06..86ad05a 100644 --- a/profile/bib.bib +++ b/profile/bib.bib @@ -1,3 +1,32 @@ +@InProceedings{karimi2021, +author = {Karimi, Amir-Hossein and Sch\"{o}lkopf, Bernhard and Valera, Isabel}, +title = {Algorithmic Recourse: from Counterfactual Explanations to Interventions}, +year = {2021}, +isbn = {9781450383097}, +publisher = {Association for Computing Machinery}, +address = {New York, NY, USA}, +url = {https://doi.org/10.1145/3442188.3445899}, +doi = {10.1145/3442188.3445899}, +abstract = {As machine learning is increasingly used to inform consequential decision-making (e.g., pre-trial bail and loan approval), it becomes important to explain how the system arrived at its decision, and also suggest actions to achieve a favorable decision. Counterfactual explanations -"how the world would have (had) to be different for a desirable outcome to occur"- aim to satisfy these criteria. Existing works have primarily focused on designing algorithms to obtain counterfactual explanations for a wide range of settings. However, it has largely been overlooked that ultimately, one of the main objectives is to allow people to act rather than just understand. In layman's terms, counterfactual explanations inform an individual where they need to get to, but not how to get there. In this work, we rely on causal reasoning to caution against the use of counterfactual explanations as a recommendable set of actions for recourse. Instead, we propose a shift of paradigm from recourse via nearest counterfactual explanations to recourse through minimal interventions, shifting the focus from explanations to interventions.}, +booktitle = {Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency}, +pages = {353–362}, +numpages = {10}, +keywords = {algorithmic recourse, causal inference, consequential recommendations, contrastive explanations, counterfactual explanations, explainable artificial intelligence, minimal interventions}, +location = {Virtual Event, Canada}, +series = {FAccT '21} +} + +@Book{pearl2009book, +author = {Pearl, Judea}, +title = {Causality: Models, Reasoning and Inference}, +year = {2009}, +isbn = {052189560X}, +publisher = {Cambridge University Press}, +address = {USA}, +edition = {2nd}, +abstract = {Written by one of the preeminent researchers in the field, this book provides a comprehensive exposition of modern analysis of causation. It shows how causality has grown from a nebulous concept into a mathematical theory with significant applications in the fields of statistics, artificial intelligence, economics, philosophy, cognitive science, and the health and social sciences. Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections and statistical associations. The book will open the way for including causal analysis in the standard curricula of statistics, artificial intelligence, business, epidemiology, social sciences, and economics. Students in these fields will find natural models, simple inferential procedures, and precise mathematical definitions of causal concepts that traditional texts have evaded or made unduly complicated. The first edition of Causality has led to a paradigmatic change in the way that causality is treated in statistics, philosophy, computer science, social science, and economics. Cited in more than 3,000 scientific publications, it continues to liberate scientists from the traditional molds of statistical thinking. In this revised edition, Judea Pearl elucidates thorny issues, answers readers' questions, and offers a panoramic view of recent advances in this field of research. Causality will be of interests to students and professionals in a wide variety of fields. Anyone who wishes to elucidate meaningful relationships from data, predict effects of actions and policies, assess explanations of reported events, or form theories of causal understanding and causal speech will find this book stimulating and invaluable.} +} + @TechReport{xu2022conformal, author = {Xu, Chen and Xie, Yao}, date = {2022-06}, diff --git a/profile/blog/posts/a-new-tool-for-explainable-ai/index.html b/profile/blog/posts/a-new-tool-for-explainable-ai/index.html new file mode 100644 index 0000000..5a8df92 --- /dev/null +++ b/profile/blog/posts/a-new-tool-for-explainable-ai/index.html @@ -0,0 +1,779 @@ + + + + + + + + + + + +A new tool for explainable AI + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+ +
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+

A new tool for explainable AI

+

Counterfactual Explanations in Julia — Part I

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counterfactuals
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explainable AI
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Julia
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+

This post introduces a new Julia package for generating counterfactual explanations. The package can be used to explain machine learning algorithms developed and trained in Julia as well as other popular programming languages like Python and R.

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Published
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April 20, 2022

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+ + + +
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+Turning a 9 (nine) into a 4 (four). +
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+ +

Counterfactual explanations, which I introduced in one of my previous posts1, offer a simple and intuitive way to explain black-box models without opening them. Still, as of today there exists only one open-source library that provides a unifying approach to generate and benchmark counterfactual explanations for models built and trained in Python [@pawelczyk2021carla]. This is great, but of limited use to users of other programming languages 🥲.

+

Enter CounterfactualExplanations.jl: a Julia package that can be used to explain machine learning algorithms developed and trained in Julia, Python and R. Counterfactual explanations fall into the broader category of explainable artificial intelligence (XAI).

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Explainable AI typically involves models that are not inherently interpretable but require additional tools to be explainable to humans. Examples of the latter include ensembles, support vector machines and deep neural networks. This is not to be confused with interpretable AI, which involves models that are inherently interpretable and transparent such as general additive models (GAM), decision trees and rule-based models.

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Some would argue that we best avoid explaining black-box models altogether [@rudin2019stop] and instead focus solely on interpretable AI. While I agree that initial efforts should always be geared towards interpretable models, stopping there would entail missed opportunities and anyway is probably not very realistic in times of DALL\(\cdot\)E and Co.

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Even though […] interpretability is of great importance and should be pursued, explanations can, in principle, be offered without opening the “black box.”

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— @wachter2017counterfactual

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This post introduces the main functionality of the new Julia package. Following a motivating example using a model trained in Julia, we will see how easy the package can be adapted to work with models trained in Python and R. Since the motivation for this post is also to hopefully attract contributors, the final section outlines some of the exciting developments we have planned.

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Counterfactuals for image data 🖼

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To introduce counterfactual explanations I used a simple binary classification problem in my previous post. It involved a linear classifier and a linearly separable, synthetic data set with just two features. This time we are going to step it up a notch: we will generate counterfactual explanations MNIST data. The MNIST dataset contains 60,000 training samples of handwritten digits in the form of 28x28 pixel grey-scale images [@lecun1998mnist]. Each image is associated with a label indicating the digit (0-9) that the image represents.

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The CounterfactualExplanations.jl package ships with two black-box models that were trained to predict labels for this data: firstly, a simple multi-layer perceptron (MLP) and, secondly, a corresponding deep ensemble. Originally proposed by @lakshminarayanan2016simple, deep ensembles are really just ensembles of deep neural networks. They are still among the most popular approaches to Bayesian deep learning.2

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Black-box models

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The code below loads relevant packages along with the MNIST data and pre-trained models.

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# Load package, models and data:
+using CounterfactualExplanations, Flux
+using CounterfactualExplanations.Data: mnist_data, mnist_model, mnist_ensemble
+data, X, ys = mnist_data()
+model = mnist_model()
+ensemble = mnist_ensemble()
+counterfactual_data = CounterfactualData(X,ys;domain=(0,1))
+
+

While the package can currently handle a few simple classification models natively, it is designed to be easily extensible through users and contributors. Extending the package to deal with custom models typically involves only two simple steps:

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  1. Subtyping: the custom model needs to be declared as a subtype of the package-internal type AbstractFittedModel.
    2. +
  2. Multiple dispatch: the package-internal functions logits and probs need to be extended through custom methods for the new model type.
    3. +
+

The following code implements these two steps first for the MLP and then for the deep ensemble.

+
+
using CounterfactualExplanations.Models
+import CounterfactualExplanations.Models: logits, probs
+# MLP:
+# Step 1)
+struct NeuralNetwork <: Models.AbstractFittedModel
+    model::Any
+end
+# Step 2)
+logits(M::NeuralNetwork, X::AbstractArray) = M.model(X)
+probs(M::NeuralNetwork, X::AbstractArray)= softmax(logits(M, X))
+M = NeuralNetwork(model)
+
+# Deep ensemble:
+using Flux: stack
+# Step 1)
+struct FittedEnsemble <: Models.AbstractFittedModel
+    ensemble::AbstractArray
+end
+# Step 2)
+using Statistics
+logits(M::FittedEnsemble, X::AbstractArray) = mean(stack([m(X) for m in M.ensemble],3),dims=3)
+probs(M::FittedEnsemble, X::AbstractArray) = mean(stack([softmax(m(X)) for m in M.ensemble],3),dims=3)
+M_ensemble = FittedEnsemble(ensemble)
+
+
+
+

Counterfactual generators

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Next, we need to specify the counterfactual generators we want to use. The package currently ships with two default generators that both need gradient access: firstly, the generic generator introduced by @wachter2017counterfactual and, secondly, a greedy generator introduced by @schut2021generating.

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The greedy generator is designed to be used with models that incorporate uncertainty in their predictions such as the deep ensemble introduced above. It works for probabilistic (Bayesian) models, because they only produce high-confidence predictions in regions of the feature domain that are populated by training samples. As long as the model is expressive enough and well-specified, counterfactuals in these regions will always be realistic and unambiguous since by construction they should look very similar to training samples. Other popular approaches to counterfactual explanations like REVISE [@joshi2019realistic] and CLUE [@antoran2020getting] also play with this simple idea.

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The following code instantiates the two generators for the problem at hand.

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generic = GenericGenerator(;loss=:logitcrossentropy)
+greedy = GreedyGenerator(;loss=:logitcrossentropy)
+
+
+
+

Explanations

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Once the model and counterfactual generator are specified, running counterfactual search is very easy using the package. For a given factual (x), target class (target) and data set (counterfactual_data), simply running

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generate_counterfactual(x, target, counterfactual_data, M, generic)
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will generate the results, in this case using the generic generator (generic) for the MLP (M). Since we have specified two different black-box models and two different counterfactual generators, we have four combinations of a model and a generator in total. For each of these combinations I have used the generate_counterfactual function to produce the results in Figure 1.

+

In every case the desired label switch is in fact achieved, but arguably from a human perspective only the counterfactuals for the deep ensemble look like a four. The generic generator produces mild perturbations in regions that seem irrelevant from a human perspective, but nonetheless yields a counterfactual that can pass as a four. The greedy approach clearly targets pixels at the top of the handwritten nine and yields the best result overall. For the non-Bayesian MLP, both the generic and the greedy approach generate counterfactuals that look much like adversarial examples: they perturb pixels in seemingly random regions on the image.

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+Figure 1: Counterfactual explanations for MNIST: turning a nine (9) into a four (4). +
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Language interoperability 👥

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The Julia language offers unique support for programming language interoperability. For example, calling R or Python is made remarkably easy through RCall.jl and PyCall.jl, respectively. This functionality can be leveraged to use CounterfactualExplanations.jl to generate explanations for models that were developed in other programming languages. At this time there is no native support for foreign programming languages, but the following example involving a torch neural network trained in R demonstrates how versatile the package is.3

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Explaining a torch model

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We will consider a simple MLP trained for a binary classification task. As before we first need to adapt this custom model for use with our package. The code below the two necessary steps - sub-typing and method extension. Logits are returned by the torch model and copied from the R environment into the Julia scope. Probabilities are then computed inside the Julia scope by passing the logits through the sigmoid function.

+
+
using Flux
+using CounterfactualExplanations, CounterfactualExplanations.Models
+import CounterfactualExplanations.Models: logits, probs # import functions in order to extend
+
+# Step 1)
+struct TorchNetwork <: Models.AbstractFittedModel
+    nn::Any
+end
+
+# Step 2)
+function logits(M::TorchNetwork, X::AbstractArray)
+  nn = M.nn
+  y = rcopy(R"as_array($nn(torch_tensor(t($X))))")
+  y = isa(y, AbstractArray) ? y : [y]
+  return y'
+end
+function probs(M::TorchNetwork, X::AbstractArray)
+  return σ.(logits(M, X))
+end
+M = TorchNetwork(R"model")
+
+

Compared to models trained in Julia, we need to do a little more work at this point. Since our counterfactual generators need gradient access, we essentially need to allow our package to communicate with the R torch library. While this may sound daunting, it turns out to be quite manageable: all we have to do is respecify the function that computes the gradient with respect to the counterfactual loss function so that it can deal with the TorchNetwork type we defined above. That is all the adjustment needed to use CounterfactualExplanations.jl for our custom R model. Figure 2 shows a counterfactual path for a randomly chosen sample with respect to the MLP trained in R.

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+ +
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+Experimental functionality +
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You may have stumbled across the term respecify above: does it really seem like a good idea to just replace an existing function from our package? Surely not! There are certainly better ways to go about this, which we will consider when adding native support for Python and R models in future package releases. Which brings us to our final section …

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+
+
import CounterfactualExplanations.Generators: ∂ℓ
+using LinearAlgebra
+
+# Countefactual loss:
+function ∂ℓ(
+    generator::AbstractGradientBasedGenerator, 
+    counterfactual_state::CounterfactualState) 
+  M = counterfactual_state.M
+  nn = M.nn
+  x′ = counterfactual_state.x′
+  t = counterfactual_state.target_encoded
+  R"""
+  x <- torch_tensor($x′, requires_grad=TRUE)
+  output <- $nn(x)
+  loss_fun <- nnf_binary_cross_entropy_with_logits
+  obj_loss <- loss_fun(output,$t)
+  obj_loss$backward()
+  """
+  grad = rcopy(R"as_array(x$grad)")
+  return grad
+end
+
+
+
+
+ +
+
+Figure 2: Counterfactual path using the generic counterfactual generator for a model trained in R. +
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+ +
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+

We need you! 🫵

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The ambition for CounterfactualExplanations.jl is to provide a go-to place for counterfactual explanations to the Julia community and beyond. This is a grand ambition, especially for a package that has so far been built by a single developer who has little prior experience with Julia. We would therefore very much like to invite community contributions. If you have an interest in trustworthy AI, the open-source community and Julia, please do get involved! This package is still in its early stages of development, so any kind of contribution is welcome: advice on the core package architecture, pull requests, issues, discussions and even just comments below would be much appreciated.

+

To give you a flavor of what type of future developments we envision, here is a non-exhaustive list:

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  1. Native support for additional counterfactual generators and predictive models including those built and trained in Python or R.
    2. +
  2. Additional datasets for testing, evaluation and benchmarking.
    3. +
  3. Improved preprocessing including native support for categorical features.
    4. +
  4. Support for regression models.
    5. +
+

Finally, if you like this project but don’t have much time, then simply sharing this article or starring the repo on GitHub would also go a long way.

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+

Further reading 📚

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If you’re interested in learning more about this development, feel free to check out the following resources:

+ +
+ + +

Footnotes

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    +

  1. See: [TDS], [blog]↩︎

    2. +

  2. For more information on Bayesian deep learning see my previous post: [TDS], [blog].↩︎

    3. +

  3. The corresponding example involving PyTorch is analogous and therefore not included here. You may find it here.↩︎

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.offcanvas{position:static;z-index:auto;flex-grow:1;-webkit-flex-grow:1;width:auto !important;height:auto !important;visibility:visible !important;background-color:rgba(0,0,0,0) !important;border:0 !important;transform:none !important;transition:none}.navbar-expand-xxl .offcanvas .offcanvas-header{display:none}.navbar-expand-xxl .offcanvas .offcanvas-body{display:flex;display:-webkit-flex;flex-grow:0;-webkit-flex-grow:0;padding:0;overflow-y:visible}}.navbar-expand{flex-wrap:nowrap;-webkit-flex-wrap:nowrap;justify-content:flex-start;-webkit-justify-content:flex-start}.navbar-expand .navbar-nav{flex-direction:row;-webkit-flex-direction:row}.navbar-expand .navbar-nav .dropdown-menu{position:absolute}.navbar-expand .navbar-nav .nav-link{padding-right:var(--bs-navbar-nav-link-padding-x);padding-left:var(--bs-navbar-nav-link-padding-x)}.navbar-expand .navbar-nav-scroll{overflow:visible}.navbar-expand .navbar-collapse{display:flex !important;display:-webkit-flex !important;flex-basis:auto;-webkit-flex-basis:auto}.navbar-expand .navbar-toggler{display:none}.navbar-expand .offcanvas{position:static;z-index:auto;flex-grow:1;-webkit-flex-grow:1;width:auto !important;height:auto !important;visibility:visible !important;background-color:rgba(0,0,0,0) !important;border:0 !important;transform:none !important;transition:none}.navbar-expand .offcanvas .offcanvas-header{display:none}.navbar-expand .offcanvas .offcanvas-body{display:flex;display:-webkit-flex;flex-grow:0;-webkit-flex-grow:0;padding:0;overflow-y:visible}.navbar-dark,.navbar[data-bs-theme=dark]{--bs-navbar-color: #fdfefe;--bs-navbar-hover-color: rgba(253, 254, 255, 0.8);--bs-navbar-disabled-color: rgba(253, 254, 254, 0.75);--bs-navbar-active-color: #fdfeff;--bs-navbar-brand-color: #fdfefe;--bs-navbar-brand-hover-color: #fdfeff;--bs-navbar-toggler-border-color: rgba(253, 254, 254, 0);--bs-navbar-toggler-icon-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 30 30'%3e%3cpath stroke='%23fdfefe' stroke-linecap='round' stroke-miterlimit='10' stroke-width='2' d='M4 7h22M4 15h22M4 23h22'/%3e%3c/svg%3e")}[data-bs-theme=dark] .navbar-toggler-icon{--bs-navbar-toggler-icon-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 30 30'%3e%3cpath stroke='%23fdfefe' stroke-linecap='round' stroke-miterlimit='10' stroke-width='2' d='M4 7h22M4 15h22M4 23h22'/%3e%3c/svg%3e")}.card{--bs-card-spacer-y: 1rem;--bs-card-spacer-x: 1rem;--bs-card-title-spacer-y: 0.5rem;--bs-card-title-color: ;--bs-card-subtitle-color: ;--bs-card-border-width: 1px;--bs-card-border-color: rgba(0, 0, 0, 0.175);--bs-card-border-radius: 0.375rem;--bs-card-box-shadow: ;--bs-card-inner-border-radius: calc(0.375rem - 1px);--bs-card-cap-padding-y: 0.5rem;--bs-card-cap-padding-x: 1rem;--bs-card-cap-bg: rgba(33, 37, 41, 0.03);--bs-card-cap-color: ;--bs-card-height: ;--bs-card-color: ;--bs-card-bg: #ffffff;--bs-card-img-overlay-padding: 1rem;--bs-card-group-margin: 0.75rem;position:relative;display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;min-width:0;height:var(--bs-card-height);color:var(--bs-body-color);word-wrap:break-word;background-color:var(--bs-card-bg);background-clip:border-box;border:var(--bs-card-border-width) solid var(--bs-card-border-color);border-radius:var(--bs-card-border-radius)}.card>hr{margin-right:0;margin-left:0}.card>.list-group{border-top:inherit;border-bottom:inherit}.card>.list-group:first-child{border-top-width:0;border-top-left-radius:var(--bs-card-inner-border-radius);border-top-right-radius:var(--bs-card-inner-border-radius)}.card>.list-group:last-child{border-bottom-width:0;border-bottom-right-radius:var(--bs-card-inner-border-radius);border-bottom-left-radius:var(--bs-card-inner-border-radius)}.card>.card-header+.list-group,.card>.list-group+.card-footer{border-top:0}.card-body{flex:1 1 auto;-webkit-flex:1 1 auto;padding:var(--bs-card-spacer-y) var(--bs-card-spacer-x);color:var(--bs-card-color)}.card-title{margin-bottom:var(--bs-card-title-spacer-y);color:var(--bs-card-title-color)}.card-subtitle{margin-top:calc(-0.5*var(--bs-card-title-spacer-y));margin-bottom:0;color:var(--bs-card-subtitle-color)}.card-text:last-child{margin-bottom:0}.card-link+.card-link{margin-left:var(--bs-card-spacer-x)}.card-header{padding:var(--bs-card-cap-padding-y) var(--bs-card-cap-padding-x);margin-bottom:0;color:var(--bs-card-cap-color);background-color:var(--bs-card-cap-bg);border-bottom:var(--bs-card-border-width) solid var(--bs-card-border-color)}.card-header:first-child{border-radius:var(--bs-card-inner-border-radius) var(--bs-card-inner-border-radius) 0 0}.card-footer{padding:var(--bs-card-cap-padding-y) var(--bs-card-cap-padding-x);color:var(--bs-card-cap-color);background-color:var(--bs-card-cap-bg);border-top:var(--bs-card-border-width) solid var(--bs-card-border-color)}.card-footer:last-child{border-radius:0 0 var(--bs-card-inner-border-radius) var(--bs-card-inner-border-radius)}.card-header-tabs{margin-right:calc(-0.5*var(--bs-card-cap-padding-x));margin-bottom:calc(-1*var(--bs-card-cap-padding-y));margin-left:calc(-0.5*var(--bs-card-cap-padding-x));border-bottom:0}.card-header-tabs .nav-link.active{background-color:var(--bs-card-bg);border-bottom-color:var(--bs-card-bg)}.card-header-pills{margin-right:calc(-0.5*var(--bs-card-cap-padding-x));margin-left:calc(-0.5*var(--bs-card-cap-padding-x))}.card-img-overlay{position:absolute;top:0;right:0;bottom:0;left:0;padding:var(--bs-card-img-overlay-padding);border-radius:var(--bs-card-inner-border-radius)}.card-img,.card-img-top,.card-img-bottom{width:100%}.card-img,.card-img-top{border-top-left-radius:var(--bs-card-inner-border-radius);border-top-right-radius:var(--bs-card-inner-border-radius)}.card-img,.card-img-bottom{border-bottom-right-radius:var(--bs-card-inner-border-radius);border-bottom-left-radius:var(--bs-card-inner-border-radius)}.card-group>.card{margin-bottom:var(--bs-card-group-margin)}@media(min-width: 576px){.card-group{display:flex;display:-webkit-flex;flex-flow:row wrap;-webkit-flex-flow:row wrap}.card-group>.card{flex:1 0 0%;-webkit-flex:1 0 0%;margin-bottom:0}.card-group>.card+.card{margin-left:0;border-left:0}.card-group>.card:not(:last-child){border-top-right-radius:0;border-bottom-right-radius:0}.card-group>.card:not(:last-child) .card-img-top,.card-group>.card:not(:last-child) .card-header{border-top-right-radius:0}.card-group>.card:not(:last-child) .card-img-bottom,.card-group>.card:not(:last-child) .card-footer{border-bottom-right-radius:0}.card-group>.card:not(:first-child){border-top-left-radius:0;border-bottom-left-radius:0}.card-group>.card:not(:first-child) .card-img-top,.card-group>.card:not(:first-child) .card-header{border-top-left-radius:0}.card-group>.card:not(:first-child) .card-img-bottom,.card-group>.card:not(:first-child) .card-footer{border-bottom-left-radius:0}}.accordion{--bs-accordion-color: #212529;--bs-accordion-bg: #ffffff;--bs-accordion-transition: color 0.15s ease-in-out, background-color 0.15s ease-in-out, border-color 0.15s ease-in-out, box-shadow 0.15s ease-in-out, border-radius 0.15s ease;--bs-accordion-border-color: #dee2e6;--bs-accordion-border-width: 1px;--bs-accordion-border-radius: 0.375rem;--bs-accordion-inner-border-radius: calc(0.375rem - 1px);--bs-accordion-btn-padding-x: 1.25rem;--bs-accordion-btn-padding-y: 1rem;--bs-accordion-btn-color: #212529;--bs-accordion-btn-bg: #ffffff;--bs-accordion-btn-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%23212529'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-icon-width: 1.25rem;--bs-accordion-btn-icon-transform: rotate(-180deg);--bs-accordion-btn-icon-transition: transform 0.2s ease-in-out;--bs-accordion-btn-active-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%23052c65'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-focus-border-color: #86b7fe;--bs-accordion-btn-focus-box-shadow: 0 0 0 0.25rem rgba(13, 110, 253, 0.25);--bs-accordion-body-padding-x: 1.25rem;--bs-accordion-body-padding-y: 1rem;--bs-accordion-active-color: #052c65;--bs-accordion-active-bg: #cfe2ff}.accordion-button{position:relative;display:flex;display:-webkit-flex;align-items:center;-webkit-align-items:center;width:100%;padding:var(--bs-accordion-btn-padding-y) var(--bs-accordion-btn-padding-x);font-size:1rem;color:var(--bs-accordion-btn-color);text-align:left;background-color:var(--bs-accordion-btn-bg);border:0;border-radius:0;overflow-anchor:none;transition:var(--bs-accordion-transition)}@media(prefers-reduced-motion: reduce){.accordion-button{transition:none}}.accordion-button:not(.collapsed){color:var(--bs-accordion-active-color);background-color:var(--bs-accordion-active-bg);box-shadow:inset 0 calc(-1*var(--bs-accordion-border-width)) 0 var(--bs-accordion-border-color)}.accordion-button:not(.collapsed)::after{background-image:var(--bs-accordion-btn-active-icon);transform:var(--bs-accordion-btn-icon-transform)}.accordion-button::after{flex-shrink:0;-webkit-flex-shrink:0;width:var(--bs-accordion-btn-icon-width);height:var(--bs-accordion-btn-icon-width);margin-left:auto;content:"";background-image:var(--bs-accordion-btn-icon);background-repeat:no-repeat;background-size:var(--bs-accordion-btn-icon-width);transition:var(--bs-accordion-btn-icon-transition)}@media(prefers-reduced-motion: reduce){.accordion-button::after{transition:none}}.accordion-button:hover{z-index:2}.accordion-button:focus{z-index:3;border-color:var(--bs-accordion-btn-focus-border-color);outline:0;box-shadow:var(--bs-accordion-btn-focus-box-shadow)}.accordion-header{margin-bottom:0}.accordion-item{color:var(--bs-accordion-color);background-color:var(--bs-accordion-bg);border:var(--bs-accordion-border-width) solid var(--bs-accordion-border-color)}.accordion-item:first-of-type{border-top-left-radius:var(--bs-accordion-border-radius);border-top-right-radius:var(--bs-accordion-border-radius)}.accordion-item:first-of-type .accordion-button{border-top-left-radius:var(--bs-accordion-inner-border-radius);border-top-right-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:not(:first-of-type){border-top:0}.accordion-item:last-of-type{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-item:last-of-type .accordion-button.collapsed{border-bottom-right-radius:var(--bs-accordion-inner-border-radius);border-bottom-left-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:last-of-type .accordion-collapse{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-body{padding:var(--bs-accordion-body-padding-y) var(--bs-accordion-body-padding-x)}.accordion-flush .accordion-collapse{border-width:0}.accordion-flush .accordion-item{border-right:0;border-left:0;border-radius:0}.accordion-flush .accordion-item:first-child{border-top:0}.accordion-flush .accordion-item:last-child{border-bottom:0}.accordion-flush .accordion-item .accordion-button,.accordion-flush .accordion-item .accordion-button.collapsed{border-radius:0}[data-bs-theme=dark] .accordion-button::after{--bs-accordion-btn-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%236ea8fe'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-active-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%236ea8fe'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e")}.breadcrumb{--bs-breadcrumb-padding-x: 0;--bs-breadcrumb-padding-y: 0;--bs-breadcrumb-margin-bottom: 1rem;--bs-breadcrumb-bg: ;--bs-breadcrumb-border-radius: ;--bs-breadcrumb-divider-color: rgba(33, 37, 41, 0.75);--bs-breadcrumb-item-padding-x: 0.5rem;--bs-breadcrumb-item-active-color: rgba(33, 37, 41, 0.75);display:flex;display:-webkit-flex;flex-wrap:wrap;-webkit-flex-wrap:wrap;padding:var(--bs-breadcrumb-padding-y) var(--bs-breadcrumb-padding-x);margin-bottom:var(--bs-breadcrumb-margin-bottom);font-size:var(--bs-breadcrumb-font-size);list-style:none;background-color:var(--bs-breadcrumb-bg);border-radius:var(--bs-breadcrumb-border-radius)}.breadcrumb-item+.breadcrumb-item{padding-left:var(--bs-breadcrumb-item-padding-x)}.breadcrumb-item+.breadcrumb-item::before{float:left;padding-right:var(--bs-breadcrumb-item-padding-x);color:var(--bs-breadcrumb-divider-color);content:var(--bs-breadcrumb-divider, ">") /* rtl: var(--bs-breadcrumb-divider, ">") */}.breadcrumb-item.active{color:var(--bs-breadcrumb-item-active-color)}.pagination{--bs-pagination-padding-x: 0.75rem;--bs-pagination-padding-y: 0.375rem;--bs-pagination-font-size:1rem;--bs-pagination-color: #0d6efd;--bs-pagination-bg: #ffffff;--bs-pagination-border-width: 1px;--bs-pagination-border-color: #dee2e6;--bs-pagination-border-radius: 0.375rem;--bs-pagination-hover-color: #0a58ca;--bs-pagination-hover-bg: #f8f9fa;--bs-pagination-hover-border-color: #dee2e6;--bs-pagination-focus-color: #0a58ca;--bs-pagination-focus-bg: #e9ecef;--bs-pagination-focus-box-shadow: 0 0 0 0.25rem rgba(13, 110, 253, 0.25);--bs-pagination-active-color: #ffffff;--bs-pagination-active-bg: #0d6efd;--bs-pagination-active-border-color: #0d6efd;--bs-pagination-disabled-color: rgba(33, 37, 41, 0.75);--bs-pagination-disabled-bg: #e9ecef;--bs-pagination-disabled-border-color: #dee2e6;display:flex;display:-webkit-flex;padding-left:0;list-style:none}.page-link{position:relative;display:block;padding:var(--bs-pagination-padding-y) var(--bs-pagination-padding-x);font-size:var(--bs-pagination-font-size);color:var(--bs-pagination-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-pagination-bg);border:var(--bs-pagination-border-width) solid var(--bs-pagination-border-color);transition:color .15s ease-in-out,background-color .15s ease-in-out,border-color .15s ease-in-out,box-shadow .15s ease-in-out}@media(prefers-reduced-motion: reduce){.page-link{transition:none}}.page-link:hover{z-index:2;color:var(--bs-pagination-hover-color);background-color:var(--bs-pagination-hover-bg);border-color:var(--bs-pagination-hover-border-color)}.page-link:focus{z-index:3;color:var(--bs-pagination-focus-color);background-color:var(--bs-pagination-focus-bg);outline:0;box-shadow:var(--bs-pagination-focus-box-shadow)}.page-link.active,.active>.page-link{z-index:3;color:var(--bs-pagination-active-color);background-color:var(--bs-pagination-active-bg);border-color:var(--bs-pagination-active-border-color)}.page-link.disabled,.disabled>.page-link{color:var(--bs-pagination-disabled-color);pointer-events:none;background-color:var(--bs-pagination-disabled-bg);border-color:var(--bs-pagination-disabled-border-color)}.page-item:not(:first-child) .page-link{margin-left:calc(1px*-1)}.page-item:first-child .page-link{border-top-left-radius:var(--bs-pagination-border-radius);border-bottom-left-radius:var(--bs-pagination-border-radius)}.page-item:last-child .page-link{border-top-right-radius:var(--bs-pagination-border-radius);border-bottom-right-radius:var(--bs-pagination-border-radius)}.pagination-lg{--bs-pagination-padding-x: 1.5rem;--bs-pagination-padding-y: 0.75rem;--bs-pagination-font-size:1.25rem;--bs-pagination-border-radius: 0.5rem}.pagination-sm{--bs-pagination-padding-x: 0.5rem;--bs-pagination-padding-y: 0.25rem;--bs-pagination-font-size:0.875rem;--bs-pagination-border-radius: 0.25rem}.badge{--bs-badge-padding-x: 0.65em;--bs-badge-padding-y: 0.35em;--bs-badge-font-size:0.75em;--bs-badge-font-weight: 700;--bs-badge-color: #ffffff;--bs-badge-border-radius: 0.375rem;display:inline-block;padding:var(--bs-badge-padding-y) var(--bs-badge-padding-x);font-size:var(--bs-badge-font-size);font-weight:var(--bs-badge-font-weight);line-height:1;color:var(--bs-badge-color);text-align:center;white-space:nowrap;vertical-align:baseline;border-radius:var(--bs-badge-border-radius)}.badge:empty{display:none}.btn .badge{position:relative;top:-1px}.alert{--bs-alert-bg: transparent;--bs-alert-padding-x: 1rem;--bs-alert-padding-y: 1rem;--bs-alert-margin-bottom: 1rem;--bs-alert-color: inherit;--bs-alert-border-color: transparent;--bs-alert-border: 1px solid var(--bs-alert-border-color);--bs-alert-border-radius: 0.375rem;--bs-alert-link-color: inherit;position:relative;padding:var(--bs-alert-padding-y) var(--bs-alert-padding-x);margin-bottom:var(--bs-alert-margin-bottom);color:var(--bs-alert-color);background-color:var(--bs-alert-bg);border:var(--bs-alert-border);border-radius:var(--bs-alert-border-radius)}.alert-heading{color:inherit}.alert-link{font-weight:700;color:var(--bs-alert-link-color)}.alert-dismissible{padding-right:3rem}.alert-dismissible .btn-close{position:absolute;top:0;right:0;z-index:2;padding:1.25rem 1rem}.alert-default{--bs-alert-color: var(--bs-default-text-emphasis);--bs-alert-bg: var(--bs-default-bg-subtle);--bs-alert-border-color: var(--bs-default-border-subtle);--bs-alert-link-color: var(--bs-default-text-emphasis)}.alert-primary{--bs-alert-color: var(--bs-primary-text-emphasis);--bs-alert-bg: var(--bs-primary-bg-subtle);--bs-alert-border-color: var(--bs-primary-border-subtle);--bs-alert-link-color: var(--bs-primary-text-emphasis)}.alert-secondary{--bs-alert-color: var(--bs-secondary-text-emphasis);--bs-alert-bg: var(--bs-secondary-bg-subtle);--bs-alert-border-color: var(--bs-secondary-border-subtle);--bs-alert-link-color: var(--bs-secondary-text-emphasis)}.alert-success{--bs-alert-color: var(--bs-success-text-emphasis);--bs-alert-bg: var(--bs-success-bg-subtle);--bs-alert-border-color: var(--bs-success-border-subtle);--bs-alert-link-color: var(--bs-success-text-emphasis)}.alert-info{--bs-alert-color: var(--bs-info-text-emphasis);--bs-alert-bg: var(--bs-info-bg-subtle);--bs-alert-border-color: var(--bs-info-border-subtle);--bs-alert-link-color: var(--bs-info-text-emphasis)}.alert-warning{--bs-alert-color: var(--bs-warning-text-emphasis);--bs-alert-bg: var(--bs-warning-bg-subtle);--bs-alert-border-color: var(--bs-warning-border-subtle);--bs-alert-link-color: var(--bs-warning-text-emphasis)}.alert-danger{--bs-alert-color: var(--bs-danger-text-emphasis);--bs-alert-bg: var(--bs-danger-bg-subtle);--bs-alert-border-color: var(--bs-danger-border-subtle);--bs-alert-link-color: var(--bs-danger-text-emphasis)}.alert-light{--bs-alert-color: var(--bs-light-text-emphasis);--bs-alert-bg: var(--bs-light-bg-subtle);--bs-alert-border-color: var(--bs-light-border-subtle);--bs-alert-link-color: var(--bs-light-text-emphasis)}.alert-dark{--bs-alert-color: var(--bs-dark-text-emphasis);--bs-alert-bg: var(--bs-dark-bg-subtle);--bs-alert-border-color: var(--bs-dark-border-subtle);--bs-alert-link-color: var(--bs-dark-text-emphasis)}@keyframes progress-bar-stripes{0%{background-position-x:1rem}}.progress,.progress-stacked{--bs-progress-height: 1rem;--bs-progress-font-size:0.75rem;--bs-progress-bg: #e9ecef;--bs-progress-border-radius: 0.375rem;--bs-progress-box-shadow: inset 0 1px 2px rgba(0, 0, 0, 0.075);--bs-progress-bar-color: #ffffff;--bs-progress-bar-bg: #0d6efd;--bs-progress-bar-transition: width 0.6s ease;display:flex;display:-webkit-flex;height:var(--bs-progress-height);overflow:hidden;font-size:var(--bs-progress-font-size);background-color:var(--bs-progress-bg);border-radius:var(--bs-progress-border-radius)}.progress-bar{display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;justify-content:center;-webkit-justify-content:center;overflow:hidden;color:var(--bs-progress-bar-color);text-align:center;white-space:nowrap;background-color:var(--bs-progress-bar-bg);transition:var(--bs-progress-bar-transition)}@media(prefers-reduced-motion: reduce){.progress-bar{transition:none}}.progress-bar-striped{background-image:linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);background-size:var(--bs-progress-height) var(--bs-progress-height)}.progress-stacked>.progress{overflow:visible}.progress-stacked>.progress>.progress-bar{width:100%}.progress-bar-animated{animation:1s linear infinite progress-bar-stripes}@media(prefers-reduced-motion: reduce){.progress-bar-animated{animation:none}}.list-group{--bs-list-group-color: #212529;--bs-list-group-bg: #ffffff;--bs-list-group-border-color: #dee2e6;--bs-list-group-border-width: 1px;--bs-list-group-border-radius: 0.375rem;--bs-list-group-item-padding-x: 1rem;--bs-list-group-item-padding-y: 0.5rem;--bs-list-group-action-color: rgba(33, 37, 41, 0.75);--bs-list-group-action-hover-color: #000;--bs-list-group-action-hover-bg: #f8f9fa;--bs-list-group-action-active-color: #212529;--bs-list-group-action-active-bg: #e9ecef;--bs-list-group-disabled-color: rgba(33, 37, 41, 0.75);--bs-list-group-disabled-bg: #ffffff;--bs-list-group-active-color: #ffffff;--bs-list-group-active-bg: #0d6efd;--bs-list-group-active-border-color: #0d6efd;display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;padding-left:0;margin-bottom:0;border-radius:var(--bs-list-group-border-radius)}.list-group-numbered{list-style-type:none;counter-reset:section}.list-group-numbered>.list-group-item::before{content:counters(section, ".") ". ";counter-increment:section}.list-group-item-action{width:100%;color:var(--bs-list-group-action-color);text-align:inherit}.list-group-item-action:hover,.list-group-item-action:focus{z-index:1;color:var(--bs-list-group-action-hover-color);text-decoration:none;background-color:var(--bs-list-group-action-hover-bg)}.list-group-item-action:active{color:var(--bs-list-group-action-active-color);background-color:var(--bs-list-group-action-active-bg)}.list-group-item{position:relative;display:block;padding:var(--bs-list-group-item-padding-y) var(--bs-list-group-item-padding-x);color:var(--bs-list-group-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-list-group-bg);border:var(--bs-list-group-border-width) solid var(--bs-list-group-border-color)}.list-group-item:first-child{border-top-left-radius:inherit;border-top-right-radius:inherit}.list-group-item:last-child{border-bottom-right-radius:inherit;border-bottom-left-radius:inherit}.list-group-item.disabled,.list-group-item:disabled{color:var(--bs-list-group-disabled-color);pointer-events:none;background-color:var(--bs-list-group-disabled-bg)}.list-group-item.active{z-index:2;color:var(--bs-list-group-active-color);background-color:var(--bs-list-group-active-bg);border-color:var(--bs-list-group-active-border-color)}.list-group-item+.list-group-item{border-top-width:0}.list-group-item+.list-group-item.active{margin-top:calc(-1*var(--bs-list-group-border-width));border-top-width:var(--bs-list-group-border-width)}.list-group-horizontal{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal>.list-group-item.active{margin-top:0}.list-group-horizontal>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}@media(min-width: 576px){.list-group-horizontal-sm{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-sm>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-sm>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-sm>.list-group-item.active{margin-top:0}.list-group-horizontal-sm>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-sm>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 768px){.list-group-horizontal-md{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-md>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-md>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-md>.list-group-item.active{margin-top:0}.list-group-horizontal-md>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-md>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 992px){.list-group-horizontal-lg{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-lg>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-lg>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-lg>.list-group-item.active{margin-top:0}.list-group-horizontal-lg>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-lg>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 1200px){.list-group-horizontal-xl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xl>.list-group-item.active{margin-top:0}.list-group-horizontal-xl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xl>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 1400px){.list-group-horizontal-xxl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xxl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xxl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xxl>.list-group-item.active{margin-top:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}.list-group-flush{border-radius:0}.list-group-flush>.list-group-item{border-width:0 0 var(--bs-list-group-border-width)}.list-group-flush>.list-group-item:last-child{border-bottom-width:0}.list-group-item-default{--bs-list-group-color: var(--bs-default-text-emphasis);--bs-list-group-bg: var(--bs-default-bg-subtle);--bs-list-group-border-color: var(--bs-default-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-default-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-default-border-subtle);--bs-list-group-active-color: var(--bs-default-bg-subtle);--bs-list-group-active-bg: var(--bs-default-text-emphasis);--bs-list-group-active-border-color: var(--bs-default-text-emphasis)}.list-group-item-primary{--bs-list-group-color: var(--bs-primary-text-emphasis);--bs-list-group-bg: var(--bs-primary-bg-subtle);--bs-list-group-border-color: var(--bs-primary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-primary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-primary-border-subtle);--bs-list-group-active-color: var(--bs-primary-bg-subtle);--bs-list-group-active-bg: var(--bs-primary-text-emphasis);--bs-list-group-active-border-color: var(--bs-primary-text-emphasis)}.list-group-item-secondary{--bs-list-group-color: var(--bs-secondary-text-emphasis);--bs-list-group-bg: var(--bs-secondary-bg-subtle);--bs-list-group-border-color: var(--bs-secondary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-secondary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-secondary-border-subtle);--bs-list-group-active-color: var(--bs-secondary-bg-subtle);--bs-list-group-active-bg: var(--bs-secondary-text-emphasis);--bs-list-group-active-border-color: var(--bs-secondary-text-emphasis)}.list-group-item-success{--bs-list-group-color: var(--bs-success-text-emphasis);--bs-list-group-bg: var(--bs-success-bg-subtle);--bs-list-group-border-color: var(--bs-success-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-success-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-success-border-subtle);--bs-list-group-active-color: var(--bs-success-bg-subtle);--bs-list-group-active-bg: var(--bs-success-text-emphasis);--bs-list-group-active-border-color: var(--bs-success-text-emphasis)}.list-group-item-info{--bs-list-group-color: var(--bs-info-text-emphasis);--bs-list-group-bg: var(--bs-info-bg-subtle);--bs-list-group-border-color: var(--bs-info-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-info-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-info-border-subtle);--bs-list-group-active-color: var(--bs-info-bg-subtle);--bs-list-group-active-bg: var(--bs-info-text-emphasis);--bs-list-group-active-border-color: var(--bs-info-text-emphasis)}.list-group-item-warning{--bs-list-group-color: var(--bs-warning-text-emphasis);--bs-list-group-bg: var(--bs-warning-bg-subtle);--bs-list-group-border-color: var(--bs-warning-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-warning-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-warning-border-subtle);--bs-list-group-active-color: var(--bs-warning-bg-subtle);--bs-list-group-active-bg: var(--bs-warning-text-emphasis);--bs-list-group-active-border-color: var(--bs-warning-text-emphasis)}.list-group-item-danger{--bs-list-group-color: var(--bs-danger-text-emphasis);--bs-list-group-bg: var(--bs-danger-bg-subtle);--bs-list-group-border-color: var(--bs-danger-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-danger-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-danger-border-subtle);--bs-list-group-active-color: var(--bs-danger-bg-subtle);--bs-list-group-active-bg: var(--bs-danger-text-emphasis);--bs-list-group-active-border-color: var(--bs-danger-text-emphasis)}.list-group-item-light{--bs-list-group-color: var(--bs-light-text-emphasis);--bs-list-group-bg: var(--bs-light-bg-subtle);--bs-list-group-border-color: var(--bs-light-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-light-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-light-border-subtle);--bs-list-group-active-color: var(--bs-light-bg-subtle);--bs-list-group-active-bg: var(--bs-light-text-emphasis);--bs-list-group-active-border-color: var(--bs-light-text-emphasis)}.list-group-item-dark{--bs-list-group-color: var(--bs-dark-text-emphasis);--bs-list-group-bg: var(--bs-dark-bg-subtle);--bs-list-group-border-color: var(--bs-dark-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-dark-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-dark-border-subtle);--bs-list-group-active-color: var(--bs-dark-bg-subtle);--bs-list-group-active-bg: var(--bs-dark-text-emphasis);--bs-list-group-active-border-color: var(--bs-dark-text-emphasis)}.btn-close{--bs-btn-close-color: #000;--bs-btn-close-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%23000'%3e%3cpath d='M.293.293a1 1 0 0 1 1.414 0L8 6.586 14.293.293a1 1 0 1 1 1.414 1.414L9.414 8l6.293 6.293a1 1 0 0 1-1.414 1.414L8 9.414l-6.293 6.293a1 1 0 0 1-1.414-1.414L6.586 8 .293 1.707a1 1 0 0 1 0-1.414z'/%3e%3c/svg%3e");--bs-btn-close-opacity: 0.5;--bs-btn-close-hover-opacity: 0.75;--bs-btn-close-focus-shadow: 0 0 0 0.25rem rgba(13, 110, 253, 0.25);--bs-btn-close-focus-opacity: 1;--bs-btn-close-disabled-opacity: 0.25;--bs-btn-close-white-filter: invert(1) grayscale(100%) brightness(200%);box-sizing:content-box;width:1em;height:1em;padding:.25em .25em;color:var(--bs-btn-close-color);background:rgba(0,0,0,0) var(--bs-btn-close-bg) center/1em auto no-repeat;border:0;border-radius:.375rem;opacity:var(--bs-btn-close-opacity)}.btn-close:hover{color:var(--bs-btn-close-color);text-decoration:none;opacity:var(--bs-btn-close-hover-opacity)}.btn-close:focus{outline:0;box-shadow:var(--bs-btn-close-focus-shadow);opacity:var(--bs-btn-close-focus-opacity)}.btn-close:disabled,.btn-close.disabled{pointer-events:none;user-select:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;-o-user-select:none;opacity:var(--bs-btn-close-disabled-opacity)}.btn-close-white{filter:var(--bs-btn-close-white-filter)}[data-bs-theme=dark] .btn-close{filter:var(--bs-btn-close-white-filter)}.toast{--bs-toast-zindex: 1090;--bs-toast-padding-x: 0.75rem;--bs-toast-padding-y: 0.5rem;--bs-toast-spacing: 1.5rem;--bs-toast-max-width: 350px;--bs-toast-font-size:0.875rem;--bs-toast-color: ;--bs-toast-bg: rgba(255, 255, 255, 0.85);--bs-toast-border-width: 1px;--bs-toast-border-color: rgba(0, 0, 0, 0.175);--bs-toast-border-radius: 0.375rem;--bs-toast-box-shadow: 0 0.5rem 1rem rgba(0, 0, 0, 0.15);--bs-toast-header-color: rgba(33, 37, 41, 0.75);--bs-toast-header-bg: rgba(255, 255, 255, 0.85);--bs-toast-header-border-color: rgba(0, 0, 0, 0.175);width:var(--bs-toast-max-width);max-width:100%;font-size:var(--bs-toast-font-size);color:var(--bs-toast-color);pointer-events:auto;background-color:var(--bs-toast-bg);background-clip:padding-box;border:var(--bs-toast-border-width) solid var(--bs-toast-border-color);box-shadow:var(--bs-toast-box-shadow);border-radius:var(--bs-toast-border-radius)}.toast.showing{opacity:0}.toast:not(.show){display:none}.toast-container{--bs-toast-zindex: 1090;position:absolute;z-index:var(--bs-toast-zindex);width:max-content;width:-webkit-max-content;width:-moz-max-content;width:-ms-max-content;width:-o-max-content;max-width:100%;pointer-events:none}.toast-container>:not(:last-child){margin-bottom:var(--bs-toast-spacing)}.toast-header{display:flex;display:-webkit-flex;align-items:center;-webkit-align-items:center;padding:var(--bs-toast-padding-y) var(--bs-toast-padding-x);color:var(--bs-toast-header-color);background-color:var(--bs-toast-header-bg);background-clip:padding-box;border-bottom:var(--bs-toast-border-width) solid var(--bs-toast-header-border-color);border-top-left-radius:calc(var(--bs-toast-border-radius) - var(--bs-toast-border-width));border-top-right-radius:calc(var(--bs-toast-border-radius) - var(--bs-toast-border-width))}.toast-header .btn-close{margin-right:calc(-0.5*var(--bs-toast-padding-x));margin-left:var(--bs-toast-padding-x)}.toast-body{padding:var(--bs-toast-padding-x);word-wrap:break-word}.modal{--bs-modal-zindex: 1055;--bs-modal-width: 500px;--bs-modal-padding: 1rem;--bs-modal-margin: 0.5rem;--bs-modal-color: ;--bs-modal-bg: #ffffff;--bs-modal-border-color: rgba(0, 0, 0, 0.175);--bs-modal-border-width: 1px;--bs-modal-border-radius: 0.5rem;--bs-modal-box-shadow: 0 0.125rem 0.25rem rgba(0, 0, 0, 0.075);--bs-modal-inner-border-radius: calc(0.5rem - 1px);--bs-modal-header-padding-x: 1rem;--bs-modal-header-padding-y: 1rem;--bs-modal-header-padding: 1rem 1rem;--bs-modal-header-border-color: #dee2e6;--bs-modal-header-border-width: 1px;--bs-modal-title-line-height: 1.5;--bs-modal-footer-gap: 0.5rem;--bs-modal-footer-bg: ;--bs-modal-footer-border-color: #dee2e6;--bs-modal-footer-border-width: 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e=/input|textarea/i.test(t.target.tagName),i="Escape"===t.key,n=[Ei,Ti].includes(t.key);if(!n&&!i)return;if(e&&!i)return;t.preventDefault();const s=this.matches(Ii)?this:z.prev(this,Ii)[0]||z.next(this,Ii)[0]||z.findOne(Ii,t.delegateTarget.parentNode),o=qi.getOrCreateInstance(s);if(n)return t.stopPropagation(),o.show(),void o._selectMenuItem(t);o._isShown()&&(t.stopPropagation(),o.hide(),s.focus())}}N.on(document,Si,Ii,qi.dataApiKeydownHandler),N.on(document,Si,Pi,qi.dataApiKeydownHandler),N.on(document,Li,qi.clearMenus),N.on(document,Di,qi.clearMenus),N.on(document,Li,Ii,(function(t){t.preventDefault(),qi.getOrCreateInstance(this).toggle()})),m(qi);const Vi="backdrop",Ki="show",Qi=`mousedown.bs.${Vi}`,Xi={className:"modal-backdrop",clickCallback:null,isAnimated:!1,isVisible:!0,rootElement:"body"},Yi={className:"string",clickCallback:"(function|null)",isAnimated:"boolean",isVisible:"boolean",rootElement:"(element|string)"};class Ui extends H{constructor(t){super(),this._config=this._getConfig(t),this._isAppended=!1,this._element=null}static get Default(){return Xi}static get DefaultType(){return Yi}static get NAME(){return Vi}show(t){if(!this._config.isVisible)return void g(t);this._append();const e=this._getElement();this._config.isAnimated&&d(e),e.classList.add(Ki),this._emulateAnimation((()=>{g(t)}))}hide(t){this._config.isVisible?(this._getElement().classList.remove(Ki),this._emulateAnimation((()=>{this.dispose(),g(t)}))):g(t)}dispose(){this._isAppended&&(N.off(this._element,Qi),this._element.remove(),this._isAppended=!1)}_getElement(){if(!this._element){const t=document.createElement("div");t.className=this._config.className,this._config.isAnimated&&t.classList.add("fade"),this._element=t}return this._element}_configAfterMerge(t){return t.rootElement=r(t.rootElement),t}_append(){if(this._isAppended)return;const t=this._getElement();this._config.rootElement.append(t),N.on(t,Qi,(()=>{g(this._config.clickCallback)})),this._isAppended=!0}_emulateAnimation(t){_(t,this._getElement(),this._config.isAnimated)}}const Gi=".bs.focustrap",Ji=`focusin${Gi}`,Zi=`keydown.tab${Gi}`,tn="backward",en={autofocus:!0,trapElement:null},nn={autofocus:"boolean",trapElement:"element"};class sn extends H{constructor(t){super(),this._config=this._getConfig(t),this._isActive=!1,this._lastTabNavDirection=null}static get Default(){return en}static get DefaultType(){return nn}static get NAME(){return"focustrap"}activate(){this._isActive||(this._config.autofocus&&this._config.trapElement.focus(),N.off(document,Gi),N.on(document,Ji,(t=>this._handleFocusin(t))),N.on(document,Zi,(t=>this._handleKeydown(t))),this._isActive=!0)}deactivate(){this._isActive&&(this._isActive=!1,N.off(document,Gi))}_handleFocusin(t){const{trapElement:e}=this._config;if(t.target===document||t.target===e||e.contains(t.target))return;const i=z.focusableChildren(e);0===i.length?e.focus():this._lastTabNavDirection===tn?i[i.length-1].focus():i[0].focus()}_handleKeydown(t){"Tab"===t.key&&(this._lastTabNavDirection=t.shiftKey?tn:"forward")}}const on=".fixed-top, .fixed-bottom, .is-fixed, .sticky-top",rn=".sticky-top",an="padding-right",ln="margin-right";class cn{constructor(){this._element=document.body}getWidth(){const t=document.documentElement.clientWidth;return Math.abs(window.innerWidth-t)}hide(){const t=this.getWidth();this._disableOverFlow(),this._setElementAttributes(this._element,an,(e=>e+t)),this._setElementAttributes(on,an,(e=>e+t)),this._setElementAttributes(rn,ln,(e=>e-t))}reset(){this._resetElementAttributes(this._element,"overflow"),this._resetElementAttributes(this._element,an),this._resetElementAttributes(on,an),this._resetElementAttributes(rn,ln)}isOverflowing(){return this.getWidth()>0}_disableOverFlow(){this._saveInitialAttribute(this._element,"overflow"),this._element.style.overflow="hidden"}_setElementAttributes(t,e,i){const n=this.getWidth();this._applyManipulationCallback(t,(t=>{if(t!==this._element&&window.innerWidth>t.clientWidth+n)return;this._saveInitialAttribute(t,e);const s=window.getComputedStyle(t).getPropertyValue(e);t.style.setProperty(e,`${i(Number.parseFloat(s))}px`)}))}_saveInitialAttribute(t,e){const i=t.style.getPropertyValue(e);i&&F.setDataAttribute(t,e,i)}_resetElementAttributes(t,e){this._applyManipulationCallback(t,(t=>{const i=F.getDataAttribute(t,e);null!==i?(F.removeDataAttribute(t,e),t.style.setProperty(e,i)):t.style.removeProperty(e)}))}_applyManipulationCallback(t,e){if(o(t))e(t);else for(const i of z.find(t,this._element))e(i)}}const hn=".bs.modal",dn=`hide${hn}`,un=`hidePrevented${hn}`,fn=`hidden${hn}`,pn=`show${hn}`,mn=`shown${hn}`,gn=`resize${hn}`,_n=`click.dismiss${hn}`,bn=`mousedown.dismiss${hn}`,vn=`keydown.dismiss${hn}`,yn=`click${hn}.data-api`,wn="modal-open",An="show",En="modal-static",Tn={backdrop:!0,focus:!0,keyboard:!0},Cn={backdrop:"(boolean|string)",focus:"boolean",keyboard:"boolean"};class On extends W{constructor(t,e){super(t,e),this._dialog=z.findOne(".modal-dialog",this._element),this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._isShown=!1,this._isTransitioning=!1,this._scrollBar=new cn,this._addEventListeners()}static get Default(){return Tn}static get DefaultType(){return Cn}static get NAME(){return"modal"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||this._isTransitioning||N.trigger(this._element,pn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._isTransitioning=!0,this._scrollBar.hide(),document.body.classList.add(wn),this._adjustDialog(),this._backdrop.show((()=>this._showElement(t))))}hide(){this._isShown&&!this._isTransitioning&&(N.trigger(this._element,dn).defaultPrevented||(this._isShown=!1,this._isTransitioning=!0,this._focustrap.deactivate(),this._element.classList.remove(An),this._queueCallback((()=>this._hideModal()),this._element,this._isAnimated())))}dispose(){N.off(window,hn),N.off(this._dialog,hn),this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}handleUpdate(){this._adjustDialog()}_initializeBackDrop(){return new Ui({isVisible:Boolean(this._config.backdrop),isAnimated:this._isAnimated()})}_initializeFocusTrap(){return new sn({trapElement:this._element})}_showElement(t){document.body.contains(this._element)||document.body.append(this._element),this._element.style.display="block",this._element.removeAttribute("aria-hidden"),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.scrollTop=0;const e=z.findOne(".modal-body",this._dialog);e&&(e.scrollTop=0),d(this._element),this._element.classList.add(An),this._queueCallback((()=>{this._config.focus&&this._focustrap.activate(),this._isTransitioning=!1,N.trigger(this._element,mn,{relatedTarget:t})}),this._dialog,this._isAnimated())}_addEventListeners(){N.on(this._element,vn,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():this._triggerBackdropTransition())})),N.on(window,gn,(()=>{this._isShown&&!this._isTransitioning&&this._adjustDialog()})),N.on(this._element,bn,(t=>{N.one(this._element,_n,(e=>{this._element===t.target&&this._element===e.target&&("static"!==this._config.backdrop?this._config.backdrop&&this.hide():this._triggerBackdropTransition())}))}))}_hideModal(){this._element.style.display="none",this._element.setAttribute("aria-hidden",!0),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._isTransitioning=!1,this._backdrop.hide((()=>{document.body.classList.remove(wn),this._resetAdjustments(),this._scrollBar.reset(),N.trigger(this._element,fn)}))}_isAnimated(){return this._element.classList.contains("fade")}_triggerBackdropTransition(){if(N.trigger(this._element,un).defaultPrevented)return;const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._element.style.overflowY;"hidden"===e||this._element.classList.contains(En)||(t||(this._element.style.overflowY="hidden"),this._element.classList.add(En),this._queueCallback((()=>{this._element.classList.remove(En),this._queueCallback((()=>{this._element.style.overflowY=e}),this._dialog)}),this._dialog),this._element.focus())}_adjustDialog(){const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._scrollBar.getWidth(),i=e>0;if(i&&!t){const t=p()?"paddingLeft":"paddingRight";this._element.style[t]=`${e}px`}if(!i&&t){const t=p()?"paddingRight":"paddingLeft";this._element.style[t]=`${e}px`}}_resetAdjustments(){this._element.style.paddingLeft="",this._element.style.paddingRight=""}static jQueryInterface(t,e){return this.each((function(){const i=On.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===i[t])throw new TypeError(`No method named "${t}"`);i[t](e)}}))}}N.on(document,yn,'[data-bs-toggle="modal"]',(function(t){const e=z.getElementFromSelector(this);["A","AREA"].includes(this.tagName)&&t.preventDefault(),N.one(e,pn,(t=>{t.defaultPrevented||N.one(e,fn,(()=>{a(this)&&this.focus()}))}));const i=z.findOne(".modal.show");i&&On.getInstance(i).hide(),On.getOrCreateInstance(e).toggle(this)})),R(On),m(On);const xn=".bs.offcanvas",kn=".data-api",Ln=`load${xn}${kn}`,Sn="show",Dn="showing",$n="hiding",In=".offcanvas.show",Nn=`show${xn}`,Pn=`shown${xn}`,Mn=`hide${xn}`,jn=`hidePrevented${xn}`,Fn=`hidden${xn}`,Hn=`resize${xn}`,Wn=`click${xn}${kn}`,Bn=`keydown.dismiss${xn}`,zn={backdrop:!0,keyboard:!0,scroll:!1},Rn={backdrop:"(boolean|string)",keyboard:"boolean",scroll:"boolean"};class qn extends W{constructor(t,e){super(t,e),this._isShown=!1,this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._addEventListeners()}static get Default(){return zn}static get DefaultType(){return Rn}static get NAME(){return"offcanvas"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||N.trigger(this._element,Nn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._backdrop.show(),this._config.scroll||(new cn).hide(),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.classList.add(Dn),this._queueCallback((()=>{this._config.scroll&&!this._config.backdrop||this._focustrap.activate(),this._element.classList.add(Sn),this._element.classList.remove(Dn),N.trigger(this._element,Pn,{relatedTarget:t})}),this._element,!0))}hide(){this._isShown&&(N.trigger(this._element,Mn).defaultPrevented||(this._focustrap.deactivate(),this._element.blur(),this._isShown=!1,this._element.classList.add($n),this._backdrop.hide(),this._queueCallback((()=>{this._element.classList.remove(Sn,$n),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._config.scroll||(new cn).reset(),N.trigger(this._element,Fn)}),this._element,!0)))}dispose(){this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}_initializeBackDrop(){const t=Boolean(this._config.backdrop);return new Ui({className:"offcanvas-backdrop",isVisible:t,isAnimated:!0,rootElement:this._element.parentNode,clickCallback:t?()=>{"static"!==this._config.backdrop?this.hide():N.trigger(this._element,jn)}:null})}_initializeFocusTrap(){return new sn({trapElement:this._element})}_addEventListeners(){N.on(this._element,Bn,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():N.trigger(this._element,jn))}))}static jQueryInterface(t){return this.each((function(){const e=qn.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t]||t.startsWith("_")||"constructor"===t)throw new TypeError(`No method named "${t}"`);e[t](this)}}))}}N.on(document,Wn,'[data-bs-toggle="offcanvas"]',(function(t){const e=z.getElementFromSelector(this);if(["A","AREA"].includes(this.tagName)&&t.preventDefault(),l(this))return;N.one(e,Fn,(()=>{a(this)&&this.focus()}));const i=z.findOne(In);i&&i!==e&&qn.getInstance(i).hide(),qn.getOrCreateInstance(e).toggle(this)})),N.on(window,Ln,(()=>{for(const t of z.find(In))qn.getOrCreateInstance(t).show()})),N.on(window,Hn,(()=>{for(const t of z.find("[aria-modal][class*=show][class*=offcanvas-]"))"fixed"!==getComputedStyle(t).position&&qn.getOrCreateInstance(t).hide()})),R(qn),m(qn);const Vn={"*":["class","dir","id","lang","role",/^aria-[\w-]*$/i],a:["target","href","title","rel"],area:[],b:[],br:[],col:[],code:[],div:[],em:[],hr:[],h1:[],h2:[],h3:[],h4:[],h5:[],h6:[],i:[],img:["src","srcset","alt","title","width","height"],li:[],ol:[],p:[],pre:[],s:[],small:[],span:[],sub:[],sup:[],strong:[],u:[],ul:[]},Kn=new Set(["background","cite","href","itemtype","longdesc","poster","src","xlink:href"]),Qn=/^(?!javascript:)(?:[a-z0-9+.-]+:|[^&:/?#]*(?:[/?#]|$))/i,Xn=(t,e)=>{const i=t.nodeName.toLowerCase();return e.includes(i)?!Kn.has(i)||Boolean(Qn.test(t.nodeValue)):e.filter((t=>t instanceof RegExp)).some((t=>t.test(i)))},Yn={allowList:Vn,content:{},extraClass:"",html:!1,sanitize:!0,sanitizeFn:null,template:"

"},Un={allowList:"object",content:"object",extraClass:"(string|function)",html:"boolean",sanitize:"boolean",sanitizeFn:"(null|function)",template:"string"},Gn={entry:"(string|element|function|null)",selector:"(string|element)"};class Jn extends H{constructor(t){super(),this._config=this._getConfig(t)}static get Default(){return Yn}static get DefaultType(){return Un}static get NAME(){return"TemplateFactory"}getContent(){return Object.values(this._config.content).map((t=>this._resolvePossibleFunction(t))).filter(Boolean)}hasContent(){return this.getContent().length>0}changeContent(t){return this._checkContent(t),this._config.content={...this._config.content,...t},this}toHtml(){const t=document.createElement("div");t.innerHTML=this._maybeSanitize(this._config.template);for(const[e,i]of Object.entries(this._config.content))this._setContent(t,i,e);const e=t.children[0],i=this._resolvePossibleFunction(this._config.extraClass);return i&&e.classList.add(...i.split(" ")),e}_typeCheckConfig(t){super._typeCheckConfig(t),this._checkContent(t.content)}_checkContent(t){for(const[e,i]of Object.entries(t))super._typeCheckConfig({selector:e,entry:i},Gn)}_setContent(t,e,i){const n=z.findOne(i,t);n&&((e=this._resolvePossibleFunction(e))?o(e)?this._putElementInTemplate(r(e),n):this._config.html?n.innerHTML=this._maybeSanitize(e):n.textContent=e:n.remove())}_maybeSanitize(t){return this._config.sanitize?function(t,e,i){if(!t.length)return t;if(i&&"function"==typeof i)return i(t);const n=(new window.DOMParser).parseFromString(t,"text/html"),s=[].concat(...n.body.querySelectorAll("*"));for(const t of s){const i=t.nodeName.toLowerCase();if(!Object.keys(e).includes(i)){t.remove();continue}const n=[].concat(...t.attributes),s=[].concat(e["*"]||[],e[i]||[]);for(const e of n)Xn(e,s)||t.removeAttribute(e.nodeName)}return n.body.innerHTML}(t,this._config.allowList,this._config.sanitizeFn):t}_resolvePossibleFunction(t){return g(t,[this])}_putElementInTemplate(t,e){if(this._config.html)return e.innerHTML="",void e.append(t);e.textContent=t.textContent}}const Zn=new Set(["sanitize","allowList","sanitizeFn"]),ts="fade",es="show",is=".modal",ns="hide.bs.modal",ss="hover",os="focus",rs={AUTO:"auto",TOP:"top",RIGHT:p()?"left":"right",BOTTOM:"bottom",LEFT:p()?"right":"left"},as={allowList:Vn,animation:!0,boundary:"clippingParents",container:!1,customClass:"",delay:0,fallbackPlacements:["top","right","bottom","left"],html:!1,offset:[0,6],placement:"top",popperConfig:null,sanitize:!0,sanitizeFn:null,selector:!1,template:'',title:"",trigger:"hover focus"},ls={allowList:"object",animation:"boolean",boundary:"(string|element)",container:"(string|element|boolean)",customClass:"(string|function)",delay:"(number|object)",fallbackPlacements:"array",html:"boolean",offset:"(array|string|function)",placement:"(string|function)",popperConfig:"(null|object|function)",sanitize:"boolean",sanitizeFn:"(null|function)",selector:"(string|boolean)",template:"string",title:"(string|element|function)",trigger:"string"};class cs extends W{constructor(t,e){if(void 0===vi)throw new TypeError("Bootstrap's tooltips require Popper (https://popper.js.org)");super(t,e),this._isEnabled=!0,this._timeout=0,this._isHovered=null,this._activeTrigger={},this._popper=null,this._templateFactory=null,this._newContent=null,this.tip=null,this._setListeners(),this._config.selector||this._fixTitle()}static get Default(){return as}static get DefaultType(){return ls}static get NAME(){return"tooltip"}enable(){this._isEnabled=!0}disable(){this._isEnabled=!1}toggleEnabled(){this._isEnabled=!this._isEnabled}toggle(){this._isEnabled&&(this._activeTrigger.click=!this._activeTrigger.click,this._isShown()?this._leave():this._enter())}dispose(){clearTimeout(this._timeout),N.off(this._element.closest(is),ns,this._hideModalHandler),this._element.getAttribute("data-bs-original-title")&&this._element.setAttribute("title",this._element.getAttribute("data-bs-original-title")),this._disposePopper(),super.dispose()}show(){if("none"===this._element.style.display)throw new Error("Please use show on visible elements");if(!this._isWithContent()||!this._isEnabled)return;const t=N.trigger(this._element,this.constructor.eventName("show")),e=(c(this._element)||this._element.ownerDocument.documentElement).contains(this._element);if(t.defaultPrevented||!e)return;this._disposePopper();const i=this._getTipElement();this._element.setAttribute("aria-describedby",i.getAttribute("id"));const{container:n}=this._config;if(this._element.ownerDocument.documentElement.contains(this.tip)||(n.append(i),N.trigger(this._element,this.constructor.eventName("inserted"))),this._popper=this._createPopper(i),i.classList.add(es),"ontouchstart"in document.documentElement)for(const t of[].concat(...document.body.children))N.on(t,"mouseover",h);this._queueCallback((()=>{N.trigger(this._element,this.constructor.eventName("shown")),!1===this._isHovered&&this._leave(),this._isHovered=!1}),this.tip,this._isAnimated())}hide(){if(this._isShown()&&!N.trigger(this._element,this.constructor.eventName("hide")).defaultPrevented){if(this._getTipElement().classList.remove(es),"ontouchstart"in document.documentElement)for(const t of[].concat(...document.body.children))N.off(t,"mouseover",h);this._activeTrigger.click=!1,this._activeTrigger[os]=!1,this._activeTrigger[ss]=!1,this._isHovered=null,this._queueCallback((()=>{this._isWithActiveTrigger()||(this._isHovered||this._disposePopper(),this._element.removeAttribute("aria-describedby"),N.trigger(this._element,this.constructor.eventName("hidden")))}),this.tip,this._isAnimated())}}update(){this._popper&&this._popper.update()}_isWithContent(){return Boolean(this._getTitle())}_getTipElement(){return this.tip||(this.tip=this._createTipElement(this._newContent||this._getContentForTemplate())),this.tip}_createTipElement(t){const e=this._getTemplateFactory(t).toHtml();if(!e)return null;e.classList.remove(ts,es),e.classList.add(`bs-${this.constructor.NAME}-auto`);const i=(t=>{do{t+=Math.floor(1e6*Math.random())}while(document.getElementById(t));return t})(this.constructor.NAME).toString();return e.setAttribute("id",i),this._isAnimated()&&e.classList.add(ts),e}setContent(t){this._newContent=t,this._isShown()&&(this._disposePopper(),this.show())}_getTemplateFactory(t){return this._templateFactory?this._templateFactory.changeContent(t):this._templateFactory=new Jn({...this._config,content:t,extraClass:this._resolvePossibleFunction(this._config.customClass)}),this._templateFactory}_getContentForTemplate(){return{".tooltip-inner":this._getTitle()}}_getTitle(){return this._resolvePossibleFunction(this._config.title)||this._element.getAttribute("data-bs-original-title")}_initializeOnDelegatedTarget(t){return this.constructor.getOrCreateInstance(t.delegateTarget,this._getDelegateConfig())}_isAnimated(){return this._config.animation||this.tip&&this.tip.classList.contains(ts)}_isShown(){return this.tip&&this.tip.classList.contains(es)}_createPopper(t){const e=g(this._config.placement,[this,t,this._element]),i=rs[e.toUpperCase()];return bi(this._element,t,this._getPopperConfig(i))}_getOffset(){const{offset:t}=this._config;return"string"==typeof t?t.split(",").map((t=>Number.parseInt(t,10))):"function"==typeof t?e=>t(e,this._element):t}_resolvePossibleFunction(t){return g(t,[this._element])}_getPopperConfig(t){const e={placement:t,modifiers:[{name:"flip",options:{fallbackPlacements:this._config.fallbackPlacements}},{name:"offset",options:{offset:this._getOffset()}},{name:"preventOverflow",options:{boundary:this._config.boundary}},{name:"arrow",options:{element:`.${this.constructor.NAME}-arrow`}},{name:"preSetPlacement",enabled:!0,phase:"beforeMain",fn:t=>{this._getTipElement().setAttribute("data-popper-placement",t.state.placement)}}]};return{...e,...g(this._config.popperConfig,[e])}}_setListeners(){const t=this._config.trigger.split(" ");for(const e of t)if("click"===e)N.on(this._element,this.constructor.eventName("click"),this._config.selector,(t=>{this._initializeOnDelegatedTarget(t).toggle()}));else if("manual"!==e){const t=e===ss?this.constructor.eventName("mouseenter"):this.constructor.eventName("focusin"),i=e===ss?this.constructor.eventName("mouseleave"):this.constructor.eventName("focusout");N.on(this._element,t,this._config.selector,(t=>{const e=this._initializeOnDelegatedTarget(t);e._activeTrigger["focusin"===t.type?os:ss]=!0,e._enter()})),N.on(this._element,i,this._config.selector,(t=>{const e=this._initializeOnDelegatedTarget(t);e._activeTrigger["focusout"===t.type?os:ss]=e._element.contains(t.relatedTarget),e._leave()}))}this._hideModalHandler=()=>{this._element&&this.hide()},N.on(this._element.closest(is),ns,this._hideModalHandler)}_fixTitle(){const 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window.document.querySelector('nav.toc-active[role="doc-toc"]'); + const sidebarEl = window.document.getElementById("quarto-sidebar"); + const leftTocEl = window.document.getElementById("quarto-sidebar-toc-left"); + const marginSidebarEl = window.document.getElementById( + "quarto-margin-sidebar" + ); + // function to determine whether the element has a previous sibling that is active + const prevSiblingIsActiveLink = (el) => { + const sibling = el.previousElementSibling; + if (sibling && sibling.tagName === "A") { + return sibling.classList.contains("active"); + } else { + return false; + } + }; + + // fire slideEnter for bootstrap tab activations (for htmlwidget resize behavior) + function fireSlideEnter(e) { + const event = window.document.createEvent("Event"); + event.initEvent("slideenter", true, true); + window.document.dispatchEvent(event); + } + const tabs = window.document.querySelectorAll('a[data-bs-toggle="tab"]'); + tabs.forEach((tab) => { + tab.addEventListener("shown.bs.tab", fireSlideEnter); + }); + + // fire slideEnter for tabby tab activations (for htmlwidget resize behavior) + document.addEventListener("tabby", fireSlideEnter, false); + + // Track scrolling and mark TOC links as active + // get table of contents and sidebar (bail if we don't have at least one) + const tocLinks = tocEl + ? [...tocEl.querySelectorAll("a[data-scroll-target]")] + : []; + const makeActive = (link) => tocLinks[link].classList.add("active"); + const removeActive = (link) => tocLinks[link].classList.remove("active"); + const removeAllActive = () => + [...Array(tocLinks.length).keys()].forEach((link) => removeActive(link)); + + // activate the anchor for a section associated with this TOC entry + tocLinks.forEach((link) => { + link.addEventListener("click", () => { + if (link.href.indexOf("#") !== -1) { + const anchor = link.href.split("#")[1]; + const heading = window.document.querySelector( + `[data-anchor-id="${anchor}"]` + ); + if (heading) { + // Add the class + heading.classList.add("reveal-anchorjs-link"); + + // function to show the anchor + const handleMouseout = () => { + heading.classList.remove("reveal-anchorjs-link"); + heading.removeEventListener("mouseout", handleMouseout); + }; + + // add a function to clear the anchor when the user mouses out of it + heading.addEventListener("mouseout", handleMouseout); + } + } + }); + }); + + const sections = tocLinks.map((link) => { + const target = link.getAttribute("data-scroll-target"); + if (target.startsWith("#")) { + return window.document.getElementById(decodeURI(`${target.slice(1)}`)); + } else { + return window.document.querySelector(decodeURI(`${target}`)); + } + }); + + const sectionMargin = 200; + let currentActive = 0; + // track whether we've initialized state the first time + let init = false; + + const updateActiveLink = () => { + // The index from bottom to top (e.g. reversed list) + let sectionIndex = -1; + if ( + window.innerHeight + window.pageYOffset >= + window.document.body.offsetHeight + ) { + // This is the no-scroll case where last section should be the active one + sectionIndex = 0; + } else { + // This finds the last section visible on screen that should be made active + sectionIndex = [...sections].reverse().findIndex((section) => { + if (section) { + return window.pageYOffset >= section.offsetTop - sectionMargin; + } else { + return false; + } + }); + } + if (sectionIndex > -1) { + const current = sections.length - sectionIndex - 1; + if (current !== currentActive) { + removeAllActive(); + currentActive = current; + makeActive(current); + if (init) { + window.dispatchEvent(sectionChanged); + } + init = true; + } + } + }; + + const inHiddenRegion = (top, bottom, hiddenRegions) => { + for (const region of hiddenRegions) { + if (top <= region.bottom && bottom >= region.top) { + return true; + } + } + return false; + }; + + const categorySelector = "header.quarto-title-block .quarto-category"; + const activateCategories = (href) => { + // Find any categories + // Surround them with a link pointing back to: + // #category=Authoring + try { + const categoryEls = window.document.querySelectorAll(categorySelector); + for (const categoryEl of categoryEls) { + const categoryText = categoryEl.textContent; + if (categoryText) { + const link = `${href}#category=${encodeURIComponent(categoryText)}`; + const linkEl = window.document.createElement("a"); + linkEl.setAttribute("href", link); + for (const child of categoryEl.childNodes) { + linkEl.append(child); + } + categoryEl.appendChild(linkEl); + } + } + } catch { + // Ignore errors + } + }; + function hasTitleCategories() { + return window.document.querySelector(categorySelector) !== null; + } + + function offsetRelativeUrl(url) { + const offset = getMeta("quarto:offset"); + return offset ? offset + url : url; + } + + function offsetAbsoluteUrl(url) { + const offset = getMeta("quarto:offset"); + const baseUrl = new URL(offset, window.location); + + const projRelativeUrl = url.replace(baseUrl, ""); + if (projRelativeUrl.startsWith("/")) { + return projRelativeUrl; + } else { + return "/" + projRelativeUrl; + } + } + + // read a meta tag value + function getMeta(metaName) { + const metas = window.document.getElementsByTagName("meta"); + for (let i = 0; i < metas.length; i++) { + if (metas[i].getAttribute("name") === metaName) { + return metas[i].getAttribute("content"); + } + } + return ""; + } + + async function findAndActivateCategories() { + const currentPagePath = offsetAbsoluteUrl(window.location.href); + const response = await fetch(offsetRelativeUrl("listings.json")); + if (response.status == 200) { + return response.json().then(function (listingPaths) { + const listingHrefs = []; + for (const listingPath of listingPaths) { + const pathWithoutLeadingSlash = listingPath.listing.substring(1); + for (const item of listingPath.items) { + if ( + item === currentPagePath || + item === currentPagePath + "index.html" + ) { + // Resolve this path against the offset to be sure + // we already are using the correct path to the listing + // (this adjusts the listing urls to be rooted against + // whatever root the page is actually running against) + const relative = offsetRelativeUrl(pathWithoutLeadingSlash); + const baseUrl = window.location; + const resolvedPath = new URL(relative, baseUrl); + listingHrefs.push(resolvedPath.pathname); + break; + } + } + } + + // Look up the tree for a nearby linting and use that if we find one + const nearestListing = findNearestParentListing( + offsetAbsoluteUrl(window.location.pathname), + listingHrefs + ); + if (nearestListing) { + activateCategories(nearestListing); + } else { + // See if the referrer is a listing page for this item + const referredRelativePath = offsetAbsoluteUrl(document.referrer); + const referrerListing = listingHrefs.find((listingHref) => { + const isListingReferrer = + listingHref === referredRelativePath || + listingHref === referredRelativePath + "index.html"; + return isListingReferrer; + }); + + if (referrerListing) { + // Try to use the referrer if possible + activateCategories(referrerListing); + } else if (listingHrefs.length > 0) { + // Otherwise, just fall back to the first listing + activateCategories(listingHrefs[0]); + } + } + }); + } + } + if (hasTitleCategories()) { + findAndActivateCategories(); + } + + const findNearestParentListing = (href, listingHrefs) => { + if (!href || !listingHrefs) { + return undefined; + } + // Look up the tree for a nearby linting and use that if we find one + const relativeParts = href.substring(1).split("/"); + while (relativeParts.length > 0) { + const path = relativeParts.join("/"); + for (const listingHref of listingHrefs) { + if (listingHref.startsWith(path)) { + return listingHref; + } + } + relativeParts.pop(); + } + + return undefined; + }; + + const manageSidebarVisiblity = (el, placeholderDescriptor) => { + let isVisible = true; + let elRect; + + return (hiddenRegions) => { + if (el === null) { + return; + } + + // Find the last element of the TOC + const lastChildEl = el.lastElementChild; + + if (lastChildEl) { + // Converts the sidebar to a menu + const convertToMenu = () => { + for (const child of el.children) { + child.style.opacity = 0; + child.style.overflow = "hidden"; + child.style.pointerEvents = "none"; + } + + nexttick(() => { + const toggleContainer = window.document.createElement("div"); + toggleContainer.style.width = "100%"; + toggleContainer.classList.add("zindex-over-content"); + toggleContainer.classList.add("quarto-sidebar-toggle"); + toggleContainer.classList.add("headroom-target"); // Marks this to be managed by headeroom + toggleContainer.id = placeholderDescriptor.id; + toggleContainer.style.position = "fixed"; + + const toggleIcon = window.document.createElement("i"); + toggleIcon.classList.add("quarto-sidebar-toggle-icon"); + toggleIcon.classList.add("bi"); + toggleIcon.classList.add("bi-caret-down-fill"); + + const toggleTitle = window.document.createElement("div"); + const titleEl = window.document.body.querySelector( + placeholderDescriptor.titleSelector + ); + if (titleEl) { + toggleTitle.append( + titleEl.textContent || titleEl.innerText, + toggleIcon + ); + } + toggleTitle.classList.add("zindex-over-content"); + toggleTitle.classList.add("quarto-sidebar-toggle-title"); + toggleContainer.append(toggleTitle); + + const toggleContents = window.document.createElement("div"); + toggleContents.classList = el.classList; + toggleContents.classList.add("zindex-over-content"); + toggleContents.classList.add("quarto-sidebar-toggle-contents"); + for (const child of el.children) { + if (child.id === "toc-title") { + continue; + } + + const clone = child.cloneNode(true); + clone.style.opacity = 1; + clone.style.pointerEvents = null; + clone.style.display = null; + toggleContents.append(clone); + } + toggleContents.style.height = "0px"; + const positionToggle = () => { + // position the element (top left of parent, same width as parent) + if (!elRect) { + elRect = el.getBoundingClientRect(); + } + toggleContainer.style.left = `${elRect.left}px`; + toggleContainer.style.top = `${elRect.top}px`; + toggleContainer.style.width = `${elRect.width}px`; + }; + positionToggle(); + + toggleContainer.append(toggleContents); + el.parentElement.prepend(toggleContainer); + + // Process clicks + let tocShowing = false; + // Allow the caller to control whether this is dismissed + // when it is clicked (e.g. sidebar navigation supports + // opening and closing the nav tree, so don't dismiss on click) + const clickEl = placeholderDescriptor.dismissOnClick + ? toggleContainer + : toggleTitle; + + const closeToggle = () => { + if (tocShowing) { + toggleContainer.classList.remove("expanded"); + toggleContents.style.height = "0px"; + tocShowing = false; + } + }; + + // Get rid of any expanded toggle if the user scrolls + window.document.addEventListener( + "scroll", + throttle(() => { + closeToggle(); + }, 50) + ); + + // Handle positioning of the toggle + window.addEventListener( + "resize", + throttle(() => { + elRect = undefined; + positionToggle(); + }, 50) + ); + + window.addEventListener("quarto-hrChanged", () => { + elRect = undefined; + }); + + // Process the click + clickEl.onclick = () => { + if (!tocShowing) { + toggleContainer.classList.add("expanded"); + toggleContents.style.height = null; + tocShowing = true; + } else { + closeToggle(); + } + }; + }); + }; + + // Converts a sidebar from a menu back to a sidebar + const convertToSidebar = () => { + for (const child of el.children) { + child.style.opacity = 1; + child.style.overflow = null; + child.style.pointerEvents = null; + } + + const placeholderEl = window.document.getElementById( + placeholderDescriptor.id + ); + if (placeholderEl) { + placeholderEl.remove(); + } + + el.classList.remove("rollup"); + }; + + if (isReaderMode()) { + convertToMenu(); + isVisible = false; + } else { + // Find the top and bottom o the element that is being managed + const elTop = el.offsetTop; + const elBottom = + elTop + lastChildEl.offsetTop + lastChildEl.offsetHeight; + + if (!isVisible) { + // If the element is current not visible reveal if there are + // no conflicts with overlay regions + if (!inHiddenRegion(elTop, elBottom, hiddenRegions)) { + convertToSidebar(); + isVisible = true; + } + } else { + // If the element is visible, hide it if it conflicts with overlay regions + // and insert a placeholder toggle (or if we're in reader mode) + if (inHiddenRegion(elTop, elBottom, hiddenRegions)) { + convertToMenu(); + isVisible = false; + } + } + } + } + }; + }; + + const tabEls = document.querySelectorAll('a[data-bs-toggle="tab"]'); + for (const tabEl of tabEls) { + const id = tabEl.getAttribute("data-bs-target"); + if (id) { + const columnEl = document.querySelector( + `${id} .column-margin, .tabset-margin-content` + ); + if (columnEl) + tabEl.addEventListener("shown.bs.tab", function (event) { + const el = event.srcElement; + if (el) { + const visibleCls = `${el.id}-margin-content`; + // walk up until we find a parent tabset + let panelTabsetEl = el.parentElement; + while (panelTabsetEl) { + if (panelTabsetEl.classList.contains("panel-tabset")) { + break; + } + panelTabsetEl = panelTabsetEl.parentElement; + } + + if (panelTabsetEl) { + const prevSib = panelTabsetEl.previousElementSibling; + if ( + prevSib && + prevSib.classList.contains("tabset-margin-container") + ) { + const childNodes = prevSib.querySelectorAll( + ".tabset-margin-content" + ); + for (const childEl of childNodes) { + if (childEl.classList.contains(visibleCls)) { + childEl.classList.remove("collapse"); + } else { + childEl.classList.add("collapse"); + } + } + } + } + } + + layoutMarginEls(); + }); + } + } + + // Manage the visibility of the toc and the sidebar + const marginScrollVisibility = manageSidebarVisiblity(marginSidebarEl, { + id: "quarto-toc-toggle", + titleSelector: "#toc-title", + dismissOnClick: true, + }); + const sidebarScrollVisiblity = manageSidebarVisiblity(sidebarEl, { + id: "quarto-sidebarnav-toggle", + titleSelector: ".title", + dismissOnClick: false, + }); + let tocLeftScrollVisibility; + if (leftTocEl) { + tocLeftScrollVisibility = manageSidebarVisiblity(leftTocEl, { + id: "quarto-lefttoc-toggle", + titleSelector: "#toc-title", + dismissOnClick: true, + }); + } + + // Find the first element that uses formatting in special columns + const conflictingEls = window.document.body.querySelectorAll( + '[class^="column-"], [class*=" column-"], aside, [class*="margin-caption"], [class*=" margin-caption"], [class*="margin-ref"], [class*=" margin-ref"]' + ); + + // Filter all the possibly conflicting elements into ones + // the do conflict on the left or ride side + const arrConflictingEls = Array.from(conflictingEls); + const leftSideConflictEls = arrConflictingEls.filter((el) => { + if (el.tagName === "ASIDE") { + return false; + } + return Array.from(el.classList).find((className) => { + return ( + className !== "column-body" && + className.startsWith("column-") && + !className.endsWith("right") && + !className.endsWith("container") && + className !== "column-margin" + ); + }); + }); + const rightSideConflictEls = arrConflictingEls.filter((el) => { + if (el.tagName === "ASIDE") { + return true; + } + + const hasMarginCaption = Array.from(el.classList).find((className) => { + return className == "margin-caption"; + }); + if (hasMarginCaption) { + return true; + } + + return Array.from(el.classList).find((className) => { + return ( + className !== "column-body" && + !className.endsWith("container") && + className.startsWith("column-") && + !className.endsWith("left") + ); + }); + }); + + const kOverlapPaddingSize = 10; + function toRegions(els) { + return els.map((el) => { + const boundRect = el.getBoundingClientRect(); + const top = + boundRect.top + + document.documentElement.scrollTop - + kOverlapPaddingSize; + return { + top, + bottom: top + el.scrollHeight + 2 * kOverlapPaddingSize, + }; + }); + } + + let hasObserved = false; + const visibleItemObserver = (els) => { + let visibleElements = [...els]; + const intersectionObserver = new IntersectionObserver( + (entries, _observer) => { + entries.forEach((entry) => { + if (entry.isIntersecting) { + if (visibleElements.indexOf(entry.target) === -1) { + visibleElements.push(entry.target); + } + } else { + visibleElements = visibleElements.filter((visibleEntry) => { + return visibleEntry !== entry; + }); + } + }); + + if (!hasObserved) { + hideOverlappedSidebars(); + } + hasObserved = true; + }, + {} + ); + els.forEach((el) => { + intersectionObserver.observe(el); + }); + + return { + getVisibleEntries: () => { + return visibleElements; + }, + }; + }; + + const rightElementObserver = visibleItemObserver(rightSideConflictEls); + const leftElementObserver = visibleItemObserver(leftSideConflictEls); + + const hideOverlappedSidebars = () => { + marginScrollVisibility(toRegions(rightElementObserver.getVisibleEntries())); + sidebarScrollVisiblity(toRegions(leftElementObserver.getVisibleEntries())); + if (tocLeftScrollVisibility) { + tocLeftScrollVisibility( + toRegions(leftElementObserver.getVisibleEntries()) + ); + } + }; + + window.quartoToggleReader = () => { + // Applies a slow class (or removes it) + // to update the transition speed + const slowTransition = (slow) => { + const manageTransition = (id, slow) => { + const el = document.getElementById(id); + if (el) { + if (slow) { + el.classList.add("slow"); + } else { + el.classList.remove("slow"); + } + } + }; + + manageTransition("TOC", slow); + manageTransition("quarto-sidebar", slow); + }; + const readerMode = !isReaderMode(); + setReaderModeValue(readerMode); + + // If we're entering reader mode, slow the transition + if (readerMode) { + slowTransition(readerMode); + } + highlightReaderToggle(readerMode); + hideOverlappedSidebars(); + + // If we're exiting reader mode, restore the non-slow transition + if (!readerMode) { + slowTransition(!readerMode); + } + }; + + const highlightReaderToggle = (readerMode) => { + const els = document.querySelectorAll(".quarto-reader-toggle"); + if (els) { + els.forEach((el) => { + if (readerMode) { + el.classList.add("reader"); + } else { + el.classList.remove("reader"); + } + }); + } + }; + + const setReaderModeValue = (val) => { + if (window.location.protocol !== "file:") { + window.localStorage.setItem("quarto-reader-mode", val); + } else { + localReaderMode = val; + } + }; + + const isReaderMode = () => { + if (window.location.protocol !== "file:") { + return window.localStorage.getItem("quarto-reader-mode") === "true"; + } else { + return localReaderMode; + } + }; + let localReaderMode = null; + + const tocOpenDepthStr = tocEl?.getAttribute("data-toc-expanded"); + const tocOpenDepth = tocOpenDepthStr ? Number(tocOpenDepthStr) : 1; + + // Walk the TOC and collapse/expand nodes + // Nodes are expanded if: + // - they are top level + // - they have children that are 'active' links + // - they are directly below an link that is 'active' + const walk = (el, depth) => { + // Tick depth when we enter a UL + if (el.tagName === "UL") { + depth = depth + 1; + } + + // It this is active link + let isActiveNode = false; + if (el.tagName === "A" && el.classList.contains("active")) { + isActiveNode = true; + } + + // See if there is an active child to this element + let hasActiveChild = false; + for (child of el.children) { + hasActiveChild = walk(child, depth) || hasActiveChild; + } + + // Process the collapse state if this is an UL + if (el.tagName === "UL") { + if (tocOpenDepth === -1 && depth > 1) { + // toc-expand: false + el.classList.add("collapse"); + } else if ( + depth <= tocOpenDepth || + hasActiveChild || + prevSiblingIsActiveLink(el) + ) { + el.classList.remove("collapse"); + } else { + el.classList.add("collapse"); + } + + // untick depth when we leave a UL + depth = depth - 1; + } + return hasActiveChild || isActiveNode; + }; + + // walk the TOC and expand / collapse any items that should be shown + if (tocEl) { + updateActiveLink(); + walk(tocEl, 0); + } + + // Throttle the scroll event and walk peridiocally + window.document.addEventListener( + "scroll", + throttle(() => { + if (tocEl) { + updateActiveLink(); + walk(tocEl, 0); + } + if (!isReaderMode()) { + hideOverlappedSidebars(); + } + }, 5) + ); + window.addEventListener( + "resize", + throttle(() => { + if (tocEl) { + updateActiveLink(); + walk(tocEl, 0); + } + if (!isReaderMode()) { + hideOverlappedSidebars(); + } + }, 10) + ); + hideOverlappedSidebars(); + highlightReaderToggle(isReaderMode()); +}); + +// grouped tabsets +window.addEventListener("pageshow", (_event) => { + function getTabSettings() { + const data = localStorage.getItem("quarto-persistent-tabsets-data"); + if (!data) { + localStorage.setItem("quarto-persistent-tabsets-data", "{}"); + return {}; + } + if (data) { + return JSON.parse(data); + } + } + + function setTabSettings(data) { + localStorage.setItem( + "quarto-persistent-tabsets-data", + JSON.stringify(data) + ); + } + + function setTabState(groupName, groupValue) { + const data = getTabSettings(); + data[groupName] = groupValue; + setTabSettings(data); + } + + function toggleTab(tab, active) { + const tabPanelId = tab.getAttribute("aria-controls"); + const tabPanel = document.getElementById(tabPanelId); + if (active) { + tab.classList.add("active"); + tabPanel.classList.add("active"); + } else { + tab.classList.remove("active"); + tabPanel.classList.remove("active"); + } + } + + function toggleAll(selectedGroup, selectorsToSync) { + for (const [thisGroup, tabs] of Object.entries(selectorsToSync)) { + const active = selectedGroup === thisGroup; + for (const tab of tabs) { + toggleTab(tab, active); + } + } + } + + function findSelectorsToSyncByLanguage() { + const result = {}; + const tabs = Array.from( + document.querySelectorAll(`div[data-group] a[id^='tabset-']`) + ); + for (const item of tabs) { + const div = item.parentElement.parentElement.parentElement; + const group = div.getAttribute("data-group"); + if (!result[group]) { + result[group] = {}; + } + const selectorsToSync = result[group]; + const value = item.innerHTML; + if (!selectorsToSync[value]) { + selectorsToSync[value] = []; + } + selectorsToSync[value].push(item); + } + return result; + } + + function setupSelectorSync() { + const selectorsToSync = findSelectorsToSyncByLanguage(); + Object.entries(selectorsToSync).forEach(([group, tabSetsByValue]) => { + Object.entries(tabSetsByValue).forEach(([value, items]) => { + items.forEach((item) => { + item.addEventListener("click", (_event) => { + setTabState(group, value); + toggleAll(value, selectorsToSync[group]); + }); + }); + }); + }); + return selectorsToSync; + } + + const selectorsToSync = setupSelectorSync(); + for (const [group, selectedName] of Object.entries(getTabSettings())) { + const selectors = selectorsToSync[group]; + // it's possible that stale state gives us empty selections, so we explicitly check here. + if (selectors) { + toggleAll(selectedName, selectors); + } + } +}); + +function throttle(func, wait) { + let waiting = false; + return function () { + if (!waiting) { + func.apply(this, arguments); + waiting = true; + setTimeout(function () { + waiting = false; + }, wait); + } + }; +} + +function nexttick(func) { + return setTimeout(func, 0); +} diff --git a/profile/blog/posts/a-new-tool-for-explainable-ai/index_files/libs/quarto-html/tippy.css b/profile/blog/posts/a-new-tool-for-explainable-ai/index_files/libs/quarto-html/tippy.css new file mode 100644 index 0000000..e6ae635 --- /dev/null +++ b/profile/blog/posts/a-new-tool-for-explainable-ai/index_files/libs/quarto-html/tippy.css @@ -0,0 +1 @@ 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b/profile/blog/posts/causal-recourse/index.html new file mode 100644 index 0000000..2e37acc --- /dev/null +++ b/profile/blog/posts/causal-recourse/index.html @@ -0,0 +1,661 @@ + + + + + + + + + + + +When Causal meets Recourse + + + + + + + + + + + + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/profile/blog/posts/causal-recourse/index.qmd b/profile/blog/posts/causal-recourse/index.qmd new file mode 100644 index 0000000..5c89885 --- /dev/null +++ b/profile/blog/posts/causal-recourse/index.qmd @@ -0,0 +1,119 @@ +--- +title: "When Causal meets Recourse" +subtitle: "Counterfactual Explanations through Structural Causal Models" +date: '2024-09-03' +description: | + This post introduces a new tool in CounterfactualExplanations.jl, enhancing the package with causal reasoning to generate counterfactual explanations. The functionality can be used to explain machine learning algorithms developed in Julia and other popular programming languages like Python and R. Unlike traditional counterfactual generators, this approach utilizes causal information to perturb features intelligently. +categories: + - counterfactuals + - explainable AI + - causality + - Julia +image: www/intro.gif +execute: + eval: false + echo: true +draft: false +--- + +# Introduction + +In recent years, the need for interpretable and explainable AI has surged, particularly in high-stakes domains. Counterfactual explanations provide a means to understand how changes to input features could alter the outcomes of machine learning models. This blog post presents a new tool in the CounterfactualExplanations.jl package, developed during my JSoC (Julia Summer of Code) project, which incorporates causal reasoning into counterfactual generation. + +# Project Overview + +This project aimed to enhance the CounterfactualExplanations.jl package by infusing it with a robust mathematical foundation for minimal algorithmic recourse, based on the principles of causal reasoning @karimi2021. + +## Key Contributions + +During the project, I contributed to two key repositories: + +1. **CounterfactualExplanations.jl**: Developed a new tool for generating counterfactual explanations using causal information. This allows users to create smarter perturbations rather than random adjustments, ultimately providing more meaningful insights. + +2. **CausalInference.jl**: Implemented a Structural Causal Model (SCM) structure that extracts information from data, laying the groundwork for the causal reasoning capabilities in CounterfactualExplanations.jl. + +This was an amazing experience, not just experience contribute to two repositories simultaneously, but also to work with the mantainers of these repos. I learned a lot about the Julia language and the Julia community. This was possible because of the mentorship of Patrick Altmeyer(CounterfactualExplanations) and Moritz Schauer (CausalInference), who guided me throughout the project and are amazing researchers. + + + +## The `MINTGenerator` + +In this project, we developed the MINTGenerator, a counterfactual generator based on the Recourse through Minimal +Intervention (MINT) method proposed by @karimi2021. + +## Description + +The MINTGenerator incorporates causal reeasoning in algorithm recourse to achieve minimal interventions when generating a counterfactual explanation. In this sense, the main ideia is that just perturbating a black box model without taking into account the causal relations in the data can guide to misleading recommendations. Here we now shift to a perspective where every action/pertubation is an intervetion in the causal graph of the problem, thus the change is not made just in the intervened upon variable, but also in its childs in the causal structure. The generator utilizes a Structural Causal Model(SCM) to encode the variables in a way that causal effects are propagated and uses a generic gradient-based generator to create the search path, that is, any gradient-base generator (ECCo, REVISE, Watcher, ...) can be used with the MINT SCM encoder to generate counterfactual samples in latent space for minimal intervetions algorithm recourse. + +The MINT algorithm minimizes a loss function that combines the causal constraints of the SCM and the distance between the generated counterfactual and the original input. Since we want a gradient-based generator, we need to pass the constrained optimizaiton problem into an unconstrained one and we do this by using the Lagrangian. Initially, as defined in [@karimi2021], we aim to aim to find the minimal cost set of actions $A$ (in the form of structural interventions) that results in a counterfactual instance yielding the favorable output from $h$, + + +\begin{aligned} + +A^* \in \arg\min_A \text{cost}(A; \mathbf{x}_F)\\ +\textrm{s.t.} \quad h(\mathbf{x}_{SCF}) \neq h(\mathbf{x}_F) \; \; \text{,}\\ + +\end{aligned} + +where $\mathbf{x}_F$ is the original input, $\mathbf{x}_{SCF}$ is the counterfactual instance, and $h$ is the black-box model. We use the $\mathbf{x}_{SCF}$ terminology because the counterfactual is derived from the SCM, + +\begin{equation} + +x_{SCF_i} = +\begin{cases} +x_{F_i} + \delta_i, & \text{if } i \in I \\ +x_{F_i} + f_i(\text{pa}_{SCF_i}) - f_i(\text{pa}_{F_i}), & \text{if } i \notin I \; \; \text{,} +\end{cases} + +\end{equation} + +where $I$ is the set of intervened upon variables, $f_i$ is the function that generates the value of the variable $i$ given its parents, and $\text{pa}_{SCF_i}$ and $\text{pa}_{F_i}$ are the parents of the variable $i$ in the counterfactual and original instance, respectively. This closed formula for the decision variable $\mathbf{x}_{SCF}$ is what makes possible to use a gradient-based generator, since with it the lagrangian is differentiable, + +\begin{equation} +\mathcal{L}(A ; \lambda) = \text{cost}(A; \mathbf{x}_F) + \lambda \left(h(\mathbf{x}_{SCF}) - h(\mathbf{x}_F) \right) \; \; \text{,} +\end{equation} + +or in simple terms and more standard, since $\lambda$ is constant, + +\begin{equation} +\mathcal{L_{\texttt{MINT}}}(\mathbf{x}_{SCF}) = \lambda \text{cost}(\mathbf{x}_{SCF}; \mathbf{x}_F) + \text{yloss}(\mathbf{x}_{SCF},y^*) \; \; \text{,} +\end{equation} + +where $y^*$ is clearly $h(x_F)$ and $\text{yloss}$ is : + +\begin{equation} +\text{yloss}(\mathbf{x}_{SCF}, y^*) = h \left(\left\{ x_{F_i} + \delta_i [i \in I] + \left(f_i(\text{pa}_{SCF_i}) - f_i(\text{pa}_{F_i}) \right) [i \notin I] \right\}_{i=1}^n \right) - y^* \; \; \text{.} +\end{equation} + + + +## Implementation + +In terms of implementation, we need to capture the causal relations from the data, that's where `CausalInference.jl` comes in. However, before the project, the package did not have a SCM structure, in the sense that the methods just captured the topological Directed Acyclic Graph (DAG) that generated the data, that is, no causal structural equations were provided, + +```{julia} +using CausalInference +using Plots, GraphRecipes +using Random +Random.seed!(1) + +N = 2000 # number of data points + +x = randn(N) +v = x + randn(N)*0.25 +w = x + randn(N)*0.25 +z = v + w + randn(N)*0.25 +s = z + randn(N)*0.25 + +df = (x=x, v=v, w=w, z=z, s=s) + +est_g, score = ges(df; penalty=1.0, parallel=true) + +graphplot(est_g, names= [String(k) for k in keys(df)]) +``` + +# Conclusion + + + +# References diff --git a/profile/blog/posts/causal-recourse/index_files/libs/bootstrap/bootstrap-icons.css b/profile/blog/posts/causal-recourse/index_files/libs/bootstrap/bootstrap-icons.css new file mode 100644 index 0000000..285e444 --- /dev/null +++ b/profile/blog/posts/causal-recourse/index_files/libs/bootstrap/bootstrap-icons.css @@ 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var(--bs-accordion-border-color)}.accordion-item:first-of-type{border-top-left-radius:var(--bs-accordion-border-radius);border-top-right-radius:var(--bs-accordion-border-radius)}.accordion-item:first-of-type .accordion-button{border-top-left-radius:var(--bs-accordion-inner-border-radius);border-top-right-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:not(:first-of-type){border-top:0}.accordion-item:last-of-type{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-item:last-of-type .accordion-button.collapsed{border-bottom-right-radius:var(--bs-accordion-inner-border-radius);border-bottom-left-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:last-of-type .accordion-collapse{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-body{padding:var(--bs-accordion-body-padding-y) var(--bs-accordion-body-padding-x)}.accordion-flush .accordion-collapse{border-width:0}.accordion-flush .accordion-item{border-right:0;border-left:0;border-radius:0}.accordion-flush .accordion-item:first-child{border-top:0}.accordion-flush .accordion-item:last-child{border-bottom:0}.accordion-flush .accordion-item .accordion-button,.accordion-flush .accordion-item .accordion-button.collapsed{border-radius:0}[data-bs-theme=dark] .accordion-button::after{--bs-accordion-btn-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%236ea8fe'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-active-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%236ea8fe'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e")}.breadcrumb{--bs-breadcrumb-padding-x: 0;--bs-breadcrumb-padding-y: 0;--bs-breadcrumb-margin-bottom: 1rem;--bs-breadcrumb-bg: ;--bs-breadcrumb-border-radius: ;--bs-breadcrumb-divider-color: rgba(33, 37, 41, 0.75);--bs-breadcrumb-item-padding-x: 0.5rem;--bs-breadcrumb-item-active-color: rgba(33, 37, 41, 0.75);display:flex;display:-webkit-flex;flex-wrap:wrap;-webkit-flex-wrap:wrap;padding:var(--bs-breadcrumb-padding-y) var(--bs-breadcrumb-padding-x);margin-bottom:var(--bs-breadcrumb-margin-bottom);font-size:var(--bs-breadcrumb-font-size);list-style:none;background-color:var(--bs-breadcrumb-bg);border-radius:var(--bs-breadcrumb-border-radius)}.breadcrumb-item+.breadcrumb-item{padding-left:var(--bs-breadcrumb-item-padding-x)}.breadcrumb-item+.breadcrumb-item::before{float:left;padding-right:var(--bs-breadcrumb-item-padding-x);color:var(--bs-breadcrumb-divider-color);content:var(--bs-breadcrumb-divider, ">") /* rtl: var(--bs-breadcrumb-divider, ">") */}.breadcrumb-item.active{color:var(--bs-breadcrumb-item-active-color)}.pagination{--bs-pagination-padding-x: 0.75rem;--bs-pagination-padding-y: 0.375rem;--bs-pagination-font-size:1rem;--bs-pagination-color: #0d6efd;--bs-pagination-bg: #ffffff;--bs-pagination-border-width: 1px;--bs-pagination-border-color: #dee2e6;--bs-pagination-border-radius: 0.375rem;--bs-pagination-hover-color: #0a58ca;--bs-pagination-hover-bg: #f8f9fa;--bs-pagination-hover-border-color: #dee2e6;--bs-pagination-focus-color: #0a58ca;--bs-pagination-focus-bg: #e9ecef;--bs-pagination-focus-box-shadow: 0 0 0 0.25rem rgba(13, 110, 253, 0.25);--bs-pagination-active-color: #ffffff;--bs-pagination-active-bg: #0d6efd;--bs-pagination-active-border-color: #0d6efd;--bs-pagination-disabled-color: rgba(33, 37, 41, 0.75);--bs-pagination-disabled-bg: #e9ecef;--bs-pagination-disabled-border-color: #dee2e6;display:flex;display:-webkit-flex;padding-left:0;list-style:none}.page-link{position:relative;display:block;padding:var(--bs-pagination-padding-y) var(--bs-pagination-padding-x);font-size:var(--bs-pagination-font-size);color:var(--bs-pagination-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-pagination-bg);border:var(--bs-pagination-border-width) solid var(--bs-pagination-border-color);transition:color .15s ease-in-out,background-color .15s ease-in-out,border-color .15s ease-in-out,box-shadow .15s ease-in-out}@media(prefers-reduced-motion: reduce){.page-link{transition:none}}.page-link:hover{z-index:2;color:var(--bs-pagination-hover-color);background-color:var(--bs-pagination-hover-bg);border-color:var(--bs-pagination-hover-border-color)}.page-link:focus{z-index:3;color:var(--bs-pagination-focus-color);background-color:var(--bs-pagination-focus-bg);outline:0;box-shadow:var(--bs-pagination-focus-box-shadow)}.page-link.active,.active>.page-link{z-index:3;color:var(--bs-pagination-active-color);background-color:var(--bs-pagination-active-bg);border-color:var(--bs-pagination-active-border-color)}.page-link.disabled,.disabled>.page-link{color:var(--bs-pagination-disabled-color);pointer-events:none;background-color:var(--bs-pagination-disabled-bg);border-color:var(--bs-pagination-disabled-border-color)}.page-item:not(:first-child) .page-link{margin-left:calc(1px*-1)}.page-item:first-child .page-link{border-top-left-radius:var(--bs-pagination-border-radius);border-bottom-left-radius:var(--bs-pagination-border-radius)}.page-item:last-child .page-link{border-top-right-radius:var(--bs-pagination-border-radius);border-bottom-right-radius:var(--bs-pagination-border-radius)}.pagination-lg{--bs-pagination-padding-x: 1.5rem;--bs-pagination-padding-y: 0.75rem;--bs-pagination-font-size:1.25rem;--bs-pagination-border-radius: 0.5rem}.pagination-sm{--bs-pagination-padding-x: 0.5rem;--bs-pagination-padding-y: 0.25rem;--bs-pagination-font-size:0.875rem;--bs-pagination-border-radius: 0.25rem}.badge{--bs-badge-padding-x: 0.65em;--bs-badge-padding-y: 0.35em;--bs-badge-font-size:0.75em;--bs-badge-font-weight: 700;--bs-badge-color: #ffffff;--bs-badge-border-radius: 0.375rem;display:inline-block;padding:var(--bs-badge-padding-y) var(--bs-badge-padding-x);font-size:var(--bs-badge-font-size);font-weight:var(--bs-badge-font-weight);line-height:1;color:var(--bs-badge-color);text-align:center;white-space:nowrap;vertical-align:baseline;border-radius:var(--bs-badge-border-radius)}.badge:empty{display:none}.btn .badge{position:relative;top:-1px}.alert{--bs-alert-bg: transparent;--bs-alert-padding-x: 1rem;--bs-alert-padding-y: 1rem;--bs-alert-margin-bottom: 1rem;--bs-alert-color: inherit;--bs-alert-border-color: transparent;--bs-alert-border: 1px solid var(--bs-alert-border-color);--bs-alert-border-radius: 0.375rem;--bs-alert-link-color: inherit;position:relative;padding:var(--bs-alert-padding-y) var(--bs-alert-padding-x);margin-bottom:var(--bs-alert-margin-bottom);color:var(--bs-alert-color);background-color:var(--bs-alert-bg);border:var(--bs-alert-border);border-radius:var(--bs-alert-border-radius)}.alert-heading{color:inherit}.alert-link{font-weight:700;color:var(--bs-alert-link-color)}.alert-dismissible{padding-right:3rem}.alert-dismissible .btn-close{position:absolute;top:0;right:0;z-index:2;padding:1.25rem 1rem}.alert-default{--bs-alert-color: var(--bs-default-text-emphasis);--bs-alert-bg: var(--bs-default-bg-subtle);--bs-alert-border-color: var(--bs-default-border-subtle);--bs-alert-link-color: var(--bs-default-text-emphasis)}.alert-primary{--bs-alert-color: var(--bs-primary-text-emphasis);--bs-alert-bg: var(--bs-primary-bg-subtle);--bs-alert-border-color: var(--bs-primary-border-subtle);--bs-alert-link-color: var(--bs-primary-text-emphasis)}.alert-secondary{--bs-alert-color: var(--bs-secondary-text-emphasis);--bs-alert-bg: var(--bs-secondary-bg-subtle);--bs-alert-border-color: var(--bs-secondary-border-subtle);--bs-alert-link-color: var(--bs-secondary-text-emphasis)}.alert-success{--bs-alert-color: var(--bs-success-text-emphasis);--bs-alert-bg: var(--bs-success-bg-subtle);--bs-alert-border-color: var(--bs-success-border-subtle);--bs-alert-link-color: var(--bs-success-text-emphasis)}.alert-info{--bs-alert-color: var(--bs-info-text-emphasis);--bs-alert-bg: var(--bs-info-bg-subtle);--bs-alert-border-color: var(--bs-info-border-subtle);--bs-alert-link-color: var(--bs-info-text-emphasis)}.alert-warning{--bs-alert-color: var(--bs-warning-text-emphasis);--bs-alert-bg: var(--bs-warning-bg-subtle);--bs-alert-border-color: var(--bs-warning-border-subtle);--bs-alert-link-color: var(--bs-warning-text-emphasis)}.alert-danger{--bs-alert-color: var(--bs-danger-text-emphasis);--bs-alert-bg: var(--bs-danger-bg-subtle);--bs-alert-border-color: var(--bs-danger-border-subtle);--bs-alert-link-color: var(--bs-danger-text-emphasis)}.alert-light{--bs-alert-color: var(--bs-light-text-emphasis);--bs-alert-bg: var(--bs-light-bg-subtle);--bs-alert-border-color: var(--bs-light-border-subtle);--bs-alert-link-color: var(--bs-light-text-emphasis)}.alert-dark{--bs-alert-color: var(--bs-dark-text-emphasis);--bs-alert-bg: var(--bs-dark-bg-subtle);--bs-alert-border-color: var(--bs-dark-border-subtle);--bs-alert-link-color: var(--bs-dark-text-emphasis)}@keyframes progress-bar-stripes{0%{background-position-x:1rem}}.progress,.progress-stacked{--bs-progress-height: 1rem;--bs-progress-font-size:0.75rem;--bs-progress-bg: #e9ecef;--bs-progress-border-radius: 0.375rem;--bs-progress-box-shadow: inset 0 1px 2px rgba(0, 0, 0, 0.075);--bs-progress-bar-color: #ffffff;--bs-progress-bar-bg: #0d6efd;--bs-progress-bar-transition: width 0.6s ease;display:flex;display:-webkit-flex;height:var(--bs-progress-height);overflow:hidden;font-size:var(--bs-progress-font-size);background-color:var(--bs-progress-bg);border-radius:var(--bs-progress-border-radius)}.progress-bar{display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;justify-content:center;-webkit-justify-content:center;overflow:hidden;color:var(--bs-progress-bar-color);text-align:center;white-space:nowrap;background-color:var(--bs-progress-bar-bg);transition:var(--bs-progress-bar-transition)}@media(prefers-reduced-motion: reduce){.progress-bar{transition:none}}.progress-bar-striped{background-image:linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);background-size:var(--bs-progress-height) var(--bs-progress-height)}.progress-stacked>.progress{overflow:visible}.progress-stacked>.progress>.progress-bar{width:100%}.progress-bar-animated{animation:1s linear infinite progress-bar-stripes}@media(prefers-reduced-motion: reduce){.progress-bar-animated{animation:none}}.list-group{--bs-list-group-color: #212529;--bs-list-group-bg: #ffffff;--bs-list-group-border-color: #dee2e6;--bs-list-group-border-width: 1px;--bs-list-group-border-radius: 0.375rem;--bs-list-group-item-padding-x: 1rem;--bs-list-group-item-padding-y: 0.5rem;--bs-list-group-action-color: rgba(33, 37, 41, 0.75);--bs-list-group-action-hover-color: #000;--bs-list-group-action-hover-bg: #f8f9fa;--bs-list-group-action-active-color: #212529;--bs-list-group-action-active-bg: #e9ecef;--bs-list-group-disabled-color: rgba(33, 37, 41, 0.75);--bs-list-group-disabled-bg: #ffffff;--bs-list-group-active-color: #ffffff;--bs-list-group-active-bg: #0d6efd;--bs-list-group-active-border-color: #0d6efd;display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;padding-left:0;margin-bottom:0;border-radius:var(--bs-list-group-border-radius)}.list-group-numbered{list-style-type:none;counter-reset:section}.list-group-numbered>.list-group-item::before{content:counters(section, ".") ". ";counter-increment:section}.list-group-item-action{width:100%;color:var(--bs-list-group-action-color);text-align:inherit}.list-group-item-action:hover,.list-group-item-action:focus{z-index:1;color:var(--bs-list-group-action-hover-color);text-decoration:none;background-color:var(--bs-list-group-action-hover-bg)}.list-group-item-action:active{color:var(--bs-list-group-action-active-color);background-color:var(--bs-list-group-action-active-bg)}.list-group-item{position:relative;display:block;padding:var(--bs-list-group-item-padding-y) var(--bs-list-group-item-padding-x);color:var(--bs-list-group-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-list-group-bg);border:var(--bs-list-group-border-width) solid var(--bs-list-group-border-color)}.list-group-item:first-child{border-top-left-radius:inherit;border-top-right-radius:inherit}.list-group-item:last-child{border-bottom-right-radius:inherit;border-bottom-left-radius:inherit}.list-group-item.disabled,.list-group-item:disabled{color:var(--bs-list-group-disabled-color);pointer-events:none;background-color:var(--bs-list-group-disabled-bg)}.list-group-item.active{z-index:2;color:var(--bs-list-group-active-color);background-color:var(--bs-list-group-active-bg);border-color:var(--bs-list-group-active-border-color)}.list-group-item+.list-group-item{border-top-width:0}.list-group-item+.list-group-item.active{margin-top:calc(-1*var(--bs-list-group-border-width));border-top-width:var(--bs-list-group-border-width)}.list-group-horizontal{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal>.list-group-item.active{margin-top:0}.list-group-horizontal>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}@media(min-width: 576px){.list-group-horizontal-sm{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-sm>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-sm>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-sm>.list-group-item.active{margin-top:0}.list-group-horizontal-sm>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-sm>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 768px){.list-group-horizontal-md{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-md>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-md>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-md>.list-group-item.active{margin-top:0}.list-group-horizontal-md>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-md>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 992px){.list-group-horizontal-lg{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-lg>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-lg>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-lg>.list-group-item.active{margin-top:0}.list-group-horizontal-lg>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-lg>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 1200px){.list-group-horizontal-xl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xl>.list-group-item.active{margin-top:0}.list-group-horizontal-xl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xl>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 1400px){.list-group-horizontal-xxl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xxl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xxl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xxl>.list-group-item.active{margin-top:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}.list-group-flush{border-radius:0}.list-group-flush>.list-group-item{border-width:0 0 var(--bs-list-group-border-width)}.list-group-flush>.list-group-item:last-child{border-bottom-width:0}.list-group-item-default{--bs-list-group-color: var(--bs-default-text-emphasis);--bs-list-group-bg: var(--bs-default-bg-subtle);--bs-list-group-border-color: var(--bs-default-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-default-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-default-border-subtle);--bs-list-group-active-color: var(--bs-default-bg-subtle);--bs-list-group-active-bg: var(--bs-default-text-emphasis);--bs-list-group-active-border-color: var(--bs-default-text-emphasis)}.list-group-item-primary{--bs-list-group-color: var(--bs-primary-text-emphasis);--bs-list-group-bg: var(--bs-primary-bg-subtle);--bs-list-group-border-color: var(--bs-primary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-primary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-primary-border-subtle);--bs-list-group-active-color: var(--bs-primary-bg-subtle);--bs-list-group-active-bg: var(--bs-primary-text-emphasis);--bs-list-group-active-border-color: var(--bs-primary-text-emphasis)}.list-group-item-secondary{--bs-list-group-color: var(--bs-secondary-text-emphasis);--bs-list-group-bg: var(--bs-secondary-bg-subtle);--bs-list-group-border-color: var(--bs-secondary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-secondary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-secondary-border-subtle);--bs-list-group-active-color: var(--bs-secondary-bg-subtle);--bs-list-group-active-bg: var(--bs-secondary-text-emphasis);--bs-list-group-active-border-color: var(--bs-secondary-text-emphasis)}.list-group-item-success{--bs-list-group-color: var(--bs-success-text-emphasis);--bs-list-group-bg: var(--bs-success-bg-subtle);--bs-list-group-border-color: var(--bs-success-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-success-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-success-border-subtle);--bs-list-group-active-color: var(--bs-success-bg-subtle);--bs-list-group-active-bg: var(--bs-success-text-emphasis);--bs-list-group-active-border-color: var(--bs-success-text-emphasis)}.list-group-item-info{--bs-list-group-color: var(--bs-info-text-emphasis);--bs-list-group-bg: var(--bs-info-bg-subtle);--bs-list-group-border-color: var(--bs-info-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-info-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-info-border-subtle);--bs-list-group-active-color: var(--bs-info-bg-subtle);--bs-list-group-active-bg: var(--bs-info-text-emphasis);--bs-list-group-active-border-color: var(--bs-info-text-emphasis)}.list-group-item-warning{--bs-list-group-color: var(--bs-warning-text-emphasis);--bs-list-group-bg: var(--bs-warning-bg-subtle);--bs-list-group-border-color: var(--bs-warning-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-warning-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-warning-border-subtle);--bs-list-group-active-color: var(--bs-warning-bg-subtle);--bs-list-group-active-bg: var(--bs-warning-text-emphasis);--bs-list-group-active-border-color: var(--bs-warning-text-emphasis)}.list-group-item-danger{--bs-list-group-color: var(--bs-danger-text-emphasis);--bs-list-group-bg: var(--bs-danger-bg-subtle);--bs-list-group-border-color: var(--bs-danger-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-danger-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-danger-border-subtle);--bs-list-group-active-color: var(--bs-danger-bg-subtle);--bs-list-group-active-bg: var(--bs-danger-text-emphasis);--bs-list-group-active-border-color: var(--bs-danger-text-emphasis)}.list-group-item-light{--bs-list-group-color: var(--bs-light-text-emphasis);--bs-list-group-bg: var(--bs-light-bg-subtle);--bs-list-group-border-color: var(--bs-light-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-light-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-light-border-subtle);--bs-list-group-active-color: var(--bs-light-bg-subtle);--bs-list-group-active-bg: var(--bs-light-text-emphasis);--bs-list-group-active-border-color: var(--bs-light-text-emphasis)}.list-group-item-dark{--bs-list-group-color: var(--bs-dark-text-emphasis);--bs-list-group-bg: var(--bs-dark-bg-subtle);--bs-list-group-border-color: var(--bs-dark-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-dark-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-dark-border-subtle);--bs-list-group-active-color: var(--bs-dark-bg-subtle);--bs-list-group-active-bg: var(--bs-dark-text-emphasis);--bs-list-group-active-border-color: var(--bs-dark-text-emphasis)}.btn-close{--bs-btn-close-color: #000;--bs-btn-close-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%23000'%3e%3cpath d='M.293.293a1 1 0 0 1 1.414 0L8 6.586 14.293.293a1 1 0 1 1 1.414 1.414L9.414 8l6.293 6.293a1 1 0 0 1-1.414 1.414L8 9.414l-6.293 6.293a1 1 0 0 1-1.414-1.414L6.586 8 .293 1.707a1 1 0 0 1 0-1.414z'/%3e%3c/svg%3e");--bs-btn-close-opacity: 0.5;--bs-btn-close-hover-opacity: 0.75;--bs-btn-close-focus-shadow: 0 0 0 0.25rem rgba(13, 110, 253, 0.25);--bs-btn-close-focus-opacity: 1;--bs-btn-close-disabled-opacity: 0.25;--bs-btn-close-white-filter: invert(1) grayscale(100%) brightness(200%);box-sizing:content-box;width:1em;height:1em;padding:.25em .25em;color:var(--bs-btn-close-color);background:rgba(0,0,0,0) var(--bs-btn-close-bg) center/1em auto 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0.375rem;--bs-toast-box-shadow: 0 0.5rem 1rem rgba(0, 0, 0, 0.15);--bs-toast-header-color: rgba(33, 37, 41, 0.75);--bs-toast-header-bg: rgba(255, 255, 255, 0.85);--bs-toast-header-border-color: rgba(0, 0, 0, 0.175);width:var(--bs-toast-max-width);max-width:100%;font-size:var(--bs-toast-font-size);color:var(--bs-toast-color);pointer-events:auto;background-color:var(--bs-toast-bg);background-clip:padding-box;border:var(--bs-toast-border-width) solid var(--bs-toast-border-color);box-shadow:var(--bs-toast-box-shadow);border-radius:var(--bs-toast-border-radius)}.toast.showing{opacity:0}.toast:not(.show){display:none}.toast-container{--bs-toast-zindex: 1090;position:absolute;z-index:var(--bs-toast-zindex);width:max-content;width:-webkit-max-content;width:-moz-max-content;width:-ms-max-content;width:-o-max-content;max-width:100%;pointer-events:none}.toast-container>:not(:last-child){margin-bottom:var(--bs-toast-spacing)}.toast-header{display:flex;display:-webkit-flex;align-items:center;-webkit-align-items:center;padding:var(--bs-toast-padding-y) var(--bs-toast-padding-x);color:var(--bs-toast-header-color);background-color:var(--bs-toast-header-bg);background-clip:padding-box;border-bottom:var(--bs-toast-border-width) solid var(--bs-toast-header-border-color);border-top-left-radius:calc(var(--bs-toast-border-radius) - var(--bs-toast-border-width));border-top-right-radius:calc(var(--bs-toast-border-radius) - var(--bs-toast-border-width))}.toast-header .btn-close{margin-right:calc(-0.5*var(--bs-toast-padding-x));margin-left:var(--bs-toast-padding-x)}.toast-body{padding:var(--bs-toast-padding-x);word-wrap:break-word}.modal{--bs-modal-zindex: 1055;--bs-modal-width: 500px;--bs-modal-padding: 1rem;--bs-modal-margin: 0.5rem;--bs-modal-color: ;--bs-modal-bg: #ffffff;--bs-modal-border-color: rgba(0, 0, 0, 0.175);--bs-modal-border-width: 1px;--bs-modal-border-radius: 0.5rem;--bs-modal-box-shadow: 0 0.125rem 0.25rem rgba(0, 0, 0, 0.075);--bs-modal-inner-border-radius: calc(0.5rem - 1px);--bs-modal-header-padding-x: 1rem;--bs-modal-header-padding-y: 1rem;--bs-modal-header-padding: 1rem 1rem;--bs-modal-header-border-color: #dee2e6;--bs-modal-header-border-width: 1px;--bs-modal-title-line-height: 1.5;--bs-modal-footer-gap: 0.5rem;--bs-modal-footer-bg: ;--bs-modal-footer-border-color: #dee2e6;--bs-modal-footer-border-width: 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var(--bs-modal-margin)*2)}.modal-content{position:relative;display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;width:100%;color:var(--bs-modal-color);pointer-events:auto;background-color:var(--bs-modal-bg);background-clip:padding-box;border:var(--bs-modal-border-width) solid var(--bs-modal-border-color);border-radius:var(--bs-modal-border-radius);outline:0}.modal-backdrop{--bs-backdrop-zindex: 1050;--bs-backdrop-bg: #000;--bs-backdrop-opacity: 0.5;position:fixed;top:0;left:0;z-index:var(--bs-backdrop-zindex);width:100vw;height:100vh;background-color:var(--bs-backdrop-bg)}.modal-backdrop.fade{opacity:0}.modal-backdrop.show{opacity:var(--bs-backdrop-opacity)}.modal-header{display:flex;display:-webkit-flex;flex-shrink:0;-webkit-flex-shrink:0;align-items:center;-webkit-align-items:center;justify-content:space-between;-webkit-justify-content:space-between;padding:var(--bs-modal-header-padding);border-bottom:var(--bs-modal-header-border-width) solid 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.modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen-sm-down .modal-header,.modal-fullscreen-sm-down .modal-footer{border-radius:0}.modal-fullscreen-sm-down .modal-body{overflow-y:auto}}@media(max-width: 767.98px){.modal-fullscreen-md-down{width:100vw;max-width:none;height:100%;margin:0}.modal-fullscreen-md-down .modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen-md-down .modal-header,.modal-fullscreen-md-down .modal-footer{border-radius:0}.modal-fullscreen-md-down .modal-body{overflow-y:auto}}@media(max-width: 991.98px){.modal-fullscreen-lg-down{width:100vw;max-width:none;height:100%;margin:0}.modal-fullscreen-lg-down .modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen-lg-down .modal-header,.modal-fullscreen-lg-down .modal-footer{border-radius:0}.modal-fullscreen-lg-down .modal-body{overflow-y:auto}}@media(max-width: 1199.98px){.modal-fullscreen-xl-down{width:100vw;max-width:none;height:100%;margin:0}.modal-fullscreen-xl-down 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s(t){i.add(t.name),[].concat(t.requires||[],t.requiresIfExists||[]).forEach((function(t){if(!i.has(t)){var n=e.get(t);n&&s(n)}})),n.push(t)}return t.forEach((function(t){e.set(t.name,t)})),t.forEach((function(t){i.has(t.name)||s(t)})),n}var fi={placement:"bottom",modifiers:[],strategy:"absolute"};function pi(){for(var t=arguments.length,e=new Array(t),i=0;iNumber.parseInt(t,10))):"function"==typeof t?e=>t(e,this._element):t}_getPopperConfig(){const t={placement:this._getPlacement(),modifiers:[{name:"preventOverflow",options:{boundary:this._config.boundary}},{name:"offset",options:{offset:this._getOffset()}}]};return(this._inNavbar||"static"===this._config.display)&&(F.setDataAttribute(this._menu,"popper","static"),t.modifiers=[{name:"applyStyles",enabled:!1}]),{...t,...g(this._config.popperConfig,[t])}}_selectMenuItem({key:t,target:e}){const i=z.find(".dropdown-menu 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e=/input|textarea/i.test(t.target.tagName),i="Escape"===t.key,n=[Ei,Ti].includes(t.key);if(!n&&!i)return;if(e&&!i)return;t.preventDefault();const s=this.matches(Ii)?this:z.prev(this,Ii)[0]||z.next(this,Ii)[0]||z.findOne(Ii,t.delegateTarget.parentNode),o=qi.getOrCreateInstance(s);if(n)return t.stopPropagation(),o.show(),void o._selectMenuItem(t);o._isShown()&&(t.stopPropagation(),o.hide(),s.focus())}}N.on(document,Si,Ii,qi.dataApiKeydownHandler),N.on(document,Si,Pi,qi.dataApiKeydownHandler),N.on(document,Li,qi.clearMenus),N.on(document,Di,qi.clearMenus),N.on(document,Li,Ii,(function(t){t.preventDefault(),qi.getOrCreateInstance(this).toggle()})),m(qi);const Vi="backdrop",Ki="show",Qi=`mousedown.bs.${Vi}`,Xi={className:"modal-backdrop",clickCallback:null,isAnimated:!1,isVisible:!0,rootElement:"body"},Yi={className:"string",clickCallback:"(function|null)",isAnimated:"boolean",isVisible:"boolean",rootElement:"(element|string)"};class Ui extends H{constructor(t){super(),this._config=this._getConfig(t),this._isAppended=!1,this._element=null}static get Default(){return Xi}static get DefaultType(){return Yi}static get NAME(){return Vi}show(t){if(!this._config.isVisible)return void g(t);this._append();const e=this._getElement();this._config.isAnimated&&d(e),e.classList.add(Ki),this._emulateAnimation((()=>{g(t)}))}hide(t){this._config.isVisible?(this._getElement().classList.remove(Ki),this._emulateAnimation((()=>{this.dispose(),g(t)}))):g(t)}dispose(){this._isAppended&&(N.off(this._element,Qi),this._element.remove(),this._isAppended=!1)}_getElement(){if(!this._element){const t=document.createElement("div");t.className=this._config.className,this._config.isAnimated&&t.classList.add("fade"),this._element=t}return this._element}_configAfterMerge(t){return t.rootElement=r(t.rootElement),t}_append(){if(this._isAppended)return;const t=this._getElement();this._config.rootElement.append(t),N.on(t,Qi,(()=>{g(this._config.clickCallback)})),this._isAppended=!0}_emulateAnimation(t){_(t,this._getElement(),this._config.isAnimated)}}const Gi=".bs.focustrap",Ji=`focusin${Gi}`,Zi=`keydown.tab${Gi}`,tn="backward",en={autofocus:!0,trapElement:null},nn={autofocus:"boolean",trapElement:"element"};class sn extends H{constructor(t){super(),this._config=this._getConfig(t),this._isActive=!1,this._lastTabNavDirection=null}static get Default(){return en}static get DefaultType(){return nn}static get NAME(){return"focustrap"}activate(){this._isActive||(this._config.autofocus&&this._config.trapElement.focus(),N.off(document,Gi),N.on(document,Ji,(t=>this._handleFocusin(t))),N.on(document,Zi,(t=>this._handleKeydown(t))),this._isActive=!0)}deactivate(){this._isActive&&(this._isActive=!1,N.off(document,Gi))}_handleFocusin(t){const{trapElement:e}=this._config;if(t.target===document||t.target===e||e.contains(t.target))return;const i=z.focusableChildren(e);0===i.length?e.focus():this._lastTabNavDirection===tn?i[i.length-1].focus():i[0].focus()}_handleKeydown(t){"Tab"===t.key&&(this._lastTabNavDirection=t.shiftKey?tn:"forward")}}const on=".fixed-top, .fixed-bottom, .is-fixed, .sticky-top",rn=".sticky-top",an="padding-right",ln="margin-right";class cn{constructor(){this._element=document.body}getWidth(){const t=document.documentElement.clientWidth;return Math.abs(window.innerWidth-t)}hide(){const t=this.getWidth();this._disableOverFlow(),this._setElementAttributes(this._element,an,(e=>e+t)),this._setElementAttributes(on,an,(e=>e+t)),this._setElementAttributes(rn,ln,(e=>e-t))}reset(){this._resetElementAttributes(this._element,"overflow"),this._resetElementAttributes(this._element,an),this._resetElementAttributes(on,an),this._resetElementAttributes(rn,ln)}isOverflowing(){return this.getWidth()>0}_disableOverFlow(){this._saveInitialAttribute(this._element,"overflow"),this._element.style.overflow="hidden"}_setElementAttributes(t,e,i){const n=this.getWidth();this._applyManipulationCallback(t,(t=>{if(t!==this._element&&window.innerWidth>t.clientWidth+n)return;this._saveInitialAttribute(t,e);const s=window.getComputedStyle(t).getPropertyValue(e);t.style.setProperty(e,`${i(Number.parseFloat(s))}px`)}))}_saveInitialAttribute(t,e){const i=t.style.getPropertyValue(e);i&&F.setDataAttribute(t,e,i)}_resetElementAttributes(t,e){this._applyManipulationCallback(t,(t=>{const i=F.getDataAttribute(t,e);null!==i?(F.removeDataAttribute(t,e),t.style.setProperty(e,i)):t.style.removeProperty(e)}))}_applyManipulationCallback(t,e){if(o(t))e(t);else for(const i of z.find(t,this._element))e(i)}}const hn=".bs.modal",dn=`hide${hn}`,un=`hidePrevented${hn}`,fn=`hidden${hn}`,pn=`show${hn}`,mn=`shown${hn}`,gn=`resize${hn}`,_n=`click.dismiss${hn}`,bn=`mousedown.dismiss${hn}`,vn=`keydown.dismiss${hn}`,yn=`click${hn}.data-api`,wn="modal-open",An="show",En="modal-static",Tn={backdrop:!0,focus:!0,keyboard:!0},Cn={backdrop:"(boolean|string)",focus:"boolean",keyboard:"boolean"};class On extends W{constructor(t,e){super(t,e),this._dialog=z.findOne(".modal-dialog",this._element),this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._isShown=!1,this._isTransitioning=!1,this._scrollBar=new cn,this._addEventListeners()}static get Default(){return Tn}static get DefaultType(){return Cn}static get NAME(){return"modal"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||this._isTransitioning||N.trigger(this._element,pn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._isTransitioning=!0,this._scrollBar.hide(),document.body.classList.add(wn),this._adjustDialog(),this._backdrop.show((()=>this._showElement(t))))}hide(){this._isShown&&!this._isTransitioning&&(N.trigger(this._element,dn).defaultPrevented||(this._isShown=!1,this._isTransitioning=!0,this._focustrap.deactivate(),this._element.classList.remove(An),this._queueCallback((()=>this._hideModal()),this._element,this._isAnimated())))}dispose(){N.off(window,hn),N.off(this._dialog,hn),this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}handleUpdate(){this._adjustDialog()}_initializeBackDrop(){return new Ui({isVisible:Boolean(this._config.backdrop),isAnimated:this._isAnimated()})}_initializeFocusTrap(){return new sn({trapElement:this._element})}_showElement(t){document.body.contains(this._element)||document.body.append(this._element),this._element.style.display="block",this._element.removeAttribute("aria-hidden"),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.scrollTop=0;const e=z.findOne(".modal-body",this._dialog);e&&(e.scrollTop=0),d(this._element),this._element.classList.add(An),this._queueCallback((()=>{this._config.focus&&this._focustrap.activate(),this._isTransitioning=!1,N.trigger(this._element,mn,{relatedTarget:t})}),this._dialog,this._isAnimated())}_addEventListeners(){N.on(this._element,vn,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():this._triggerBackdropTransition())})),N.on(window,gn,(()=>{this._isShown&&!this._isTransitioning&&this._adjustDialog()})),N.on(this._element,bn,(t=>{N.one(this._element,_n,(e=>{this._element===t.target&&this._element===e.target&&("static"!==this._config.backdrop?this._config.backdrop&&this.hide():this._triggerBackdropTransition())}))}))}_hideModal(){this._element.style.display="none",this._element.setAttribute("aria-hidden",!0),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._isTransitioning=!1,this._backdrop.hide((()=>{document.body.classList.remove(wn),this._resetAdjustments(),this._scrollBar.reset(),N.trigger(this._element,fn)}))}_isAnimated(){return this._element.classList.contains("fade")}_triggerBackdropTransition(){if(N.trigger(this._element,un).defaultPrevented)return;const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._element.style.overflowY;"hidden"===e||this._element.classList.contains(En)||(t||(this._element.style.overflowY="hidden"),this._element.classList.add(En),this._queueCallback((()=>{this._element.classList.remove(En),this._queueCallback((()=>{this._element.style.overflowY=e}),this._dialog)}),this._dialog),this._element.focus())}_adjustDialog(){const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._scrollBar.getWidth(),i=e>0;if(i&&!t){const t=p()?"paddingLeft":"paddingRight";this._element.style[t]=`${e}px`}if(!i&&t){const t=p()?"paddingRight":"paddingLeft";this._element.style[t]=`${e}px`}}_resetAdjustments(){this._element.style.paddingLeft="",this._element.style.paddingRight=""}static jQueryInterface(t,e){return this.each((function(){const 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W{constructor(t,e){super(t,e),this._isShown=!1,this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._addEventListeners()}static get Default(){return zn}static get DefaultType(){return Rn}static get NAME(){return"offcanvas"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||N.trigger(this._element,Nn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._backdrop.show(),this._config.scroll||(new cn).hide(),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.classList.add(Dn),this._queueCallback((()=>{this._config.scroll&&!this._config.backdrop||this._focustrap.activate(),this._element.classList.add(Sn),this._element.classList.remove(Dn),N.trigger(this._element,Pn,{relatedTarget:t})}),this._element,!0))}hide(){this._isShown&&(N.trigger(this._element,Mn).defaultPrevented||(this._focustrap.deactivate(),this._element.blur(),this._isShown=!1,this._element.classList.add($n),this._backdrop.hide(),this._queueCallback((()=>{this._element.classList.remove(Sn,$n),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._config.scroll||(new cn).reset(),N.trigger(this._element,Fn)}),this._element,!0)))}dispose(){this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}_initializeBackDrop(){const t=Boolean(this._config.backdrop);return new Ui({className:"offcanvas-backdrop",isVisible:t,isAnimated:!0,rootElement:this._element.parentNode,clickCallback:t?()=>{"static"!==this._config.backdrop?this.hide():N.trigger(this._element,jn)}:null})}_initializeFocusTrap(){return new sn({trapElement:this._element})}_addEventListeners(){N.on(this._element,Bn,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():N.trigger(this._element,jn))}))}static jQueryInterface(t){return this.each((function(){const e=qn.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t]||t.startsWith("_")||"constructor"===t)throw new TypeError(`No method named "${t}"`);e[t](this)}}))}}N.on(document,Wn,'[data-bs-toggle="offcanvas"]',(function(t){const e=z.getElementFromSelector(this);if(["A","AREA"].includes(this.tagName)&&t.preventDefault(),l(this))return;N.one(e,Fn,(()=>{a(this)&&this.focus()}));const i=z.findOne(In);i&&i!==e&&qn.getInstance(i).hide(),qn.getOrCreateInstance(e).toggle(this)})),N.on(window,Ln,(()=>{for(const t of z.find(In))qn.getOrCreateInstance(t).show()})),N.on(window,Hn,(()=>{for(const t of z.find("[aria-modal][class*=show][class*=offcanvas-]"))"fixed"!==getComputedStyle(t).position&&qn.getOrCreateInstance(t).hide()})),R(qn),m(qn);const Vn={"*":["class","dir","id","lang","role",/^aria-[\w-]*$/i],a:["target","href","title","rel"],area:[],b:[],br:[],col:[],code:[],div:[],em:[],hr:[],h1:[],h2:[],h3:[],h4:[],h5:[],h6:[],i:[],img:["src","srcset","alt","title","width","height"],li:[],ol:[],p:[],pre:[],s:[],small:[],span:[],sub:[],sup:[],strong:[],u:[],ul:[]},Kn=new Set(["background","cite","href","itemtype","longdesc","poster","src","xlink:href"]),Qn=/^(?!javascript:)(?:[a-z0-9+.-]+:|[^&:/?#]*(?:[/?#]|$))/i,Xn=(t,e)=>{const i=t.nodeName.toLowerCase();return e.includes(i)?!Kn.has(i)||Boolean(Qn.test(t.nodeValue)):e.filter((t=>t instanceof RegExp)).some((t=>t.test(i)))},Yn={allowList:Vn,content:{},extraClass:"",html:!1,sanitize:!0,sanitizeFn:null,template:"

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b/profile/blog/posts/causal-recourse/index_files/libs/quarto-html/quarto-syntax-highlighting.css new file mode 100644 index 0000000..b30ce57 --- /dev/null +++ b/profile/blog/posts/causal-recourse/index_files/libs/quarto-html/quarto-syntax-highlighting.css @@ -0,0 +1,205 @@ +/* quarto syntax highlight colors */ +:root { + --quarto-hl-ot-color: #003B4F; + --quarto-hl-at-color: #657422; + --quarto-hl-ss-color: #20794D; + --quarto-hl-an-color: #5E5E5E; + --quarto-hl-fu-color: #4758AB; + --quarto-hl-st-color: #20794D; + --quarto-hl-cf-color: #003B4F; + --quarto-hl-op-color: #5E5E5E; + --quarto-hl-er-color: #AD0000; + --quarto-hl-bn-color: #AD0000; + --quarto-hl-al-color: #AD0000; + --quarto-hl-va-color: #111111; + --quarto-hl-bu-color: inherit; + --quarto-hl-ex-color: inherit; + --quarto-hl-pp-color: #AD0000; + --quarto-hl-in-color: #5E5E5E; + --quarto-hl-vs-color: #20794D; + --quarto-hl-wa-color: #5E5E5E; + --quarto-hl-do-color: #5E5E5E; + --quarto-hl-im-color: #00769E; + --quarto-hl-ch-color: #20794D; + --quarto-hl-dt-color: #AD0000; + --quarto-hl-fl-color: #AD0000; + --quarto-hl-co-color: #5E5E5E; + --quarto-hl-cv-color: #5E5E5E; + --quarto-hl-cn-color: #8f5902; + --quarto-hl-sc-color: #5E5E5E; + --quarto-hl-dv-color: #AD0000; + --quarto-hl-kw-color: #003B4F; +} + +/* other quarto variables */ +:root { + --quarto-font-monospace: SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", "Courier New", monospace; +} + +pre > code.sourceCode > span { + color: #003B4F; +} + +code span { + color: #003B4F; +} + +code.sourceCode > span { + color: #003B4F; +} + +div.sourceCode, +div.sourceCode pre.sourceCode { + color: #003B4F; +} + +code span.ot { + color: #003B4F; + font-style: inherit; +} + +code span.at { + color: #657422; + font-style: inherit; +} + +code span.ss { + color: #20794D; + font-style: inherit; +} + +code span.an { + color: #5E5E5E; + font-style: inherit; +} + +code span.fu { + color: #4758AB; + font-style: inherit; +} + +code span.st { + color: #20794D; + font-style: inherit; +} + +code span.cf { + color: #003B4F; + font-weight: bold; + font-style: inherit; +} + +code span.op { + color: #5E5E5E; + font-style: inherit; +} + +code span.er { + color: #AD0000; + font-style: inherit; +} + +code span.bn { + color: #AD0000; + font-style: inherit; +} + +code span.al { + color: #AD0000; + font-style: inherit; +} + +code span.va { + color: #111111; + font-style: inherit; +} + +code span.bu { + font-style: inherit; +} + +code span.ex { + font-style: inherit; +} + +code span.pp { + color: #AD0000; + font-style: inherit; +} + +code span.in { + color: #5E5E5E; + font-style: inherit; +} + +code span.vs { + color: #20794D; + font-style: inherit; +} + +code span.wa { + color: #5E5E5E; + font-style: italic; +} + +code span.do { + color: #5E5E5E; + font-style: italic; +} + +code span.im { + color: #00769E; + font-style: inherit; +} + +code span.ch { + color: #20794D; + font-style: inherit; +} + +code span.dt { + color: #AD0000; + font-style: inherit; +} + +code span.fl { + color: #AD0000; + font-style: inherit; +} + +code span.co { + color: #5E5E5E; + font-style: inherit; +} + +code span.cv { + color: #5E5E5E; + font-style: italic; +} + +code span.cn { + color: #8f5902; + font-style: inherit; +} + +code span.sc { + color: #5E5E5E; + font-style: inherit; +} + +code span.dv { + color: #AD0000; + font-style: inherit; +} + +code span.kw { + color: #003B4F; + font-weight: bold; + font-style: inherit; +} + +.prevent-inlining { + content: " { + // Find any conflicting margin elements and add margins to the + // top to prevent overlap + const marginChildren = window.document.querySelectorAll( + ".column-margin.column-container > *, .margin-caption, .aside" + ); + + let lastBottom = 0; + for (const marginChild of marginChildren) { + if (marginChild.offsetParent !== null) { + // clear the top margin so we recompute it + marginChild.style.marginTop = null; + const top = marginChild.getBoundingClientRect().top + window.scrollY; + if (top < lastBottom) { + const marginChildStyle = window.getComputedStyle(marginChild); + const marginBottom = parseFloat(marginChildStyle["marginBottom"]); + const margin = lastBottom - top + marginBottom; + marginChild.style.marginTop = `${margin}px`; + } + const styles = window.getComputedStyle(marginChild); + const marginTop = parseFloat(styles["marginTop"]); + lastBottom = top + marginChild.getBoundingClientRect().height + marginTop; + } + } +}; + +window.document.addEventListener("DOMContentLoaded", function (_event) { + // Recompute the position of margin elements anytime the body size changes + if (window.ResizeObserver) { + const resizeObserver = new window.ResizeObserver( + throttle(() => { + layoutMarginEls(); + if ( + window.document.body.getBoundingClientRect().width < 990 && + isReaderMode() + ) { + quartoToggleReader(); + } + }, 50) + ); + resizeObserver.observe(window.document.body); + } + + const tocEl = window.document.querySelector('nav.toc-active[role="doc-toc"]'); + const sidebarEl = window.document.getElementById("quarto-sidebar"); + const leftTocEl = window.document.getElementById("quarto-sidebar-toc-left"); + const marginSidebarEl = window.document.getElementById( + "quarto-margin-sidebar" + ); + // function to determine whether the element has a previous sibling that is active + const prevSiblingIsActiveLink = (el) => { + const sibling = el.previousElementSibling; + if (sibling && sibling.tagName === "A") { + return sibling.classList.contains("active"); + } else { + return false; + } + }; + + // fire slideEnter for bootstrap tab activations (for htmlwidget resize behavior) + function fireSlideEnter(e) { + const event = window.document.createEvent("Event"); + event.initEvent("slideenter", true, true); + window.document.dispatchEvent(event); + } + const tabs = window.document.querySelectorAll('a[data-bs-toggle="tab"]'); + tabs.forEach((tab) => { + tab.addEventListener("shown.bs.tab", fireSlideEnter); + }); + + // fire slideEnter for tabby tab activations (for htmlwidget resize behavior) + document.addEventListener("tabby", fireSlideEnter, false); + + // Track scrolling and mark TOC links as active + // get table of contents and sidebar (bail if we don't have at least one) + const tocLinks = tocEl + ? [...tocEl.querySelectorAll("a[data-scroll-target]")] + : []; + const makeActive = (link) => tocLinks[link].classList.add("active"); + const removeActive = (link) => tocLinks[link].classList.remove("active"); + const removeAllActive = () => + [...Array(tocLinks.length).keys()].forEach((link) => removeActive(link)); + + // activate the anchor for a section associated with this TOC entry + tocLinks.forEach((link) => { + link.addEventListener("click", () => { + if (link.href.indexOf("#") !== -1) { + const anchor = link.href.split("#")[1]; + const heading = window.document.querySelector( + `[data-anchor-id="${anchor}"]` + ); + if (heading) { + // Add the class + heading.classList.add("reveal-anchorjs-link"); + + // function to show the anchor + const handleMouseout = () => { + heading.classList.remove("reveal-anchorjs-link"); + heading.removeEventListener("mouseout", handleMouseout); + }; + + // add a function to clear the anchor when the user mouses out of it + heading.addEventListener("mouseout", handleMouseout); + } + } + }); + }); + + const sections = tocLinks.map((link) => { + const target = link.getAttribute("data-scroll-target"); + if (target.startsWith("#")) { + return window.document.getElementById(decodeURI(`${target.slice(1)}`)); + } else { + return window.document.querySelector(decodeURI(`${target}`)); + } + }); + + const sectionMargin = 200; + let currentActive = 0; + // track whether we've initialized state the first time + let init = false; + + const updateActiveLink = () => { + // The index from bottom to top (e.g. reversed list) + let sectionIndex = -1; + if ( + window.innerHeight + window.pageYOffset >= + window.document.body.offsetHeight + ) { + // This is the no-scroll case where last section should be the active one + sectionIndex = 0; + } else { + // This finds the last section visible on screen that should be made active + sectionIndex = [...sections].reverse().findIndex((section) => { + if (section) { + return window.pageYOffset >= section.offsetTop - sectionMargin; + } else { + return false; + } + }); + } + if (sectionIndex > -1) { + const current = sections.length - sectionIndex - 1; + if (current !== currentActive) { + removeAllActive(); + currentActive = current; + makeActive(current); + if (init) { + window.dispatchEvent(sectionChanged); + } + init = true; + } + } + }; + + const inHiddenRegion = (top, bottom, hiddenRegions) => { + for (const region of hiddenRegions) { + if (top <= region.bottom && bottom >= region.top) { + return true; + } + } + return false; + }; + + const categorySelector = "header.quarto-title-block .quarto-category"; + const activateCategories = (href) => { + // Find any categories + // Surround them with a link pointing back to: + // #category=Authoring + try { + const categoryEls = window.document.querySelectorAll(categorySelector); + for (const categoryEl of categoryEls) { + const categoryText = categoryEl.textContent; + if (categoryText) { + const link = `${href}#category=${encodeURIComponent(categoryText)}`; + const linkEl = window.document.createElement("a"); + linkEl.setAttribute("href", link); + for (const child of categoryEl.childNodes) { + linkEl.append(child); + } + categoryEl.appendChild(linkEl); + } + } + } catch { + // Ignore errors + } + }; + function hasTitleCategories() { + return window.document.querySelector(categorySelector) !== null; + } + + function offsetRelativeUrl(url) { + const offset = getMeta("quarto:offset"); + return offset ? offset + url : url; + } + + function offsetAbsoluteUrl(url) { + const offset = getMeta("quarto:offset"); + const baseUrl = new URL(offset, window.location); + + const projRelativeUrl = url.replace(baseUrl, ""); + if (projRelativeUrl.startsWith("/")) { + return projRelativeUrl; + } else { + return "/" + projRelativeUrl; + } + } + + // read a meta tag value + function getMeta(metaName) { + const metas = window.document.getElementsByTagName("meta"); + for (let i = 0; i < metas.length; i++) { + if (metas[i].getAttribute("name") === metaName) { + return metas[i].getAttribute("content"); + } + } + return ""; + } + + async function findAndActivateCategories() { + const currentPagePath = offsetAbsoluteUrl(window.location.href); + const response = await fetch(offsetRelativeUrl("listings.json")); + if (response.status == 200) { + return response.json().then(function (listingPaths) { + const listingHrefs = []; + for (const listingPath of listingPaths) { + const pathWithoutLeadingSlash = listingPath.listing.substring(1); + for (const item of listingPath.items) { + if ( + item === currentPagePath || + item === currentPagePath + "index.html" + ) { + // Resolve this path against the offset to be sure + // we already are using the correct path to the listing + // (this adjusts the listing urls to be rooted against + // whatever root the page is actually running against) + const relative = offsetRelativeUrl(pathWithoutLeadingSlash); + const baseUrl = window.location; + const resolvedPath = new URL(relative, baseUrl); + listingHrefs.push(resolvedPath.pathname); + break; + } + } + } + + // Look up the tree for a nearby linting and use that if we find one + const nearestListing = findNearestParentListing( + offsetAbsoluteUrl(window.location.pathname), + listingHrefs + ); + if (nearestListing) { + activateCategories(nearestListing); + } else { + // See if the referrer is a listing page for this item + const referredRelativePath = offsetAbsoluteUrl(document.referrer); + const referrerListing = listingHrefs.find((listingHref) => { + const isListingReferrer = + listingHref === referredRelativePath || + listingHref === referredRelativePath + "index.html"; + return isListingReferrer; + }); + + if (referrerListing) { + // Try to use the referrer if possible + activateCategories(referrerListing); + } else if (listingHrefs.length > 0) { + // Otherwise, just fall back to the first listing + activateCategories(listingHrefs[0]); + } + } + }); + } + } + if (hasTitleCategories()) { + findAndActivateCategories(); + } + + const findNearestParentListing = (href, listingHrefs) => { + if (!href || !listingHrefs) { + return undefined; + } + // Look up the tree for a nearby linting and use that if we find one + const relativeParts = href.substring(1).split("/"); + while (relativeParts.length > 0) { + const path = relativeParts.join("/"); + for (const listingHref of listingHrefs) { + if (listingHref.startsWith(path)) { + return listingHref; + } + } + relativeParts.pop(); + } + + return undefined; + }; + + const manageSidebarVisiblity = (el, placeholderDescriptor) => { + let isVisible = true; + let elRect; + + return (hiddenRegions) => { + if (el === null) { + return; + } + + // Find the last element of the TOC + const lastChildEl = el.lastElementChild; + + if (lastChildEl) { + // Converts the sidebar to a menu + const convertToMenu = () => { + for (const child of el.children) { + child.style.opacity = 0; + child.style.overflow = "hidden"; + child.style.pointerEvents = "none"; + } + + nexttick(() => { + const toggleContainer = window.document.createElement("div"); + toggleContainer.style.width = "100%"; + toggleContainer.classList.add("zindex-over-content"); + toggleContainer.classList.add("quarto-sidebar-toggle"); + toggleContainer.classList.add("headroom-target"); // Marks this to be managed by headeroom + toggleContainer.id = placeholderDescriptor.id; + toggleContainer.style.position = "fixed"; + + const toggleIcon = window.document.createElement("i"); + toggleIcon.classList.add("quarto-sidebar-toggle-icon"); + toggleIcon.classList.add("bi"); + toggleIcon.classList.add("bi-caret-down-fill"); + + const toggleTitle = window.document.createElement("div"); + const titleEl = window.document.body.querySelector( + placeholderDescriptor.titleSelector + ); + if (titleEl) { + toggleTitle.append( + titleEl.textContent || titleEl.innerText, + toggleIcon + ); + } + toggleTitle.classList.add("zindex-over-content"); + toggleTitle.classList.add("quarto-sidebar-toggle-title"); + toggleContainer.append(toggleTitle); + + const toggleContents = window.document.createElement("div"); + toggleContents.classList = el.classList; + toggleContents.classList.add("zindex-over-content"); + toggleContents.classList.add("quarto-sidebar-toggle-contents"); + for (const child of el.children) { + if (child.id === "toc-title") { + continue; + } + + const clone = child.cloneNode(true); + clone.style.opacity = 1; + clone.style.pointerEvents = null; + clone.style.display = null; + toggleContents.append(clone); + } + toggleContents.style.height = "0px"; + const positionToggle = () => { + // position the element (top left of parent, same width as parent) + if (!elRect) { + elRect = el.getBoundingClientRect(); + } + toggleContainer.style.left = `${elRect.left}px`; + toggleContainer.style.top = `${elRect.top}px`; + toggleContainer.style.width = `${elRect.width}px`; + }; + positionToggle(); + + toggleContainer.append(toggleContents); + el.parentElement.prepend(toggleContainer); + + // Process clicks + let tocShowing = false; + // Allow the caller to control whether this is dismissed + // when it is clicked (e.g. sidebar navigation supports + // opening and closing the nav tree, so don't dismiss on click) + const clickEl = placeholderDescriptor.dismissOnClick + ? toggleContainer + : toggleTitle; + + const closeToggle = () => { + if (tocShowing) { + toggleContainer.classList.remove("expanded"); + toggleContents.style.height = "0px"; + tocShowing = false; + } + }; + + // Get rid of any expanded toggle if the user scrolls + window.document.addEventListener( + "scroll", + throttle(() => { + closeToggle(); + }, 50) + ); + + // Handle positioning of the toggle + window.addEventListener( + "resize", + throttle(() => { + elRect = undefined; + positionToggle(); + }, 50) + ); + + window.addEventListener("quarto-hrChanged", () => { + elRect = undefined; + }); + + // Process the click + clickEl.onclick = () => { + if (!tocShowing) { + toggleContainer.classList.add("expanded"); + toggleContents.style.height = null; + tocShowing = true; + } else { + closeToggle(); + } + }; + }); + }; + + // Converts a sidebar from a menu back to a sidebar + const convertToSidebar = () => { + for (const child of el.children) { + child.style.opacity = 1; + child.style.overflow = null; + child.style.pointerEvents = null; + } + + const placeholderEl = window.document.getElementById( + placeholderDescriptor.id + ); + if (placeholderEl) { + placeholderEl.remove(); + } + + el.classList.remove("rollup"); + }; + + if (isReaderMode()) { + convertToMenu(); + isVisible = false; + } else { + // Find the top and bottom o the element that is being managed + const elTop = el.offsetTop; + const elBottom = + elTop + lastChildEl.offsetTop + lastChildEl.offsetHeight; + + if (!isVisible) { + // If the element is current not visible reveal if there are + // no conflicts with overlay regions + if (!inHiddenRegion(elTop, elBottom, hiddenRegions)) { + convertToSidebar(); + isVisible = true; + } + } else { + // If the element is visible, hide it if it conflicts with overlay regions + // and insert a placeholder toggle (or if we're in reader mode) + if (inHiddenRegion(elTop, elBottom, hiddenRegions)) { + convertToMenu(); + isVisible = false; + } + } + } + } + }; + }; + + const tabEls = document.querySelectorAll('a[data-bs-toggle="tab"]'); + for (const tabEl of tabEls) { + const id = tabEl.getAttribute("data-bs-target"); + if (id) { + const columnEl = document.querySelector( + `${id} .column-margin, .tabset-margin-content` + ); + if (columnEl) + tabEl.addEventListener("shown.bs.tab", function (event) { + const el = event.srcElement; + if (el) { + const visibleCls = `${el.id}-margin-content`; + // walk up until we find a parent tabset + let panelTabsetEl = el.parentElement; + while (panelTabsetEl) { + if (panelTabsetEl.classList.contains("panel-tabset")) { + break; + } + panelTabsetEl = panelTabsetEl.parentElement; + } + + if (panelTabsetEl) { + const prevSib = panelTabsetEl.previousElementSibling; + if ( + prevSib && + prevSib.classList.contains("tabset-margin-container") + ) { + const childNodes = prevSib.querySelectorAll( + ".tabset-margin-content" + ); + for (const childEl of childNodes) { + if (childEl.classList.contains(visibleCls)) { + childEl.classList.remove("collapse"); + } else { + childEl.classList.add("collapse"); + } + } + } + } + } + + layoutMarginEls(); + }); + } + } + + // Manage the visibility of the toc and the sidebar + const marginScrollVisibility = manageSidebarVisiblity(marginSidebarEl, { + id: "quarto-toc-toggle", + titleSelector: "#toc-title", + dismissOnClick: true, + }); + const sidebarScrollVisiblity = manageSidebarVisiblity(sidebarEl, { + id: "quarto-sidebarnav-toggle", + titleSelector: ".title", + dismissOnClick: false, + }); + let tocLeftScrollVisibility; + if (leftTocEl) { + tocLeftScrollVisibility = manageSidebarVisiblity(leftTocEl, { + id: "quarto-lefttoc-toggle", + titleSelector: "#toc-title", + dismissOnClick: true, + }); + } + + // Find the first element that uses formatting in special columns + const conflictingEls = window.document.body.querySelectorAll( + '[class^="column-"], [class*=" column-"], aside, [class*="margin-caption"], [class*=" margin-caption"], [class*="margin-ref"], [class*=" margin-ref"]' + ); + + // Filter all the possibly conflicting elements into ones + // the do conflict on the left or ride side + const arrConflictingEls = Array.from(conflictingEls); + const leftSideConflictEls = arrConflictingEls.filter((el) => { + if (el.tagName === "ASIDE") { + return false; + } + return Array.from(el.classList).find((className) => { + return ( + className !== "column-body" && + className.startsWith("column-") && + !className.endsWith("right") && + !className.endsWith("container") && + className !== "column-margin" + ); + }); + }); + const rightSideConflictEls = arrConflictingEls.filter((el) => { + if (el.tagName === "ASIDE") { + return true; + } + + const hasMarginCaption = Array.from(el.classList).find((className) => { + return className == "margin-caption"; + }); + if (hasMarginCaption) { + return true; + } + + return Array.from(el.classList).find((className) => { + return ( + className !== "column-body" && + !className.endsWith("container") && + className.startsWith("column-") && + !className.endsWith("left") + ); + }); + }); + + const kOverlapPaddingSize = 10; + function toRegions(els) { + return els.map((el) => { + const boundRect = el.getBoundingClientRect(); + const top = + boundRect.top + + document.documentElement.scrollTop - + kOverlapPaddingSize; + return { + top, + bottom: top + el.scrollHeight + 2 * kOverlapPaddingSize, + }; + }); + } + + let hasObserved = false; + const visibleItemObserver = (els) => { + let visibleElements = [...els]; + const intersectionObserver = new IntersectionObserver( + (entries, _observer) => { + entries.forEach((entry) => { + if (entry.isIntersecting) { + if (visibleElements.indexOf(entry.target) === -1) { + visibleElements.push(entry.target); + } + } else { + visibleElements = visibleElements.filter((visibleEntry) => { + return visibleEntry !== entry; + }); + } + }); + + if (!hasObserved) { + hideOverlappedSidebars(); + } + hasObserved = true; + }, + {} + ); + els.forEach((el) => { + intersectionObserver.observe(el); + }); + + return { + getVisibleEntries: () => { + return visibleElements; + }, + }; + }; + + const rightElementObserver = visibleItemObserver(rightSideConflictEls); + const leftElementObserver = visibleItemObserver(leftSideConflictEls); + + const hideOverlappedSidebars = () => { + marginScrollVisibility(toRegions(rightElementObserver.getVisibleEntries())); + sidebarScrollVisiblity(toRegions(leftElementObserver.getVisibleEntries())); + if (tocLeftScrollVisibility) { + tocLeftScrollVisibility( + toRegions(leftElementObserver.getVisibleEntries()) + ); + } + }; + + window.quartoToggleReader = () => { + // Applies a slow class (or removes it) + // to update the transition speed + const slowTransition = (slow) => { + const manageTransition = (id, slow) => { + const el = document.getElementById(id); 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b/profile/blog/posts/conformal-image-classifier/index.qmd index c39db7b..d3f7e2c 100644 --- a/profile/blog/posts/conformal-image-classifier/index.qmd +++ b/profile/blog/posts/conformal-image-classifier/index.qmd @@ -9,7 +9,7 @@ categories: description: >- A guide demonstrating how to use [`ConformalPrediction.jl`](https://github.com/juliatrustworthyai/ConformalPrediction.jl) to conformalize a deep image classifier in a few lines of code. image: www/intro.gif -jupyter: julia-1.10 +engine: julia draft: false --- diff --git a/profile/blog/posts/conformal-image-classifier/index.quarto_ipynb b/profile/blog/posts/conformal-image-classifier/index.quarto_ipynb new file mode 100644 index 0000000..49536af --- /dev/null +++ b/profile/blog/posts/conformal-image-classifier/index.quarto_ipynb @@ -0,0 +1,467 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "---\n", + "title: How to Conformalize a Deep Image Classifier\n", + "subtitle: Conformal Prediction in Julia --- Part 2\n", + "date: '2022-12-05'\n", + "categories:\n", + " - conformal prediction\n", + " - uncertainty\n", + " - Julia\n", + "description: >-\n", + " A guide demonstrating how to use [`ConformalPrediction.jl`](https://github.com/juliatrustworthyai/ConformalPrediction.jl) to conformalize a deep image classifier in a few lines of code.\n", + "image: www/intro.gif\n", + "jupyter: julia-1.10\n", + "draft: false\n", + "---" + ], + "id": "8176359d" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "#| echo: false\n", + "\n", + "using Pkg; Pkg.activate(\"blog/posts/conformal-image-classifier/\")\n", + "using Plots\n", + "using Random\n", + "Random.seed!(2022)\n", + "www_path = \"blog/posts/conformal-image-classifier/www\"" + ], + "id": "a460d2ab", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + "
\n", + " \n", + "
Conformalized prediction sets for a
simple Deep Image Classifier.
\n", + "
\n", + "
\n", + "\n", + "Deep Learning is popular and --- for some tasks like image classification --- remarkably powerful. But it is also well-known that Deep Neural Networks (DNN) can be unstable [@goodfellow2014explaining] and poorly calibrated. Conformal Prediction can be used to mitigate these pitfalls. \n", + "\n", + "In the [first part](../conformal-prediction/index.qmd) of this series of posts on Conformal Prediction, we looked at the basic underlying methodology and how CP can be implemented in Julia using [`ConformalPrediction.jl`](https://github.com/juliatrustworthyai/ConformalPrediction.jl). This second part of the series is a more goal-oriented how-to guide: it demonstrates how you can conformalize a deep learning image classifier built in `Flux.jl` in just a few lines of code. \n", + "\n", + "Since this is meant to be more of a hands-on article, we will avoid diving too deeply into methodological concepts. If you need more colour on this, be sure to check out the [first article](../conformal-prediction/index.qmd) on this topic and also @angelopoulos2021gentle. For a more formal treatment of Conformal Prediction see also @angelopoulos2022uncertainty.\n", + "\n", + "## 🎯 The Task at Hand \n", + "\n", + "The task at hand is to predict the labels of handwritten images of digits using the famous MNIST dataset [@lecun1998mnist]. Importing this popular machine learning dataset in Julia is made remarkably easy through `MLDatasets.jl`:\n" + ], + "id": "c999a1ef" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "using MLDatasets\n", + "N = 1000\n", + "Xraw, yraw = MNIST(split=:train)[:]\n", + "Xraw = Xraw[:,:,1:N]\n", + "yraw = yraw[1:N]" + ], + "id": "9dd29092", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "@fig-samples below shows a few random samples from the training data:\n" + ], + "id": "7563f26c" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "#| output: true\n", + "#| label: fig-samples\n", + "#| fig-cap: Random samples from the MNIST dataset.\n", + "\n", + "using MLJ\n", + "using Images\n", + "X = map(x -> convert2image(MNIST, x), eachslice(Xraw, dims=3))\n", + "y = coerce(yraw, Multiclass)\n", + "\n", + "n_samples = 10\n", + "mosaic(rand(X, n_samples)..., ncol=n_samples)" + ], + "id": "fig-samples", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 🚧 Building the Network\n", + "\n", + "To model the mapping from image inputs to labels will rely on a simple Multi-Layer Perceptron (MLP). A great Julia library for Deep Learning is `Flux.jl`. But wait ... doesn't `ConformalPrediction.jl` work with models trained in `MLJ.jl`? That's right, but fortunately there exists a `Flux.jl` interface to `MLJ.jl`, namely `MLJFlux.jl`. The interface is still in its early stages, but already very powerful and easily accessible for anyone (like myself) who is used to building Neural Networks in `Flux.jl`. \n", + "\n", + "In `Flux.jl`, you could build an MLP for this task as follows,\n" + ], + "id": "ee7cd4e3" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "using Flux\n", + "\n", + "mlp = Chain(\n", + " Flux.flatten,\n", + " Dense(prod((28,28)), 32, relu),\n", + " Dense(32, 10)\n", + ")" + ], + "id": "615f0c67", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where `(28,28)` is just the input dimension (28x28 pixel images). Since we have ten digits, our output dimension is ten.^[For a full tutorial on how to build an MNIST image classifier relying solely on `Flux.jl`, check out this [tutorial](https://fluxml.ai/Flux.jl/stable/tutorials/2021-01-26-mlp/).]\n", + "\n", + "We can do the exact same thing in `MLJFlux.jl` as follows,\n" + ], + "id": "af3024e0" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "using MLJFlux\n", + "\n", + "builder = MLJFlux.@builder Chain(\n", + " Flux.flatten,\n", + " Dense(prod(n_in), 32, relu),\n", + " Dense(32, n_out)\n", + ")" + ], + "id": "ade5e902", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where here we rely on the `@builder` macro to make the transition from `Flux.jl` to `MLJ.jl` as seamless as possible. Finally, `MLJFlux.jl` already comes with a number of helper functions to define plain-vanilla networks. In this case, we will use the `ImageClassifier` with our custom builder and cross-entropy loss:\n" + ], + "id": "bc8462c6" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "ImageClassifier = @load ImageClassifier\n", + "clf = ImageClassifier(\n", + " builder=builder,\n", + " epochs=10,\n", + " loss=Flux.crossentropy\n", + ")" + ], + "id": "6a20328e", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The generated instance `clf` is a model (in the `MLJ.jl` sense) so from this point on we can rely on standard `MLJ.jl` workflows. For example, we can wrap our model in data to create a machine and then evaluate it on a holdout set as follows:\n" + ], + "id": "afddd059" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "mach = machine(clf, X, y)\n", + "\n", + "evaluate!(\n", + " mach,\n", + " resampling=Holdout(rng=123, fraction_train=0.8),\n", + " operation=predict_mode,\n", + " measure=[accuracy]\n", + ")" + ], + "id": "b4cda2b2", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The accuracy of our very simple model is not amazing, but good enough for the purpose of this tutorial. For each image, our MLP returns a softmax output for each possible digit: 0,1,2,3,...,9. Since each individual softmax output is valued between zero and one, $y_k\\in(0,1)$, this is commonly interpreted as a probability: $y_k \\coloneqq p(y=k|X)$. Edge cases -- that is values close to either zero or one -- indicate high predictive certainty. But this is only a heuristic notion of predictive uncertainty [@angelopoulos2021gentle]. Next, we will turn this heuristic notion of uncertainty into a rigorous one using Conformal Prediction.\n", + "\n", + "## 🔥 Conformalizing the Network\n", + "\n", + "Since `clf` is a model, it is also compatible with our package: `ConformalPrediction.jl`. To conformalize our MLP, we therefore only need to call `conformal_model(clf)`. Since the generated instance `conf_model` is also just a model, we can still rely on standard `MLJ.jl` workflows. Below we first wrap it in data and then fit it. Aaaand ... we're done! Let's look at the results in the next section.\n" + ], + "id": "89881e01" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "using ConformalPrediction\n", + "conf_model = conformal_model(clf; method=:simple_inductive, coverage=.95)\n", + "mach = machine(conf_model, X, y)\n", + "fit!(mach)" + ], + "id": "504f90e0", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 📊 Results\n" + ], + "id": "bd472b66" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "#| echo: false\n", + "\n", + "using Plots\n", + "using Plots.PlotMeasures\n", + "using StatsBase: sample\n", + "\n", + "cw = [1, 253, 253] |> (x -> x./sum(x))\n", + "function plot_results(mach, X, y; set_size=1, n_samples=3, c_weights=cw, c_inv=0, kwargs...)\n", + "\n", + " # Choose images:\n", + " set_sizes = ConformalPrediction.set_size.(predict(mach, X))\n", + " candidates = findall(set_sizes .== set_size)\n", + " @assert length(candidates) > 0 \"No sets of size $set_size.\"\n", + " chosen = sample(candidates, n_samples, replace=false)\n", + "\n", + " plt_lst = []\n", + " for i in chosen\n", + " ytrue = y[i]\n", + " x = X[i]\n", + " ŷ = predict(mach, x)[1]\n", + " title = join([\"$(Int(key)-1) ($(Int(round(val*100)))%)\" for (key, val) in ŷ.prob_given_ref], \", \")\n", + " title = \"C={$title}\\nytrue=$ytrue\"\n", + " # Colouring:\n", + " x = abs.(c_inv .- (c_weights .* channelview(RGB.(x))))\n", + " prominent_col = median(x, dims=(2,3))\n", + " x = colorview(RGB, eachslice(x, dims=1)...)\n", + " bg_color = RGB(prominent_col...) # most common image colour\n", + " plt = plot(x; axis=([],false), bottom_margin=10mm, bg_color=bg_color, bg_color_inside=bg_color, kwargs...)\n", + " ann_colour = RGB((1 .- prominent_col)...) # opposite of background\n", + " annotate!(plt, (14, 31, (title, 14-set_size), ann_colour))\n", + " push!(plt_lst, plt)\n", + " end\n", + "\n", + " plot(plt_lst..., size=(n_samples*300, 300), layout=(1,n_samples))\n", + "end" + ], + "id": "c541838e", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "@fig-plots below presents the results. @fig-plots-1 displays highly certain predictions, now defined in the rigorous sense of Conformal Prediction: in each case, the conformal set (just beneath the image) includes only one label. \n", + "\n", + "@fig-plots-2 and @fig-plots-3 display increasingly uncertain predictions of set size two and three, respectively. They demonstrate that CP is well equipped to deal with samples characterized by high aleatoric uncertainty: digits four (4), seven (7) and nine (9) share certain similarities. So do digits five (5) and six (6) as well as three (3) and eight (8). These may be hard to distinguish from each other even after seeing many examples (and even for a human). It is therefore unsurprising to see that these digits often end up together in conformal sets. \n" + ], + "id": "9fc928dc" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "#| output: true\n", + "#| label: fig-plots\n", + "#| fig-cap: Conformalized predictions from an image classifier.\n", + "#| fig-subcap:\n", + "#| - Randomly selected prediction sets of size $|C|=1$.\n", + "#| - Randomly selected prediction sets of size $|C|=2$.\n", + "#| - Randomly selected prediction sets of size $|C|=3$.\n", + "#| layout-nrow: 3\n", + "#| echo: false\n", + "\n", + "display(plot_results(mach, X, y; set_size=1))\n", + "display(plot_results(mach, X, y; set_size=2))\n", + "display(plot_results(mach, X, y; set_size=3))" + ], + "id": "fig-plots", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "#| echo: false\n", + "#| output: false\n", + "\n", + "n_total = 10\n", + "\n", + "anim = @animate for i in repeat([1,2,3],n_total)\n", + " plot_results(mach, X, y; set_size=i, n_samples=1, c_weights=rand(3), c_inv=rand([0,1],3))\n", + "end\n", + "gif(anim, joinpath(www_path, \"intro.gif\"), fps=1)\n", + "\n", + "anim = @animate for i in repeat([1,2,3],n_total)\n", + " plot_results(mach, X, y; set_size=i, n_samples=3, c_weights=rand(3), c_inv=rand([0,1],3))\n", + "end\n", + "gif(anim, joinpath(www_path, \"medium.gif\"), fps=1)" + ], + "id": "950d3ae2", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 🧐 Evaluation\n", + "\n", + "To evaluate the performance of conformal models, specific performance measures can be used to assess if the model is correctly specified and well-calibrated [@angelopoulos2021gentle]. We will look at this in some more detail in another post in the future. For now, just be aware that these measures are already available in `ConformalPrediction.jl` and we will briefly showcase them here.\n", + "\n", + "As for many other things, `ConformalPrediction.jl` taps into the existing functionality of `MLJ.jl` for model evaluation. In particular, we will see below how we can use the generic `evaluate!` method on our machine. To assess the correctness of our conformal predictor, we can compute the empirical coverage rate using the custom performance measure `emp_coverage`. With respect to model calibration we will look at the model's conditional coverage. For adaptive, well-calibrated conformal models, conditional coverage is high. One general go-to measure for assessing conditional coverage is size-stratified coverage. The custom measure for this purpose is just called `size_stratified_coverage`, aliased by `ssc`. \n", + "\n", + "The code below implements the model evaluation using cross-validation. The Simple Inductive Classifier that we used above is not adaptive and hence the attained conditional coverage is low compared to the overall empirical coverage, which is close to $0.95$, so in line with the desired coverage rate specified above.\n" + ], + "id": "a6a420b1" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "#| output: true\n", + "\n", + "_eval = evaluate!(\n", + " mach,\n", + " resampling=CV(),\n", + " operation=predict,\n", + " measure=[emp_coverage, ssc]\n", + ")\n", + "display(_eval)\n", + "println(\"Empirical coverage: $(round(_eval.measurement[1], digits=3))\")\n", + "println(\"SSC: $(round(_eval.measurement[2], digits=3))\")" + ], + "id": "e1d41fd0", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "#| echo: false\n", + "\n", + "results = Dict{Symbol,Any}(:simple_inductive => mach) # store results" + ], + "id": "19bbb6e0", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can attain higher adaptivity (SSC) when using adaptive prediction sets:\n" + ], + "id": "20b1056b" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "#| output: true\n", + "\n", + "conf_model = conformal_model(clf; method=:adaptive_inductive, coverage=.95)\n", + "mach = machine(conf_model, X, y)\n", + "fit!(mach)\n", + "_eval = evaluate!(\n", + " mach,\n", + " resampling=CV(),\n", + " operation=predict,\n", + " measure=[emp_coverage, ssc]\n", + ")\n", + "results[:adaptive_inductive] = mach\n", + "display(_eval)\n", + "println(\"Empirical coverage: $(round(_eval.measurement[1], digits=3))\")\n", + "println(\"SSC: $(round(_eval.measurement[2], digits=3))\")" + ], + "id": "9f6e5bf0", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can also have a look at the resulting set size for both approaches using a custom `Plots.jl` recipe (fig-setsize). In line with the above, the spread is wider for the adaptive approach, which reflects that \"the procedure is effectively distinguishing between easy and hard inputs\" [@angelopoulos2021gentle].\n" + ], + "id": "d905f996" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "#| output: true\n", + "#| label: fig-setsize\n", + "#| fig-cap: Distribution of set sizes for both approaches.\n", + "\n", + "plt_list = []\n", + "for (_mod, mach) in results\n", + " push!(plt_list, bar(mach.model, mach.fitresult, X; title=String(_mod)))\n", + "end\n", + "plot(plt_list..., size=(800,300))\n", + "plot(plt_list..., size=(800,300),bg_colour=:transparent)" + ], + "id": "fig-setsize", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 🔁 Recap\n", + "\n", + "In this short guide, we have seen how easy it is to conformalize a deep learning image classifier in Julia using `ConformalPrediction.jl`. Almost any deep neural network trained in `Flux.jl` is compatible with `MLJ.jl` and can therefore be conformalized in just a few lines of code. This makes it remarkably easy to move uncertainty heuristics to rigorous predictive uncertainty estimates. We have also seen a sneak peek at the performance evaluation of conformal predictors. Stay tuned for more!\n", + "\n", + "## 🎓 References" + ], + "id": "a32d5bcb" + } + ], + "metadata": { + "kernelspec": { + "name": "julia-1.10", + "language": "julia", + "display_name": "Julia 1.10.4", + "path": "/home/jorge/.local/share/jupyter/kernels/julia-1.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} \ No newline at end of file diff --git a/profile/blog/posts/guest-students-laplace/index.html b/profile/blog/posts/guest-students-laplace/index.html new file mode 100644 index 0000000..bf011ea --- /dev/null +++ b/profile/blog/posts/guest-students-laplace/index.html @@ -0,0 +1,691 @@ + + + + + + + + + + + + + + + + + +Paving the Way Towards Low-Overhead Uncertainty Calibration + + + + + + + + + + + + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/profile/blog/posts/guest-students-laplace/index_files/libs/bootstrap/bootstrap-icons.css b/profile/blog/posts/guest-students-laplace/index_files/libs/bootstrap/bootstrap-icons.css new file mode 100644 index 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#fdfeff;--bs-navbar-nav-link-padding-x: 0.5rem;--bs-navbar-toggler-padding-y: 0.25;--bs-navbar-toggler-padding-x: 0;--bs-navbar-toggler-font-size: 1.25rem;--bs-navbar-toggler-icon-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 30 30'%3e%3cpath stroke='%23fdfefe' stroke-linecap='round' stroke-miterlimit='10' stroke-width='2' d='M4 7h22M4 15h22M4 23h22'/%3e%3c/svg%3e");--bs-navbar-toggler-border-color: rgba(253, 254, 254, 0);--bs-navbar-toggler-border-radius: 0.375rem;--bs-navbar-toggler-focus-width: 0.25rem;--bs-navbar-toggler-transition: box-shadow 0.15s ease-in-out;position:relative;display:flex;display:-webkit-flex;flex-wrap:wrap;-webkit-flex-wrap:wrap;align-items:center;-webkit-align-items:center;justify-content:space-between;-webkit-justify-content:space-between;padding:var(--bs-navbar-padding-y) 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992px){.navbar-expand-lg{flex-wrap:nowrap;-webkit-flex-wrap:nowrap;justify-content:flex-start;-webkit-justify-content:flex-start}.navbar-expand-lg .navbar-nav{flex-direction:row;-webkit-flex-direction:row}.navbar-expand-lg .navbar-nav .dropdown-menu{position:absolute}.navbar-expand-lg .navbar-nav .nav-link{padding-right:var(--bs-navbar-nav-link-padding-x);padding-left:var(--bs-navbar-nav-link-padding-x)}.navbar-expand-lg .navbar-nav-scroll{overflow:visible}.navbar-expand-lg .navbar-collapse{display:flex !important;display:-webkit-flex !important;flex-basis:auto;-webkit-flex-basis:auto}.navbar-expand-lg .navbar-toggler{display:none}.navbar-expand-lg .offcanvas{position:static;z-index:auto;flex-grow:1;-webkit-flex-grow:1;width:auto !important;height:auto !important;visibility:visible !important;background-color:rgba(0,0,0,0) !important;border:0 !important;transform:none !important;transition:none}.navbar-expand-lg .offcanvas .offcanvas-header{display:none}.navbar-expand-lg .offcanvas 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.offcanvas{position:static;z-index:auto;flex-grow:1;-webkit-flex-grow:1;width:auto !important;height:auto !important;visibility:visible !important;background-color:rgba(0,0,0,0) !important;border:0 !important;transform:none !important;transition:none}.navbar-expand-xxl .offcanvas .offcanvas-header{display:none}.navbar-expand-xxl .offcanvas .offcanvas-body{display:flex;display:-webkit-flex;flex-grow:0;-webkit-flex-grow:0;padding:0;overflow-y:visible}}.navbar-expand{flex-wrap:nowrap;-webkit-flex-wrap:nowrap;justify-content:flex-start;-webkit-justify-content:flex-start}.navbar-expand .navbar-nav{flex-direction:row;-webkit-flex-direction:row}.navbar-expand .navbar-nav .dropdown-menu{position:absolute}.navbar-expand .navbar-nav .nav-link{padding-right:var(--bs-navbar-nav-link-padding-x);padding-left:var(--bs-navbar-nav-link-padding-x)}.navbar-expand .navbar-nav-scroll{overflow:visible}.navbar-expand .navbar-collapse{display:flex !important;display:-webkit-flex 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var(--bs-accordion-border-color)}.accordion-item:first-of-type{border-top-left-radius:var(--bs-accordion-border-radius);border-top-right-radius:var(--bs-accordion-border-radius)}.accordion-item:first-of-type .accordion-button{border-top-left-radius:var(--bs-accordion-inner-border-radius);border-top-right-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:not(:first-of-type){border-top:0}.accordion-item:last-of-type{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-item:last-of-type .accordion-button.collapsed{border-bottom-right-radius:var(--bs-accordion-inner-border-radius);border-bottom-left-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:last-of-type .accordion-collapse{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-body{padding:var(--bs-accordion-body-padding-y) var(--bs-accordion-body-padding-x)}.accordion-flush .accordion-collapse{border-width:0}.accordion-flush .accordion-item{border-right:0;border-left:0;border-radius:0}.accordion-flush .accordion-item:first-child{border-top:0}.accordion-flush .accordion-item:last-child{border-bottom:0}.accordion-flush .accordion-item .accordion-button,.accordion-flush .accordion-item .accordion-button.collapsed{border-radius:0}[data-bs-theme=dark] .accordion-button::after{--bs-accordion-btn-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%236ea8fe'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-active-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%236ea8fe'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e")}.breadcrumb{--bs-breadcrumb-padding-x: 0;--bs-breadcrumb-padding-y: 0;--bs-breadcrumb-margin-bottom: 1rem;--bs-breadcrumb-bg: ;--bs-breadcrumb-border-radius: ;--bs-breadcrumb-divider-color: rgba(33, 37, 41, 0.75);--bs-breadcrumb-item-padding-x: 0.5rem;--bs-breadcrumb-item-active-color: rgba(33, 37, 41, 0.75);display:flex;display:-webkit-flex;flex-wrap:wrap;-webkit-flex-wrap:wrap;padding:var(--bs-breadcrumb-padding-y) var(--bs-breadcrumb-padding-x);margin-bottom:var(--bs-breadcrumb-margin-bottom);font-size:var(--bs-breadcrumb-font-size);list-style:none;background-color:var(--bs-breadcrumb-bg);border-radius:var(--bs-breadcrumb-border-radius)}.breadcrumb-item+.breadcrumb-item{padding-left:var(--bs-breadcrumb-item-padding-x)}.breadcrumb-item+.breadcrumb-item::before{float:left;padding-right:var(--bs-breadcrumb-item-padding-x);color:var(--bs-breadcrumb-divider-color);content:var(--bs-breadcrumb-divider, ">") /* rtl: var(--bs-breadcrumb-divider, ">") */}.breadcrumb-item.active{color:var(--bs-breadcrumb-item-active-color)}.pagination{--bs-pagination-padding-x: 0.75rem;--bs-pagination-padding-y: 0.375rem;--bs-pagination-font-size:1rem;--bs-pagination-color: #0d6efd;--bs-pagination-bg: #ffffff;--bs-pagination-border-width: 1px;--bs-pagination-border-color: #dee2e6;--bs-pagination-border-radius: 0.375rem;--bs-pagination-hover-color: #0a58ca;--bs-pagination-hover-bg: #f8f9fa;--bs-pagination-hover-border-color: #dee2e6;--bs-pagination-focus-color: #0a58ca;--bs-pagination-focus-bg: #e9ecef;--bs-pagination-focus-box-shadow: 0 0 0 0.25rem rgba(13, 110, 253, 0.25);--bs-pagination-active-color: #ffffff;--bs-pagination-active-bg: #0d6efd;--bs-pagination-active-border-color: #0d6efd;--bs-pagination-disabled-color: rgba(33, 37, 41, 0.75);--bs-pagination-disabled-bg: #e9ecef;--bs-pagination-disabled-border-color: #dee2e6;display:flex;display:-webkit-flex;padding-left:0;list-style:none}.page-link{position:relative;display:block;padding:var(--bs-pagination-padding-y) var(--bs-pagination-padding-x);font-size:var(--bs-pagination-font-size);color:var(--bs-pagination-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-pagination-bg);border:var(--bs-pagination-border-width) solid var(--bs-pagination-border-color);transition:color .15s ease-in-out,background-color .15s ease-in-out,border-color .15s ease-in-out,box-shadow .15s ease-in-out}@media(prefers-reduced-motion: reduce){.page-link{transition:none}}.page-link:hover{z-index:2;color:var(--bs-pagination-hover-color);background-color:var(--bs-pagination-hover-bg);border-color:var(--bs-pagination-hover-border-color)}.page-link:focus{z-index:3;color:var(--bs-pagination-focus-color);background-color:var(--bs-pagination-focus-bg);outline:0;box-shadow:var(--bs-pagination-focus-box-shadow)}.page-link.active,.active>.page-link{z-index:3;color:var(--bs-pagination-active-color);background-color:var(--bs-pagination-active-bg);border-color:var(--bs-pagination-active-border-color)}.page-link.disabled,.disabled>.page-link{color:var(--bs-pagination-disabled-color);pointer-events:none;background-color:var(--bs-pagination-disabled-bg);border-color:var(--bs-pagination-disabled-border-color)}.page-item:not(:first-child) .page-link{margin-left:calc(1px*-1)}.page-item:first-child .page-link{border-top-left-radius:var(--bs-pagination-border-radius);border-bottom-left-radius:var(--bs-pagination-border-radius)}.page-item:last-child .page-link{border-top-right-radius:var(--bs-pagination-border-radius);border-bottom-right-radius:var(--bs-pagination-border-radius)}.pagination-lg{--bs-pagination-padding-x: 1.5rem;--bs-pagination-padding-y: 0.75rem;--bs-pagination-font-size:1.25rem;--bs-pagination-border-radius: 0.5rem}.pagination-sm{--bs-pagination-padding-x: 0.5rem;--bs-pagination-padding-y: 0.25rem;--bs-pagination-font-size:0.875rem;--bs-pagination-border-radius: 0.25rem}.badge{--bs-badge-padding-x: 0.65em;--bs-badge-padding-y: 0.35em;--bs-badge-font-size:0.75em;--bs-badge-font-weight: 700;--bs-badge-color: #ffffff;--bs-badge-border-radius: 0.375rem;display:inline-block;padding:var(--bs-badge-padding-y) var(--bs-badge-padding-x);font-size:var(--bs-badge-font-size);font-weight:var(--bs-badge-font-weight);line-height:1;color:var(--bs-badge-color);text-align:center;white-space:nowrap;vertical-align:baseline;border-radius:var(--bs-badge-border-radius)}.badge:empty{display:none}.btn .badge{position:relative;top:-1px}.alert{--bs-alert-bg: transparent;--bs-alert-padding-x: 1rem;--bs-alert-padding-y: 1rem;--bs-alert-margin-bottom: 1rem;--bs-alert-color: inherit;--bs-alert-border-color: transparent;--bs-alert-border: 1px solid var(--bs-alert-border-color);--bs-alert-border-radius: 0.375rem;--bs-alert-link-color: inherit;position:relative;padding:var(--bs-alert-padding-y) var(--bs-alert-padding-x);margin-bottom:var(--bs-alert-margin-bottom);color:var(--bs-alert-color);background-color:var(--bs-alert-bg);border:var(--bs-alert-border);border-radius:var(--bs-alert-border-radius)}.alert-heading{color:inherit}.alert-link{font-weight:700;color:var(--bs-alert-link-color)}.alert-dismissible{padding-right:3rem}.alert-dismissible .btn-close{position:absolute;top:0;right:0;z-index:2;padding:1.25rem 1rem}.alert-default{--bs-alert-color: var(--bs-default-text-emphasis);--bs-alert-bg: var(--bs-default-bg-subtle);--bs-alert-border-color: var(--bs-default-border-subtle);--bs-alert-link-color: var(--bs-default-text-emphasis)}.alert-primary{--bs-alert-color: var(--bs-primary-text-emphasis);--bs-alert-bg: var(--bs-primary-bg-subtle);--bs-alert-border-color: var(--bs-primary-border-subtle);--bs-alert-link-color: var(--bs-primary-text-emphasis)}.alert-secondary{--bs-alert-color: var(--bs-secondary-text-emphasis);--bs-alert-bg: var(--bs-secondary-bg-subtle);--bs-alert-border-color: var(--bs-secondary-border-subtle);--bs-alert-link-color: var(--bs-secondary-text-emphasis)}.alert-success{--bs-alert-color: var(--bs-success-text-emphasis);--bs-alert-bg: var(--bs-success-bg-subtle);--bs-alert-border-color: var(--bs-success-border-subtle);--bs-alert-link-color: var(--bs-success-text-emphasis)}.alert-info{--bs-alert-color: var(--bs-info-text-emphasis);--bs-alert-bg: var(--bs-info-bg-subtle);--bs-alert-border-color: var(--bs-info-border-subtle);--bs-alert-link-color: var(--bs-info-text-emphasis)}.alert-warning{--bs-alert-color: var(--bs-warning-text-emphasis);--bs-alert-bg: var(--bs-warning-bg-subtle);--bs-alert-border-color: var(--bs-warning-border-subtle);--bs-alert-link-color: var(--bs-warning-text-emphasis)}.alert-danger{--bs-alert-color: var(--bs-danger-text-emphasis);--bs-alert-bg: var(--bs-danger-bg-subtle);--bs-alert-border-color: var(--bs-danger-border-subtle);--bs-alert-link-color: var(--bs-danger-text-emphasis)}.alert-light{--bs-alert-color: var(--bs-light-text-emphasis);--bs-alert-bg: var(--bs-light-bg-subtle);--bs-alert-border-color: var(--bs-light-border-subtle);--bs-alert-link-color: var(--bs-light-text-emphasis)}.alert-dark{--bs-alert-color: var(--bs-dark-text-emphasis);--bs-alert-bg: var(--bs-dark-bg-subtle);--bs-alert-border-color: var(--bs-dark-border-subtle);--bs-alert-link-color: var(--bs-dark-text-emphasis)}@keyframes progress-bar-stripes{0%{background-position-x:1rem}}.progress,.progress-stacked{--bs-progress-height: 1rem;--bs-progress-font-size:0.75rem;--bs-progress-bg: #e9ecef;--bs-progress-border-radius: 0.375rem;--bs-progress-box-shadow: inset 0 1px 2px rgba(0, 0, 0, 0.075);--bs-progress-bar-color: #ffffff;--bs-progress-bar-bg: #0d6efd;--bs-progress-bar-transition: width 0.6s ease;display:flex;display:-webkit-flex;height:var(--bs-progress-height);overflow:hidden;font-size:var(--bs-progress-font-size);background-color:var(--bs-progress-bg);border-radius:var(--bs-progress-border-radius)}.progress-bar{display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;justify-content:center;-webkit-justify-content:center;overflow:hidden;color:var(--bs-progress-bar-color);text-align:center;white-space:nowrap;background-color:var(--bs-progress-bar-bg);transition:var(--bs-progress-bar-transition)}@media(prefers-reduced-motion: reduce){.progress-bar{transition:none}}.progress-bar-striped{background-image:linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);background-size:var(--bs-progress-height) var(--bs-progress-height)}.progress-stacked>.progress{overflow:visible}.progress-stacked>.progress>.progress-bar{width:100%}.progress-bar-animated{animation:1s linear infinite progress-bar-stripes}@media(prefers-reduced-motion: reduce){.progress-bar-animated{animation:none}}.list-group{--bs-list-group-color: #212529;--bs-list-group-bg: #ffffff;--bs-list-group-border-color: #dee2e6;--bs-list-group-border-width: 1px;--bs-list-group-border-radius: 0.375rem;--bs-list-group-item-padding-x: 1rem;--bs-list-group-item-padding-y: 0.5rem;--bs-list-group-action-color: rgba(33, 37, 41, 0.75);--bs-list-group-action-hover-color: #000;--bs-list-group-action-hover-bg: #f8f9fa;--bs-list-group-action-active-color: #212529;--bs-list-group-action-active-bg: #e9ecef;--bs-list-group-disabled-color: rgba(33, 37, 41, 0.75);--bs-list-group-disabled-bg: #ffffff;--bs-list-group-active-color: #ffffff;--bs-list-group-active-bg: #0d6efd;--bs-list-group-active-border-color: #0d6efd;display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;padding-left:0;margin-bottom:0;border-radius:var(--bs-list-group-border-radius)}.list-group-numbered{list-style-type:none;counter-reset:section}.list-group-numbered>.list-group-item::before{content:counters(section, ".") ". ";counter-increment:section}.list-group-item-action{width:100%;color:var(--bs-list-group-action-color);text-align:inherit}.list-group-item-action:hover,.list-group-item-action:focus{z-index:1;color:var(--bs-list-group-action-hover-color);text-decoration:none;background-color:var(--bs-list-group-action-hover-bg)}.list-group-item-action:active{color:var(--bs-list-group-action-active-color);background-color:var(--bs-list-group-action-active-bg)}.list-group-item{position:relative;display:block;padding:var(--bs-list-group-item-padding-y) var(--bs-list-group-item-padding-x);color:var(--bs-list-group-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-list-group-bg);border:var(--bs-list-group-border-width) solid var(--bs-list-group-border-color)}.list-group-item:first-child{border-top-left-radius:inherit;border-top-right-radius:inherit}.list-group-item:last-child{border-bottom-right-radius:inherit;border-bottom-left-radius:inherit}.list-group-item.disabled,.list-group-item:disabled{color:var(--bs-list-group-disabled-color);pointer-events:none;background-color:var(--bs-list-group-disabled-bg)}.list-group-item.active{z-index:2;color:var(--bs-list-group-active-color);background-color:var(--bs-list-group-active-bg);border-color:var(--bs-list-group-active-border-color)}.list-group-item+.list-group-item{border-top-width:0}.list-group-item+.list-group-item.active{margin-top:calc(-1*var(--bs-list-group-border-width));border-top-width:var(--bs-list-group-border-width)}.list-group-horizontal{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal>.list-group-item.active{margin-top:0}.list-group-horizontal>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}@media(min-width: 576px){.list-group-horizontal-sm{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-sm>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-sm>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-sm>.list-group-item.active{margin-top:0}.list-group-horizontal-sm>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-sm>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 768px){.list-group-horizontal-md{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-md>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-md>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-md>.list-group-item.active{margin-top:0}.list-group-horizontal-md>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-md>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 992px){.list-group-horizontal-lg{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-lg>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-lg>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-lg>.list-group-item.active{margin-top:0}.list-group-horizontal-lg>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-lg>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 1200px){.list-group-horizontal-xl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xl>.list-group-item.active{margin-top:0}.list-group-horizontal-xl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xl>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 1400px){.list-group-horizontal-xxl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xxl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xxl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xxl>.list-group-item.active{margin-top:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}.list-group-flush{border-radius:0}.list-group-flush>.list-group-item{border-width:0 0 var(--bs-list-group-border-width)}.list-group-flush>.list-group-item:last-child{border-bottom-width:0}.list-group-item-default{--bs-list-group-color: var(--bs-default-text-emphasis);--bs-list-group-bg: var(--bs-default-bg-subtle);--bs-list-group-border-color: var(--bs-default-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-default-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-default-border-subtle);--bs-list-group-active-color: var(--bs-default-bg-subtle);--bs-list-group-active-bg: var(--bs-default-text-emphasis);--bs-list-group-active-border-color: var(--bs-default-text-emphasis)}.list-group-item-primary{--bs-list-group-color: var(--bs-primary-text-emphasis);--bs-list-group-bg: var(--bs-primary-bg-subtle);--bs-list-group-border-color: var(--bs-primary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-primary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-primary-border-subtle);--bs-list-group-active-color: var(--bs-primary-bg-subtle);--bs-list-group-active-bg: var(--bs-primary-text-emphasis);--bs-list-group-active-border-color: var(--bs-primary-text-emphasis)}.list-group-item-secondary{--bs-list-group-color: var(--bs-secondary-text-emphasis);--bs-list-group-bg: var(--bs-secondary-bg-subtle);--bs-list-group-border-color: var(--bs-secondary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-secondary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-secondary-border-subtle);--bs-list-group-active-color: var(--bs-secondary-bg-subtle);--bs-list-group-active-bg: var(--bs-secondary-text-emphasis);--bs-list-group-active-border-color: var(--bs-secondary-text-emphasis)}.list-group-item-success{--bs-list-group-color: var(--bs-success-text-emphasis);--bs-list-group-bg: var(--bs-success-bg-subtle);--bs-list-group-border-color: var(--bs-success-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-success-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-success-border-subtle);--bs-list-group-active-color: var(--bs-success-bg-subtle);--bs-list-group-active-bg: var(--bs-success-text-emphasis);--bs-list-group-active-border-color: var(--bs-success-text-emphasis)}.list-group-item-info{--bs-list-group-color: var(--bs-info-text-emphasis);--bs-list-group-bg: var(--bs-info-bg-subtle);--bs-list-group-border-color: var(--bs-info-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-info-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-info-border-subtle);--bs-list-group-active-color: var(--bs-info-bg-subtle);--bs-list-group-active-bg: var(--bs-info-text-emphasis);--bs-list-group-active-border-color: var(--bs-info-text-emphasis)}.list-group-item-warning{--bs-list-group-color: var(--bs-warning-text-emphasis);--bs-list-group-bg: var(--bs-warning-bg-subtle);--bs-list-group-border-color: var(--bs-warning-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-warning-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-warning-border-subtle);--bs-list-group-active-color: var(--bs-warning-bg-subtle);--bs-list-group-active-bg: var(--bs-warning-text-emphasis);--bs-list-group-active-border-color: var(--bs-warning-text-emphasis)}.list-group-item-danger{--bs-list-group-color: var(--bs-danger-text-emphasis);--bs-list-group-bg: var(--bs-danger-bg-subtle);--bs-list-group-border-color: var(--bs-danger-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-danger-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-danger-border-subtle);--bs-list-group-active-color: var(--bs-danger-bg-subtle);--bs-list-group-active-bg: var(--bs-danger-text-emphasis);--bs-list-group-active-border-color: var(--bs-danger-text-emphasis)}.list-group-item-light{--bs-list-group-color: var(--bs-light-text-emphasis);--bs-list-group-bg: var(--bs-light-bg-subtle);--bs-list-group-border-color: var(--bs-light-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-light-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-light-border-subtle);--bs-list-group-active-color: var(--bs-light-bg-subtle);--bs-list-group-active-bg: var(--bs-light-text-emphasis);--bs-list-group-active-border-color: var(--bs-light-text-emphasis)}.list-group-item-dark{--bs-list-group-color: var(--bs-dark-text-emphasis);--bs-list-group-bg: var(--bs-dark-bg-subtle);--bs-list-group-border-color: var(--bs-dark-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-dark-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-dark-border-subtle);--bs-list-group-active-color: var(--bs-dark-bg-subtle);--bs-list-group-active-bg: var(--bs-dark-text-emphasis);--bs-list-group-active-border-color: var(--bs-dark-text-emphasis)}.btn-close{--bs-btn-close-color: #000;--bs-btn-close-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%23000'%3e%3cpath d='M.293.293a1 1 0 0 1 1.414 0L8 6.586 14.293.293a1 1 0 1 1 1.414 1.414L9.414 8l6.293 6.293a1 1 0 0 1-1.414 1.414L8 9.414l-6.293 6.293a1 1 0 0 1-1.414-1.414L6.586 8 .293 1.707a1 1 0 0 1 0-1.414z'/%3e%3c/svg%3e");--bs-btn-close-opacity: 0.5;--bs-btn-close-hover-opacity: 0.75;--bs-btn-close-focus-shadow: 0 0 0 0.25rem rgba(13, 110, 253, 0.25);--bs-btn-close-focus-opacity: 1;--bs-btn-close-disabled-opacity: 0.25;--bs-btn-close-white-filter: invert(1) grayscale(100%) brightness(200%);box-sizing:content-box;width:1em;height:1em;padding:.25em .25em;color:var(--bs-btn-close-color);background:rgba(0,0,0,0) var(--bs-btn-close-bg) center/1em auto no-repeat;border:0;border-radius:.375rem;opacity:var(--bs-btn-close-opacity)}.btn-close:hover{color:var(--bs-btn-close-color);text-decoration:none;opacity:var(--bs-btn-close-hover-opacity)}.btn-close:focus{outline:0;box-shadow:var(--bs-btn-close-focus-shadow);opacity:var(--bs-btn-close-focus-opacity)}.btn-close:disabled,.btn-close.disabled{pointer-events:none;user-select:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;-o-user-select:none;opacity:var(--bs-btn-close-disabled-opacity)}.btn-close-white{filter:var(--bs-btn-close-white-filter)}[data-bs-theme=dark] .btn-close{filter:var(--bs-btn-close-white-filter)}.toast{--bs-toast-zindex: 1090;--bs-toast-padding-x: 0.75rem;--bs-toast-padding-y: 0.5rem;--bs-toast-spacing: 1.5rem;--bs-toast-max-width: 350px;--bs-toast-font-size:0.875rem;--bs-toast-color: ;--bs-toast-bg: rgba(255, 255, 255, 0.85);--bs-toast-border-width: 1px;--bs-toast-border-color: rgba(0, 0, 0, 0.175);--bs-toast-border-radius: 0.375rem;--bs-toast-box-shadow: 0 0.5rem 1rem rgba(0, 0, 0, 0.15);--bs-toast-header-color: rgba(33, 37, 41, 0.75);--bs-toast-header-bg: rgba(255, 255, 255, 0.85);--bs-toast-header-border-color: rgba(0, 0, 0, 0.175);width:var(--bs-toast-max-width);max-width:100%;font-size:var(--bs-toast-font-size);color:var(--bs-toast-color);pointer-events:auto;background-color:var(--bs-toast-bg);background-clip:padding-box;border:var(--bs-toast-border-width) solid var(--bs-toast-border-color);box-shadow:var(--bs-toast-box-shadow);border-radius:var(--bs-toast-border-radius)}.toast.showing{opacity:0}.toast:not(.show){display:none}.toast-container{--bs-toast-zindex: 1090;position:absolute;z-index:var(--bs-toast-zindex);width:max-content;width:-webkit-max-content;width:-moz-max-content;width:-ms-max-content;width:-o-max-content;max-width:100%;pointer-events:none}.toast-container>:not(:last-child){margin-bottom:var(--bs-toast-spacing)}.toast-header{display:flex;display:-webkit-flex;align-items:center;-webkit-align-items:center;padding:var(--bs-toast-padding-y) var(--bs-toast-padding-x);color:var(--bs-toast-header-color);background-color:var(--bs-toast-header-bg);background-clip:padding-box;border-bottom:var(--bs-toast-border-width) solid var(--bs-toast-header-border-color);border-top-left-radius:calc(var(--bs-toast-border-radius) - var(--bs-toast-border-width));border-top-right-radius:calc(var(--bs-toast-border-radius) - var(--bs-toast-border-width))}.toast-header .btn-close{margin-right:calc(-0.5*var(--bs-toast-padding-x));margin-left:var(--bs-toast-padding-x)}.toast-body{padding:var(--bs-toast-padding-x);word-wrap:break-word}.modal{--bs-modal-zindex: 1055;--bs-modal-width: 500px;--bs-modal-padding: 1rem;--bs-modal-margin: 0.5rem;--bs-modal-color: ;--bs-modal-bg: #ffffff;--bs-modal-border-color: rgba(0, 0, 0, 0.175);--bs-modal-border-width: 1px;--bs-modal-border-radius: 0.5rem;--bs-modal-box-shadow: 0 0.125rem 0.25rem rgba(0, 0, 0, 0.075);--bs-modal-inner-border-radius: calc(0.5rem - 1px);--bs-modal-header-padding-x: 1rem;--bs-modal-header-padding-y: 1rem;--bs-modal-header-padding: 1rem 1rem;--bs-modal-header-border-color: #dee2e6;--bs-modal-header-border-width: 1px;--bs-modal-title-line-height: 1.5;--bs-modal-footer-gap: 0.5rem;--bs-modal-footer-bg: ;--bs-modal-footer-border-color: #dee2e6;--bs-modal-footer-border-width: 1px;position:fixed;top:0;left:0;z-index:var(--bs-modal-zindex);display:none;width:100%;height:100%;overflow-x:hidden;overflow-y:auto;outline:0}.modal-dialog{position:relative;width:auto;margin:var(--bs-modal-margin);pointer-events:none}.modal.fade .modal-dialog{transition:transform .3s ease-out;transform:translate(0, -50px)}@media(prefers-reduced-motion: reduce){.modal.fade .modal-dialog{transition:none}}.modal.show .modal-dialog{transform:none}.modal.modal-static .modal-dialog{transform:scale(1.02)}.modal-dialog-scrollable{height:calc(100% - var(--bs-modal-margin)*2)}.modal-dialog-scrollable .modal-content{max-height:100%;overflow:hidden}.modal-dialog-scrollable .modal-body{overflow-y:auto}.modal-dialog-centered{display:flex;display:-webkit-flex;align-items:center;-webkit-align-items:center;min-height:calc(100% - var(--bs-modal-margin)*2)}.modal-content{position:relative;display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;width:100%;color:var(--bs-modal-color);pointer-events:auto;background-color:var(--bs-modal-bg);background-clip:padding-box;border:var(--bs-modal-border-width) solid var(--bs-modal-border-color);border-radius:var(--bs-modal-border-radius);outline:0}.modal-backdrop{--bs-backdrop-zindex: 1050;--bs-backdrop-bg: #000;--bs-backdrop-opacity: 0.5;position:fixed;top:0;left:0;z-index:var(--bs-backdrop-zindex);width:100vw;height:100vh;background-color:var(--bs-backdrop-bg)}.modal-backdrop.fade{opacity:0}.modal-backdrop.show{opacity:var(--bs-backdrop-opacity)}.modal-header{display:flex;display:-webkit-flex;flex-shrink:0;-webkit-flex-shrink:0;align-items:center;-webkit-align-items:center;justify-content:space-between;-webkit-justify-content:space-between;padding:var(--bs-modal-header-padding);border-bottom:var(--bs-modal-header-border-width) solid var(--bs-modal-header-border-color);border-top-left-radius:var(--bs-modal-inner-border-radius);border-top-right-radius:var(--bs-modal-inner-border-radius)}.modal-header .btn-close{padding:calc(var(--bs-modal-header-padding-y)*.5) calc(var(--bs-modal-header-padding-x)*.5);margin:calc(-0.5*var(--bs-modal-header-padding-y)) calc(-0.5*var(--bs-modal-header-padding-x)) calc(-0.5*var(--bs-modal-header-padding-y)) auto}.modal-title{margin-bottom:0;line-height:var(--bs-modal-title-line-height)}.modal-body{position:relative;flex:1 1 auto;-webkit-flex:1 1 auto;padding:var(--bs-modal-padding)}.modal-footer{display:flex;display:-webkit-flex;flex-shrink:0;-webkit-flex-shrink:0;flex-wrap:wrap;-webkit-flex-wrap:wrap;align-items:center;-webkit-align-items:center;justify-content:flex-end;-webkit-justify-content:flex-end;padding:calc(var(--bs-modal-padding) - var(--bs-modal-footer-gap)*.5);background-color:var(--bs-modal-footer-bg);border-top:var(--bs-modal-footer-border-width) solid var(--bs-modal-footer-border-color);border-bottom-right-radius:var(--bs-modal-inner-border-radius);border-bottom-left-radius:var(--bs-modal-inner-border-radius)}.modal-footer>*{margin:calc(var(--bs-modal-footer-gap)*.5)}@media(min-width: 576px){.modal{--bs-modal-margin: 1.75rem;--bs-modal-box-shadow: 0 0.5rem 1rem rgba(0, 0, 0, 0.15)}.modal-dialog{max-width:var(--bs-modal-width);margin-right:auto;margin-left:auto}.modal-sm{--bs-modal-width: 300px}}@media(min-width: 992px){.modal-lg,.modal-xl{--bs-modal-width: 800px}}@media(min-width: 1200px){.modal-xl{--bs-modal-width: 1140px}}.modal-fullscreen{width:100vw;max-width:none;height:100%;margin:0}.modal-fullscreen .modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen .modal-header,.modal-fullscreen .modal-footer{border-radius:0}.modal-fullscreen .modal-body{overflow-y:auto}@media(max-width: 575.98px){.modal-fullscreen-sm-down{width:100vw;max-width:none;height:100%;margin:0}.modal-fullscreen-sm-down .modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen-sm-down .modal-header,.modal-fullscreen-sm-down .modal-footer{border-radius:0}.modal-fullscreen-sm-down .modal-body{overflow-y:auto}}@media(max-width: 767.98px){.modal-fullscreen-md-down{width:100vw;max-width:none;height:100%;margin:0}.modal-fullscreen-md-down .modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen-md-down .modal-header,.modal-fullscreen-md-down .modal-footer{border-radius:0}.modal-fullscreen-md-down .modal-body{overflow-y:auto}}@media(max-width: 991.98px){.modal-fullscreen-lg-down{width:100vw;max-width:none;height:100%;margin:0}.modal-fullscreen-lg-down .modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen-lg-down .modal-header,.modal-fullscreen-lg-down .modal-footer{border-radius:0}.modal-fullscreen-lg-down .modal-body{overflow-y:auto}}@media(max-width: 1199.98px){.modal-fullscreen-xl-down{width:100vw;max-width:none;height:100%;margin:0}.modal-fullscreen-xl-down .modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen-xl-down .modal-header,.modal-fullscreen-xl-down .modal-footer{border-radius:0}.modal-fullscreen-xl-down .modal-body{overflow-y:auto}}@media(max-width: 1399.98px){.modal-fullscreen-xxl-down{width:100vw;max-width:none;height:100%;margin:0}.modal-fullscreen-xxl-down .modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen-xxl-down .modal-header,.modal-fullscreen-xxl-down .modal-footer{border-radius:0}.modal-fullscreen-xxl-down .modal-body{overflow-y:auto}}.tooltip{--bs-tooltip-zindex: 1080;--bs-tooltip-max-width: 200px;--bs-tooltip-padding-x: 0.5rem;--bs-tooltip-padding-y: 0.25rem;--bs-tooltip-margin: ;--bs-tooltip-font-size:0.875rem;--bs-tooltip-color: #ffffff;--bs-tooltip-bg: #000;--bs-tooltip-border-radius: 0.375rem;--bs-tooltip-opacity: 0.9;--bs-tooltip-arrow-width: 0.8rem;--bs-tooltip-arrow-height: 0.4rem;z-index:var(--bs-tooltip-zindex);display:block;margin:var(--bs-tooltip-margin);font-family:system-ui,-apple-system,"Segoe UI",Roboto,"Helvetica Neue","Noto Sans","Liberation Sans",Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol","Noto Color Emoji";font-style:normal;font-weight:400;line-height:1.5;text-align:left;text-align:start;text-decoration:none;text-shadow:none;text-transform:none;letter-spacing:normal;word-break:normal;white-space:normal;word-spacing:normal;line-break:auto;font-size:var(--bs-tooltip-font-size);word-wrap:break-word;opacity:0}.tooltip.show{opacity:var(--bs-tooltip-opacity)}.tooltip .tooltip-arrow{display:block;width:var(--bs-tooltip-arrow-width);height:var(--bs-tooltip-arrow-height)}.tooltip .tooltip-arrow::before{position:absolute;content:"";border-color:rgba(0,0,0,0);border-style:solid}.bs-tooltip-top .tooltip-arrow,.bs-tooltip-auto[data-popper-placement^=top] .tooltip-arrow{bottom:calc(-1*var(--bs-tooltip-arrow-height))}.bs-tooltip-top .tooltip-arrow::before,.bs-tooltip-auto[data-popper-placement^=top] .tooltip-arrow::before{top:-1px;border-width:var(--bs-tooltip-arrow-height) calc(var(--bs-tooltip-arrow-width)*.5) 0;border-top-color:var(--bs-tooltip-bg)}.bs-tooltip-end .tooltip-arrow,.bs-tooltip-auto[data-popper-placement^=right] .tooltip-arrow{left:calc(-1*var(--bs-tooltip-arrow-height));width:var(--bs-tooltip-arrow-height);height:var(--bs-tooltip-arrow-width)}.bs-tooltip-end .tooltip-arrow::before,.bs-tooltip-auto[data-popper-placement^=right] .tooltip-arrow::before{right:-1px;border-width:calc(var(--bs-tooltip-arrow-width)*.5) var(--bs-tooltip-arrow-height) calc(var(--bs-tooltip-arrow-width)*.5) 0;border-right-color:var(--bs-tooltip-bg)}.bs-tooltip-bottom .tooltip-arrow,.bs-tooltip-auto[data-popper-placement^=bottom] .tooltip-arrow{top:calc(-1*var(--bs-tooltip-arrow-height))}.bs-tooltip-bottom .tooltip-arrow::before,.bs-tooltip-auto[data-popper-placement^=bottom] .tooltip-arrow::before{bottom:-1px;border-width:0 calc(var(--bs-tooltip-arrow-width)*.5) var(--bs-tooltip-arrow-height);border-bottom-color:var(--bs-tooltip-bg)}.bs-tooltip-start .tooltip-arrow,.bs-tooltip-auto[data-popper-placement^=left] .tooltip-arrow{right:calc(-1*var(--bs-tooltip-arrow-height));width:var(--bs-tooltip-arrow-height);height:var(--bs-tooltip-arrow-width)}.bs-tooltip-start .tooltip-arrow::before,.bs-tooltip-auto[data-popper-placement^=left] .tooltip-arrow::before{left:-1px;border-width:calc(var(--bs-tooltip-arrow-width)*.5) 0 calc(var(--bs-tooltip-arrow-width)*.5) var(--bs-tooltip-arrow-height);border-left-color:var(--bs-tooltip-bg)}.tooltip-inner{max-width:var(--bs-tooltip-max-width);padding:var(--bs-tooltip-padding-y) var(--bs-tooltip-padding-x);color:var(--bs-tooltip-color);text-align:center;background-color:var(--bs-tooltip-bg);border-radius:var(--bs-tooltip-border-radius)}.popover{--bs-popover-zindex: 1070;--bs-popover-max-width: 276px;--bs-popover-font-size:0.875rem;--bs-popover-bg: #ffffff;--bs-popover-border-width: 1px;--bs-popover-border-color: rgba(0, 0, 0, 0.175);--bs-popover-border-radius: 0.5rem;--bs-popover-inner-border-radius: calc(0.5rem - 1px);--bs-popover-box-shadow: 0 0.5rem 1rem rgba(0, 0, 0, 0.15);--bs-popover-header-padding-x: 1rem;--bs-popover-header-padding-y: 0.5rem;--bs-popover-header-font-size:1rem;--bs-popover-header-color: inherit;--bs-popover-header-bg: #e9ecef;--bs-popover-body-padding-x: 1rem;--bs-popover-body-padding-y: 1rem;--bs-popover-body-color: #212529;--bs-popover-arrow-width: 1rem;--bs-popover-arrow-height: 0.5rem;--bs-popover-arrow-border: 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.sidebar-title{font-size:1.25rem;line-height:1.25;margin-top:0;margin-bottom:1rem;padding-bottom:1rem;border-bottom:var(--bslib-sidebar-border)}.bslib-sidebar-layout.sidebar-right{grid-template-columns:var(--bslib-sidebar-column-main) min(100% - var(--bslib-sidebar-icon-size),var(--bslib-sidebar-width, 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J,Z="x"===y?zt:Vt,tt="x"===y?Rt:qt,et=A[w],it="y"===w?"height":"width",nt=et+g[Z],st=et-g[tt],ot=-1!==[zt,Vt].indexOf(_),rt=null!=(J=null==x?void 0:x[w])?J:0,at=ot?nt:et-E[it]-T[it]-rt+O.altAxis,lt=ot?et+E[it]+T[it]-rt-O.altAxis:st,ct=f&&ot?function(t,e,i){var n=Ne(t,e,i);return n>i?i:n}(at,et,lt):Ne(f?at:nt,et,f?lt:st);A[w]=ct,k[w]=ct-et}e.modifiersData[n]=k}},requiresIfExists:["offset"]};function di(t,e,i){void 0===i&&(i=!1);var n,s,o=me(e),r=me(e)&&function(t){var e=t.getBoundingClientRect(),i=we(e.width)/t.offsetWidth||1,n=we(e.height)/t.offsetHeight||1;return 1!==i||1!==n}(e),a=Le(e),l=Te(t,r,i),c={scrollLeft:0,scrollTop:0},h={x:0,y:0};return(o||!o&&!i)&&(("body"!==ue(e)||Ue(a))&&(c=(n=e)!==fe(n)&&me(n)?{scrollLeft:(s=n).scrollLeft,scrollTop:s.scrollTop}:Xe(n)),me(e)?((h=Te(e,!0)).x+=e.clientLeft,h.y+=e.clientTop):a&&(h.x=Ye(a))),{x:l.left+c.scrollLeft-h.x,y:l.top+c.scrollTop-h.y,width:l.width,height:l.height}}function ui(t){var e=new Map,i=new Set,n=[];function s(t){i.add(t.name),[].concat(t.requires||[],t.requiresIfExists||[]).forEach((function(t){if(!i.has(t)){var n=e.get(t);n&&s(n)}})),n.push(t)}return t.forEach((function(t){e.set(t.name,t)})),t.forEach((function(t){i.has(t.name)||s(t)})),n}var fi={placement:"bottom",modifiers:[],strategy:"absolute"};function pi(){for(var t=arguments.length,e=new Array(t),i=0;iNumber.parseInt(t,10))):"function"==typeof t?e=>t(e,this._element):t}_getPopperConfig(){const t={placement:this._getPlacement(),modifiers:[{name:"preventOverflow",options:{boundary:this._config.boundary}},{name:"offset",options:{offset:this._getOffset()}}]};return(this._inNavbar||"static"===this._config.display)&&(F.setDataAttribute(this._menu,"popper","static"),t.modifiers=[{name:"applyStyles",enabled:!1}]),{...t,...g(this._config.popperConfig,[t])}}_selectMenuItem({key:t,target:e}){const i=z.find(".dropdown-menu 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e=/input|textarea/i.test(t.target.tagName),i="Escape"===t.key,n=[Ei,Ti].includes(t.key);if(!n&&!i)return;if(e&&!i)return;t.preventDefault();const s=this.matches(Ii)?this:z.prev(this,Ii)[0]||z.next(this,Ii)[0]||z.findOne(Ii,t.delegateTarget.parentNode),o=qi.getOrCreateInstance(s);if(n)return t.stopPropagation(),o.show(),void o._selectMenuItem(t);o._isShown()&&(t.stopPropagation(),o.hide(),s.focus())}}N.on(document,Si,Ii,qi.dataApiKeydownHandler),N.on(document,Si,Pi,qi.dataApiKeydownHandler),N.on(document,Li,qi.clearMenus),N.on(document,Di,qi.clearMenus),N.on(document,Li,Ii,(function(t){t.preventDefault(),qi.getOrCreateInstance(this).toggle()})),m(qi);const Vi="backdrop",Ki="show",Qi=`mousedown.bs.${Vi}`,Xi={className:"modal-backdrop",clickCallback:null,isAnimated:!1,isVisible:!0,rootElement:"body"},Yi={className:"string",clickCallback:"(function|null)",isAnimated:"boolean",isVisible:"boolean",rootElement:"(element|string)"};class Ui extends H{constructor(t){super(),this._config=this._getConfig(t),this._isAppended=!1,this._element=null}static get Default(){return Xi}static get DefaultType(){return Yi}static get NAME(){return Vi}show(t){if(!this._config.isVisible)return void g(t);this._append();const e=this._getElement();this._config.isAnimated&&d(e),e.classList.add(Ki),this._emulateAnimation((()=>{g(t)}))}hide(t){this._config.isVisible?(this._getElement().classList.remove(Ki),this._emulateAnimation((()=>{this.dispose(),g(t)}))):g(t)}dispose(){this._isAppended&&(N.off(this._element,Qi),this._element.remove(),this._isAppended=!1)}_getElement(){if(!this._element){const t=document.createElement("div");t.className=this._config.className,this._config.isAnimated&&t.classList.add("fade"),this._element=t}return this._element}_configAfterMerge(t){return t.rootElement=r(t.rootElement),t}_append(){if(this._isAppended)return;const t=this._getElement();this._config.rootElement.append(t),N.on(t,Qi,(()=>{g(this._config.clickCallback)})),this._isAppended=!0}_emulateAnimation(t){_(t,this._getElement(),this._config.isAnimated)}}const Gi=".bs.focustrap",Ji=`focusin${Gi}`,Zi=`keydown.tab${Gi}`,tn="backward",en={autofocus:!0,trapElement:null},nn={autofocus:"boolean",trapElement:"element"};class sn extends H{constructor(t){super(),this._config=this._getConfig(t),this._isActive=!1,this._lastTabNavDirection=null}static get Default(){return en}static get DefaultType(){return nn}static get NAME(){return"focustrap"}activate(){this._isActive||(this._config.autofocus&&this._config.trapElement.focus(),N.off(document,Gi),N.on(document,Ji,(t=>this._handleFocusin(t))),N.on(document,Zi,(t=>this._handleKeydown(t))),this._isActive=!0)}deactivate(){this._isActive&&(this._isActive=!1,N.off(document,Gi))}_handleFocusin(t){const{trapElement:e}=this._config;if(t.target===document||t.target===e||e.contains(t.target))return;const i=z.focusableChildren(e);0===i.length?e.focus():this._lastTabNavDirection===tn?i[i.length-1].focus():i[0].focus()}_handleKeydown(t){"Tab"===t.key&&(this._lastTabNavDirection=t.shiftKey?tn:"forward")}}const on=".fixed-top, .fixed-bottom, .is-fixed, .sticky-top",rn=".sticky-top",an="padding-right",ln="margin-right";class cn{constructor(){this._element=document.body}getWidth(){const t=document.documentElement.clientWidth;return Math.abs(window.innerWidth-t)}hide(){const t=this.getWidth();this._disableOverFlow(),this._setElementAttributes(this._element,an,(e=>e+t)),this._setElementAttributes(on,an,(e=>e+t)),this._setElementAttributes(rn,ln,(e=>e-t))}reset(){this._resetElementAttributes(this._element,"overflow"),this._resetElementAttributes(this._element,an),this._resetElementAttributes(on,an),this._resetElementAttributes(rn,ln)}isOverflowing(){return this.getWidth()>0}_disableOverFlow(){this._saveInitialAttribute(this._element,"overflow"),this._element.style.overflow="hidden"}_setElementAttributes(t,e,i){const n=this.getWidth();this._applyManipulationCallback(t,(t=>{if(t!==this._element&&window.innerWidth>t.clientWidth+n)return;this._saveInitialAttribute(t,e);const s=window.getComputedStyle(t).getPropertyValue(e);t.style.setProperty(e,`${i(Number.parseFloat(s))}px`)}))}_saveInitialAttribute(t,e){const i=t.style.getPropertyValue(e);i&&F.setDataAttribute(t,e,i)}_resetElementAttributes(t,e){this._applyManipulationCallback(t,(t=>{const i=F.getDataAttribute(t,e);null!==i?(F.removeDataAttribute(t,e),t.style.setProperty(e,i)):t.style.removeProperty(e)}))}_applyManipulationCallback(t,e){if(o(t))e(t);else for(const i of z.find(t,this._element))e(i)}}const hn=".bs.modal",dn=`hide${hn}`,un=`hidePrevented${hn}`,fn=`hidden${hn}`,pn=`show${hn}`,mn=`shown${hn}`,gn=`resize${hn}`,_n=`click.dismiss${hn}`,bn=`mousedown.dismiss${hn}`,vn=`keydown.dismiss${hn}`,yn=`click${hn}.data-api`,wn="modal-open",An="show",En="modal-static",Tn={backdrop:!0,focus:!0,keyboard:!0},Cn={backdrop:"(boolean|string)",focus:"boolean",keyboard:"boolean"};class On extends W{constructor(t,e){super(t,e),this._dialog=z.findOne(".modal-dialog",this._element),this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._isShown=!1,this._isTransitioning=!1,this._scrollBar=new cn,this._addEventListeners()}static get Default(){return Tn}static get DefaultType(){return Cn}static get NAME(){return"modal"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||this._isTransitioning||N.trigger(this._element,pn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._isTransitioning=!0,this._scrollBar.hide(),document.body.classList.add(wn),this._adjustDialog(),this._backdrop.show((()=>this._showElement(t))))}hide(){this._isShown&&!this._isTransitioning&&(N.trigger(this._element,dn).defaultPrevented||(this._isShown=!1,this._isTransitioning=!0,this._focustrap.deactivate(),this._element.classList.remove(An),this._queueCallback((()=>this._hideModal()),this._element,this._isAnimated())))}dispose(){N.off(window,hn),N.off(this._dialog,hn),this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}handleUpdate(){this._adjustDialog()}_initializeBackDrop(){return new Ui({isVisible:Boolean(this._config.backdrop),isAnimated:this._isAnimated()})}_initializeFocusTrap(){return new sn({trapElement:this._element})}_showElement(t){document.body.contains(this._element)||document.body.append(this._element),this._element.style.display="block",this._element.removeAttribute("aria-hidden"),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.scrollTop=0;const e=z.findOne(".modal-body",this._dialog);e&&(e.scrollTop=0),d(this._element),this._element.classList.add(An),this._queueCallback((()=>{this._config.focus&&this._focustrap.activate(),this._isTransitioning=!1,N.trigger(this._element,mn,{relatedTarget:t})}),this._dialog,this._isAnimated())}_addEventListeners(){N.on(this._element,vn,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():this._triggerBackdropTransition())})),N.on(window,gn,(()=>{this._isShown&&!this._isTransitioning&&this._adjustDialog()})),N.on(this._element,bn,(t=>{N.one(this._element,_n,(e=>{this._element===t.target&&this._element===e.target&&("static"!==this._config.backdrop?this._config.backdrop&&this.hide():this._triggerBackdropTransition())}))}))}_hideModal(){this._element.style.display="none",this._element.setAttribute("aria-hidden",!0),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._isTransitioning=!1,this._backdrop.hide((()=>{document.body.classList.remove(wn),this._resetAdjustments(),this._scrollBar.reset(),N.trigger(this._element,fn)}))}_isAnimated(){return this._element.classList.contains("fade")}_triggerBackdropTransition(){if(N.trigger(this._element,un).defaultPrevented)return;const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._element.style.overflowY;"hidden"===e||this._element.classList.contains(En)||(t||(this._element.style.overflowY="hidden"),this._element.classList.add(En),this._queueCallback((()=>{this._element.classList.remove(En),this._queueCallback((()=>{this._element.style.overflowY=e}),this._dialog)}),this._dialog),this._element.focus())}_adjustDialog(){const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._scrollBar.getWidth(),i=e>0;if(i&&!t){const t=p()?"paddingLeft":"paddingRight";this._element.style[t]=`${e}px`}if(!i&&t){const t=p()?"paddingRight":"paddingLeft";this._element.style[t]=`${e}px`}}_resetAdjustments(){this._element.style.paddingLeft="",this._element.style.paddingRight=""}static jQueryInterface(t,e){return this.each((function(){const i=On.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===i[t])throw new TypeError(`No method named "${t}"`);i[t](e)}}))}}N.on(document,yn,'[data-bs-toggle="modal"]',(function(t){const e=z.getElementFromSelector(this);["A","AREA"].includes(this.tagName)&&t.preventDefault(),N.one(e,pn,(t=>{t.defaultPrevented||N.one(e,fn,(()=>{a(this)&&this.focus()}))}));const i=z.findOne(".modal.show");i&&On.getInstance(i).hide(),On.getOrCreateInstance(e).toggle(this)})),R(On),m(On);const xn=".bs.offcanvas",kn=".data-api",Ln=`load${xn}${kn}`,Sn="show",Dn="showing",$n="hiding",In=".offcanvas.show",Nn=`show${xn}`,Pn=`shown${xn}`,Mn=`hide${xn}`,jn=`hidePrevented${xn}`,Fn=`hidden${xn}`,Hn=`resize${xn}`,Wn=`click${xn}${kn}`,Bn=`keydown.dismiss${xn}`,zn={backdrop:!0,keyboard:!0,scroll:!1},Rn={backdrop:"(boolean|string)",keyboard:"boolean",scroll:"boolean"};class qn extends W{constructor(t,e){super(t,e),this._isShown=!1,this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._addEventListeners()}static get Default(){return zn}static get DefaultType(){return Rn}static get NAME(){return"offcanvas"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||N.trigger(this._element,Nn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._backdrop.show(),this._config.scroll||(new cn).hide(),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.classList.add(Dn),this._queueCallback((()=>{this._config.scroll&&!this._config.backdrop||this._focustrap.activate(),this._element.classList.add(Sn),this._element.classList.remove(Dn),N.trigger(this._element,Pn,{relatedTarget:t})}),this._element,!0))}hide(){this._isShown&&(N.trigger(this._element,Mn).defaultPrevented||(this._focustrap.deactivate(),this._element.blur(),this._isShown=!1,this._element.classList.add($n),this._backdrop.hide(),this._queueCallback((()=>{this._element.classList.remove(Sn,$n),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._config.scroll||(new cn).reset(),N.trigger(this._element,Fn)}),this._element,!0)))}dispose(){this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}_initializeBackDrop(){const t=Boolean(this._config.backdrop);return new Ui({className:"offcanvas-backdrop",isVisible:t,isAnimated:!0,rootElement:this._element.parentNode,clickCallback:t?()=>{"static"!==this._config.backdrop?this.hide():N.trigger(this._element,jn)}:null})}_initializeFocusTrap(){return new sn({trapElement:this._element})}_addEventListeners(){N.on(this._element,Bn,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():N.trigger(this._element,jn))}))}static jQueryInterface(t){return this.each((function(){const e=qn.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t]||t.startsWith("_")||"constructor"===t)throw new TypeError(`No method named "${t}"`);e[t](this)}}))}}N.on(document,Wn,'[data-bs-toggle="offcanvas"]',(function(t){const e=z.getElementFromSelector(this);if(["A","AREA"].includes(this.tagName)&&t.preventDefault(),l(this))return;N.one(e,Fn,(()=>{a(this)&&this.focus()}));const i=z.findOne(In);i&&i!==e&&qn.getInstance(i).hide(),qn.getOrCreateInstance(e).toggle(this)})),N.on(window,Ln,(()=>{for(const t of z.find(In))qn.getOrCreateInstance(t).show()})),N.on(window,Hn,(()=>{for(const t of z.find("[aria-modal][class*=show][class*=offcanvas-]"))"fixed"!==getComputedStyle(t).position&&qn.getOrCreateInstance(t).hide()})),R(qn),m(qn);const Vn={"*":["class","dir","id","lang","role",/^aria-[\w-]*$/i],a:["target","href","title","rel"],area:[],b:[],br:[],col:[],code:[],div:[],em:[],hr:[],h1:[],h2:[],h3:[],h4:[],h5:[],h6:[],i:[],img:["src","srcset","alt","title","width","height"],li:[],ol:[],p:[],pre:[],s:[],small:[],span:[],sub:[],sup:[],strong:[],u:[],ul:[]},Kn=new Set(["background","cite","href","itemtype","longdesc","poster","src","xlink:href"]),Qn=/^(?!javascript:)(?:[a-z0-9+.-]+:|[^&:/?#]*(?:[/?#]|$))/i,Xn=(t,e)=>{const i=t.nodeName.toLowerCase();return e.includes(i)?!Kn.has(i)||Boolean(Qn.test(t.nodeValue)):e.filter((t=>t instanceof RegExp)).some((t=>t.test(i)))},Yn={allowList:Vn,content:{},extraClass:"",html:!1,sanitize:!0,sanitizeFn:null,template:"

"},Un={allowList:"object",content:"object",extraClass:"(string|function)",html:"boolean",sanitize:"boolean",sanitizeFn:"(null|function)",template:"string"},Gn={entry:"(string|element|function|null)",selector:"(string|element)"};class Jn extends H{constructor(t){super(),this._config=this._getConfig(t)}static get Default(){return Yn}static get DefaultType(){return Un}static get NAME(){return"TemplateFactory"}getContent(){return Object.values(this._config.content).map((t=>this._resolvePossibleFunction(t))).filter(Boolean)}hasContent(){return this.getContent().length>0}changeContent(t){return this._checkContent(t),this._config.content={...this._config.content,...t},this}toHtml(){const t=document.createElement("div");t.innerHTML=this._maybeSanitize(this._config.template);for(const[e,i]of Object.entries(this._config.content))this._setContent(t,i,e);const e=t.children[0],i=this._resolvePossibleFunction(this._config.extraClass);return i&&e.classList.add(...i.split(" ")),e}_typeCheckConfig(t){super._typeCheckConfig(t),this._checkContent(t.content)}_checkContent(t){for(const[e,i]of Object.entries(t))super._typeCheckConfig({selector:e,entry:i},Gn)}_setContent(t,e,i){const n=z.findOne(i,t);n&&((e=this._resolvePossibleFunction(e))?o(e)?this._putElementInTemplate(r(e),n):this._config.html?n.innerHTML=this._maybeSanitize(e):n.textContent=e:n.remove())}_maybeSanitize(t){return this._config.sanitize?function(t,e,i){if(!t.length)return t;if(i&&"function"==typeof i)return i(t);const n=(new window.DOMParser).parseFromString(t,"text/html"),s=[].concat(...n.body.querySelectorAll("*"));for(const t of s){const i=t.nodeName.toLowerCase();if(!Object.keys(e).includes(i)){t.remove();continue}const n=[].concat(...t.attributes),s=[].concat(e["*"]||[],e[i]||[]);for(const e of n)Xn(e,s)||t.removeAttribute(e.nodeName)}return n.body.innerHTML}(t,this._config.allowList,this._config.sanitizeFn):t}_resolvePossibleFunction(t){return g(t,[this])}_putElementInTemplate(t,e){if(this._config.html)return e.innerHTML="",void e.append(t);e.textContent=t.textContent}}const Zn=new Set(["sanitize","allowList","sanitizeFn"]),ts="fade",es="show",is=".modal",ns="hide.bs.modal",ss="hover",os="focus",rs={AUTO:"auto",TOP:"top",RIGHT:p()?"left":"right",BOTTOM:"bottom",LEFT:p()?"right":"left"},as={allowList:Vn,animation:!0,boundary:"clippingParents",container:!1,customClass:"",delay:0,fallbackPlacements:["top","right","bottom","left"],html:!1,offset:[0,6],placement:"top",popperConfig:null,sanitize:!0,sanitizeFn:null,selector:!1,template:'',title:"",trigger:"hover focus"},ls={allowList:"object",animation:"boolean",boundary:"(string|element)",container:"(string|element|boolean)",customClass:"(string|function)",delay:"(number|object)",fallbackPlacements:"array",html:"boolean",offset:"(array|string|function)",placement:"(string|function)",popperConfig:"(null|object|function)",sanitize:"boolean",sanitizeFn:"(null|function)",selector:"(string|boolean)",template:"string",title:"(string|element|function)",trigger:"string"};class cs extends W{constructor(t,e){if(void 0===vi)throw new TypeError("Bootstrap's tooltips require Popper (https://popper.js.org)");super(t,e),this._isEnabled=!0,this._timeout=0,this._isHovered=null,this._activeTrigger={},this._popper=null,this._templateFactory=null,this._newContent=null,this.tip=null,this._setListeners(),this._config.selector||this._fixTitle()}static get Default(){return as}static get DefaultType(){return ls}static get 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b/profile/blog/posts/guest-students-laplace/index_files/libs/quarto-html/quarto-syntax-highlighting.css new file mode 100644 index 0000000..b30ce57 --- /dev/null +++ b/profile/blog/posts/guest-students-laplace/index_files/libs/quarto-html/quarto-syntax-highlighting.css @@ -0,0 +1,205 @@ +/* quarto syntax highlight colors */ +:root { + --quarto-hl-ot-color: #003B4F; + --quarto-hl-at-color: #657422; + --quarto-hl-ss-color: #20794D; + --quarto-hl-an-color: #5E5E5E; + --quarto-hl-fu-color: #4758AB; + --quarto-hl-st-color: #20794D; + --quarto-hl-cf-color: #003B4F; + --quarto-hl-op-color: #5E5E5E; + --quarto-hl-er-color: #AD0000; + --quarto-hl-bn-color: #AD0000; + --quarto-hl-al-color: #AD0000; + --quarto-hl-va-color: #111111; + --quarto-hl-bu-color: inherit; + --quarto-hl-ex-color: inherit; + --quarto-hl-pp-color: #AD0000; + --quarto-hl-in-color: #5E5E5E; + --quarto-hl-vs-color: #20794D; + --quarto-hl-wa-color: #5E5E5E; + --quarto-hl-do-color: #5E5E5E; + --quarto-hl-im-color: #00769E; + --quarto-hl-ch-color: #20794D; + --quarto-hl-dt-color: #AD0000; + --quarto-hl-fl-color: #AD0000; + --quarto-hl-co-color: #5E5E5E; + --quarto-hl-cv-color: #5E5E5E; + --quarto-hl-cn-color: #8f5902; + --quarto-hl-sc-color: #5E5E5E; + --quarto-hl-dv-color: #AD0000; + --quarto-hl-kw-color: #003B4F; +} + +/* other quarto variables */ +:root { + --quarto-font-monospace: SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", "Courier New", monospace; +} + +pre > code.sourceCode > span { + color: #003B4F; +} + +code span { + color: #003B4F; +} + +code.sourceCode > span { + color: #003B4F; +} + +div.sourceCode, +div.sourceCode pre.sourceCode { + color: #003B4F; +} + +code span.ot { + color: #003B4F; + font-style: inherit; +} + +code span.at { + color: #657422; + font-style: inherit; +} + +code span.ss { + color: #20794D; + font-style: inherit; +} + +code span.an { + color: #5E5E5E; + font-style: inherit; +} + +code span.fu { + color: #4758AB; + font-style: inherit; +} + +code span.st { + color: #20794D; + font-style: inherit; +} + +code span.cf { + color: #003B4F; + font-weight: bold; + font-style: inherit; +} + +code span.op { + color: #5E5E5E; + font-style: inherit; +} + +code span.er { + color: #AD0000; + font-style: inherit; +} + +code span.bn { + color: #AD0000; + font-style: inherit; +} + +code span.al { + color: #AD0000; + font-style: inherit; +} + +code span.va { + color: #111111; + font-style: inherit; +} + +code span.bu { + font-style: inherit; +} + +code span.ex { + font-style: inherit; +} + +code span.pp { + color: #AD0000; + font-style: inherit; +} + +code span.in { + color: #5E5E5E; + font-style: inherit; +} + +code span.vs { + color: #20794D; + font-style: inherit; +} + +code span.wa { + color: #5E5E5E; + font-style: italic; +} + +code span.do { + color: #5E5E5E; + font-style: italic; +} + +code span.im { + color: #00769E; + font-style: inherit; +} + +code span.ch { + color: #20794D; + font-style: inherit; +} + +code span.dt { + color: #AD0000; + font-style: inherit; +} + +code span.fl { + color: #AD0000; + font-style: inherit; +} + +code span.co { + color: #5E5E5E; + font-style: inherit; +} + +code span.cv { + color: #5E5E5E; + font-style: italic; +} + +code span.cn { + color: #8f5902; + font-style: inherit; +} + +code span.sc { + color: #5E5E5E; + font-style: inherit; +} + +code span.dv { + color: #AD0000; + font-style: inherit; +} + +code span.kw { + color: #003B4F; + font-weight: bold; + font-style: inherit; +} + +.prevent-inlining { + content: " { + // Find any conflicting margin elements and add margins to the + // top to prevent overlap + const marginChildren = window.document.querySelectorAll( + ".column-margin.column-container > *, .margin-caption, .aside" + ); + + let lastBottom = 0; + for (const marginChild of marginChildren) { + if (marginChild.offsetParent !== null) { + // clear the top margin so we recompute it + marginChild.style.marginTop = null; + const top = marginChild.getBoundingClientRect().top + window.scrollY; + if (top < lastBottom) { + const marginChildStyle = window.getComputedStyle(marginChild); + const marginBottom = parseFloat(marginChildStyle["marginBottom"]); + const margin = lastBottom - top + marginBottom; + marginChild.style.marginTop = `${margin}px`; + } + const styles = window.getComputedStyle(marginChild); + const marginTop = parseFloat(styles["marginTop"]); + lastBottom = top + marginChild.getBoundingClientRect().height + marginTop; + } + } +}; + +window.document.addEventListener("DOMContentLoaded", function (_event) { + // Recompute the position of margin elements anytime the body size changes + if (window.ResizeObserver) { + const resizeObserver = new window.ResizeObserver( + throttle(() => { + layoutMarginEls(); + if ( + window.document.body.getBoundingClientRect().width < 990 && + isReaderMode() + ) { + quartoToggleReader(); + } + }, 50) + ); + resizeObserver.observe(window.document.body); + } + + const tocEl = window.document.querySelector('nav.toc-active[role="doc-toc"]'); + const sidebarEl = window.document.getElementById("quarto-sidebar"); + const leftTocEl = window.document.getElementById("quarto-sidebar-toc-left"); + const marginSidebarEl = window.document.getElementById( + "quarto-margin-sidebar" + ); + // function to determine whether the element has a previous sibling that is active + const prevSiblingIsActiveLink = (el) => { + const sibling = el.previousElementSibling; + if (sibling && sibling.tagName === "A") { + return sibling.classList.contains("active"); + } else { + return false; + } + }; + + // fire slideEnter for bootstrap tab activations (for htmlwidget resize behavior) + function fireSlideEnter(e) { + const event = window.document.createEvent("Event"); + event.initEvent("slideenter", true, true); + window.document.dispatchEvent(event); + } + const tabs = window.document.querySelectorAll('a[data-bs-toggle="tab"]'); + tabs.forEach((tab) => { + tab.addEventListener("shown.bs.tab", fireSlideEnter); + }); + + // fire slideEnter for tabby tab activations (for htmlwidget resize behavior) + document.addEventListener("tabby", fireSlideEnter, false); + + // Track scrolling and mark TOC links as active + // get table of contents and sidebar (bail if we don't have at least one) + const tocLinks = tocEl + ? [...tocEl.querySelectorAll("a[data-scroll-target]")] + : []; + const makeActive = (link) => tocLinks[link].classList.add("active"); + const removeActive = (link) => tocLinks[link].classList.remove("active"); + const removeAllActive = () => + [...Array(tocLinks.length).keys()].forEach((link) => removeActive(link)); + + // activate the anchor for a section associated with this TOC entry + tocLinks.forEach((link) => { + link.addEventListener("click", () => { + if (link.href.indexOf("#") !== -1) { + const anchor = link.href.split("#")[1]; + const heading = window.document.querySelector( + `[data-anchor-id="${anchor}"]` + ); + if (heading) { + // Add the class + heading.classList.add("reveal-anchorjs-link"); + + // function to show the anchor + const handleMouseout = () => { + heading.classList.remove("reveal-anchorjs-link"); + heading.removeEventListener("mouseout", handleMouseout); + }; + + // add a function to clear the anchor when the user mouses out of it + heading.addEventListener("mouseout", handleMouseout); + } + } + }); + }); + + const sections = tocLinks.map((link) => { + const target = link.getAttribute("data-scroll-target"); + if (target.startsWith("#")) { + return window.document.getElementById(decodeURI(`${target.slice(1)}`)); + } else { + return window.document.querySelector(decodeURI(`${target}`)); + } + }); + + const sectionMargin = 200; + let currentActive = 0; + // track whether we've initialized state the first time + let init = false; + + const updateActiveLink = () => { + // The index from bottom to top (e.g. reversed list) + let sectionIndex = -1; + if ( + window.innerHeight + window.pageYOffset >= + window.document.body.offsetHeight + ) { + // This is the no-scroll case where last section should be the active one + sectionIndex = 0; + } else { + // This finds the last section visible on screen that should be made active + sectionIndex = [...sections].reverse().findIndex((section) => { + if (section) { + return window.pageYOffset >= section.offsetTop - sectionMargin; + } else { + return false; + } + }); + } + if (sectionIndex > -1) { + const current = sections.length - sectionIndex - 1; + if (current !== currentActive) { + removeAllActive(); + currentActive = current; + makeActive(current); + if (init) { + window.dispatchEvent(sectionChanged); + } + init = true; + } + } + }; + + const inHiddenRegion = (top, bottom, hiddenRegions) => { + for (const region of hiddenRegions) { + if (top <= region.bottom && bottom >= region.top) { + return true; + } + } + return false; + }; + + const categorySelector = "header.quarto-title-block .quarto-category"; + const activateCategories = (href) => { + // Find any categories + // Surround them with a link pointing back to: + // #category=Authoring + try { + const categoryEls = window.document.querySelectorAll(categorySelector); + for (const categoryEl of categoryEls) { + const categoryText = categoryEl.textContent; + if (categoryText) { + const link = `${href}#category=${encodeURIComponent(categoryText)}`; + const linkEl = window.document.createElement("a"); + linkEl.setAttribute("href", link); + for (const child of categoryEl.childNodes) { + linkEl.append(child); + } + categoryEl.appendChild(linkEl); + } + } + } catch { + // Ignore errors + } + }; + function hasTitleCategories() { + return window.document.querySelector(categorySelector) !== null; + } + + function offsetRelativeUrl(url) { + const offset = getMeta("quarto:offset"); + return offset ? offset + url : url; + } + + function offsetAbsoluteUrl(url) { + const offset = getMeta("quarto:offset"); + const baseUrl = new URL(offset, window.location); + + const projRelativeUrl = url.replace(baseUrl, ""); + if (projRelativeUrl.startsWith("/")) { + return projRelativeUrl; + } else { + return "/" + projRelativeUrl; + } + } + + // read a meta tag value + function getMeta(metaName) { + const metas = window.document.getElementsByTagName("meta"); + for (let i = 0; i < metas.length; i++) { + if (metas[i].getAttribute("name") === metaName) { + return metas[i].getAttribute("content"); + } + } + return ""; + } + + async function findAndActivateCategories() { + const currentPagePath = offsetAbsoluteUrl(window.location.href); + const response = await fetch(offsetRelativeUrl("listings.json")); + if (response.status == 200) { + return response.json().then(function (listingPaths) { + const listingHrefs = []; + for (const listingPath of listingPaths) { + const pathWithoutLeadingSlash = listingPath.listing.substring(1); + for (const item of listingPath.items) { + if ( + item === currentPagePath || + item === currentPagePath + "index.html" + ) { + // Resolve this path against the offset to be sure + // we already are using the correct path to the listing + // (this adjusts the listing urls to be rooted against + // whatever root the page is actually running against) + const relative = offsetRelativeUrl(pathWithoutLeadingSlash); + const baseUrl = window.location; + const resolvedPath = new URL(relative, baseUrl); + listingHrefs.push(resolvedPath.pathname); + break; + } + } + } + + // Look up the tree for a nearby linting and use that if we find one + const nearestListing = findNearestParentListing( + offsetAbsoluteUrl(window.location.pathname), + listingHrefs + ); + if (nearestListing) { + activateCategories(nearestListing); + } else { + // See if the referrer is a listing page for this item + const referredRelativePath = offsetAbsoluteUrl(document.referrer); + const referrerListing = listingHrefs.find((listingHref) => { + const isListingReferrer = + listingHref === referredRelativePath || + listingHref === referredRelativePath + "index.html"; + return isListingReferrer; + }); + + if (referrerListing) { + // Try to use the referrer if possible + activateCategories(referrerListing); + } else if (listingHrefs.length > 0) { + // Otherwise, just fall back to the first listing + activateCategories(listingHrefs[0]); + } + } + }); + } + } + if (hasTitleCategories()) { + findAndActivateCategories(); + } + + const findNearestParentListing = (href, listingHrefs) => { + if (!href || !listingHrefs) { + return undefined; + } + // Look up the tree for a nearby linting and use that if we find one + const relativeParts = href.substring(1).split("/"); + while (relativeParts.length > 0) { + const path = relativeParts.join("/"); + for (const listingHref of listingHrefs) { + if (listingHref.startsWith(path)) { + return listingHref; + } + } + relativeParts.pop(); + } + + return undefined; + }; + + const manageSidebarVisiblity = (el, placeholderDescriptor) => { + let isVisible = true; + let elRect; + + return (hiddenRegions) => { + if (el === null) { + return; + } + + // Find the last element of the TOC + const lastChildEl = el.lastElementChild; + + if (lastChildEl) { + // Converts the sidebar to a menu + const convertToMenu = () => { + for (const child of el.children) { + child.style.opacity = 0; + child.style.overflow = "hidden"; + child.style.pointerEvents = "none"; + } + + nexttick(() => { + const toggleContainer = window.document.createElement("div"); + toggleContainer.style.width = "100%"; + toggleContainer.classList.add("zindex-over-content"); + toggleContainer.classList.add("quarto-sidebar-toggle"); + toggleContainer.classList.add("headroom-target"); // Marks this to be managed by headeroom + toggleContainer.id = placeholderDescriptor.id; + toggleContainer.style.position = "fixed"; + + const toggleIcon = window.document.createElement("i"); + toggleIcon.classList.add("quarto-sidebar-toggle-icon"); + toggleIcon.classList.add("bi"); + toggleIcon.classList.add("bi-caret-down-fill"); + + const toggleTitle = window.document.createElement("div"); + const titleEl = window.document.body.querySelector( + placeholderDescriptor.titleSelector + ); + if (titleEl) { + toggleTitle.append( + titleEl.textContent || titleEl.innerText, + toggleIcon + ); + } + toggleTitle.classList.add("zindex-over-content"); + toggleTitle.classList.add("quarto-sidebar-toggle-title"); + toggleContainer.append(toggleTitle); + + const toggleContents = window.document.createElement("div"); + toggleContents.classList = el.classList; + toggleContents.classList.add("zindex-over-content"); + toggleContents.classList.add("quarto-sidebar-toggle-contents"); + for (const child of el.children) { + if (child.id === "toc-title") { + continue; + } + + const clone = child.cloneNode(true); + clone.style.opacity = 1; + clone.style.pointerEvents = null; + clone.style.display = null; + toggleContents.append(clone); + } + toggleContents.style.height = "0px"; + const positionToggle = () => { + // position the element (top left of parent, same width as parent) + if (!elRect) { + elRect = el.getBoundingClientRect(); + } + toggleContainer.style.left = `${elRect.left}px`; + toggleContainer.style.top = `${elRect.top}px`; + toggleContainer.style.width = `${elRect.width}px`; + }; + positionToggle(); + + toggleContainer.append(toggleContents); + el.parentElement.prepend(toggleContainer); + + // Process clicks + let tocShowing = false; + // Allow the caller to control whether this is dismissed + // when it is clicked (e.g. sidebar navigation supports + // opening and closing the nav tree, so don't dismiss on click) + const clickEl = placeholderDescriptor.dismissOnClick + ? toggleContainer + : toggleTitle; + + const closeToggle = () => { + if (tocShowing) { + toggleContainer.classList.remove("expanded"); + toggleContents.style.height = "0px"; + tocShowing = false; + } + }; + + // Get rid of any expanded toggle if the user scrolls + window.document.addEventListener( + "scroll", + throttle(() => { + closeToggle(); + }, 50) + ); + + // Handle positioning of the toggle + window.addEventListener( + "resize", + throttle(() => { + elRect = undefined; + positionToggle(); + }, 50) + ); + + window.addEventListener("quarto-hrChanged", () => { + elRect = undefined; + }); + + // Process the click + clickEl.onclick = () => { + if (!tocShowing) { + toggleContainer.classList.add("expanded"); + toggleContents.style.height = null; + tocShowing = true; + } else { + closeToggle(); + } + }; + }); + }; + + // Converts a sidebar from a menu back to a sidebar + const convertToSidebar = () => { + for (const child of el.children) { + child.style.opacity = 1; + child.style.overflow = null; + child.style.pointerEvents = null; + } + + const placeholderEl = window.document.getElementById( + placeholderDescriptor.id + ); + if (placeholderEl) { + placeholderEl.remove(); + } + + el.classList.remove("rollup"); + }; + + if (isReaderMode()) { + convertToMenu(); + isVisible = false; + } else { + // Find the top and bottom o the element that is being managed + const elTop = el.offsetTop; + const elBottom = + elTop + lastChildEl.offsetTop + lastChildEl.offsetHeight; + + if (!isVisible) { + // If the element is current not visible reveal if there are + // no conflicts with overlay regions + if (!inHiddenRegion(elTop, elBottom, hiddenRegions)) { + convertToSidebar(); + isVisible = true; + } + } else { + // If the element is visible, hide it if it conflicts with overlay regions + // and insert a placeholder toggle (or if we're in reader mode) + if (inHiddenRegion(elTop, elBottom, hiddenRegions)) { + convertToMenu(); + isVisible = false; + } + } + } + } + }; + }; + + const tabEls = document.querySelectorAll('a[data-bs-toggle="tab"]'); + for (const tabEl of tabEls) { + const id = tabEl.getAttribute("data-bs-target"); + if (id) { + const columnEl = document.querySelector( + `${id} .column-margin, .tabset-margin-content` + ); + if (columnEl) + tabEl.addEventListener("shown.bs.tab", function (event) { + const el = event.srcElement; + if (el) { + const visibleCls = `${el.id}-margin-content`; + // walk up until we find a parent tabset + let panelTabsetEl = el.parentElement; + while (panelTabsetEl) { + if (panelTabsetEl.classList.contains("panel-tabset")) { + break; + } + panelTabsetEl = panelTabsetEl.parentElement; + } + + if (panelTabsetEl) { + const prevSib = panelTabsetEl.previousElementSibling; + if ( + prevSib && + prevSib.classList.contains("tabset-margin-container") + ) { + const childNodes = prevSib.querySelectorAll( + ".tabset-margin-content" + ); + for (const childEl of childNodes) { + if (childEl.classList.contains(visibleCls)) { + childEl.classList.remove("collapse"); + } else { + childEl.classList.add("collapse"); + } + } + } + } + } + + layoutMarginEls(); + }); + } + } + + // Manage the visibility of the toc and the sidebar + const marginScrollVisibility = manageSidebarVisiblity(marginSidebarEl, { + id: "quarto-toc-toggle", + titleSelector: "#toc-title", + dismissOnClick: true, + }); + const sidebarScrollVisiblity = manageSidebarVisiblity(sidebarEl, { + id: "quarto-sidebarnav-toggle", + titleSelector: ".title", + dismissOnClick: false, + }); + let tocLeftScrollVisibility; + if (leftTocEl) { + tocLeftScrollVisibility = manageSidebarVisiblity(leftTocEl, { + id: "quarto-lefttoc-toggle", + titleSelector: "#toc-title", + dismissOnClick: true, + }); + } + + // Find the first element that uses formatting in special columns + const conflictingEls = window.document.body.querySelectorAll( + '[class^="column-"], [class*=" column-"], aside, [class*="margin-caption"], [class*=" margin-caption"], [class*="margin-ref"], [class*=" margin-ref"]' + ); + + // Filter all the possibly conflicting elements into ones + // the do conflict on the left or ride side + const arrConflictingEls = Array.from(conflictingEls); + const leftSideConflictEls = arrConflictingEls.filter((el) => { + if (el.tagName === "ASIDE") { + return false; + } + return Array.from(el.classList).find((className) => { + return ( + className !== "column-body" && + className.startsWith("column-") && + !className.endsWith("right") && + !className.endsWith("container") && + className !== "column-margin" + ); + }); + }); + const rightSideConflictEls = arrConflictingEls.filter((el) => { + if (el.tagName === "ASIDE") { + return true; + } + + const hasMarginCaption = Array.from(el.classList).find((className) => { + return className == "margin-caption"; + }); + if (hasMarginCaption) { + return true; + } + + return Array.from(el.classList).find((className) => { + return ( + className !== "column-body" && + !className.endsWith("container") && + className.startsWith("column-") && + !className.endsWith("left") + ); + }); + }); + + const kOverlapPaddingSize = 10; + function toRegions(els) { + return els.map((el) => { + const boundRect = el.getBoundingClientRect(); + const top = + boundRect.top + + document.documentElement.scrollTop - + kOverlapPaddingSize; + return { + top, + bottom: top + el.scrollHeight + 2 * kOverlapPaddingSize, + }; + }); + } + + let hasObserved = false; + const visibleItemObserver = (els) => { + let visibleElements = [...els]; + const intersectionObserver = new IntersectionObserver( + (entries, _observer) => { + entries.forEach((entry) => { + if (entry.isIntersecting) { + if (visibleElements.indexOf(entry.target) === -1) { + visibleElements.push(entry.target); + } + } else { + visibleElements = visibleElements.filter((visibleEntry) => { + return visibleEntry !== entry; + }); + } + }); + + if (!hasObserved) { + hideOverlappedSidebars(); + } + hasObserved = true; + }, + {} + ); + els.forEach((el) => { + intersectionObserver.observe(el); + }); + + return { + getVisibleEntries: () => { + return visibleElements; + }, + }; + }; + + const rightElementObserver = visibleItemObserver(rightSideConflictEls); + const leftElementObserver = visibleItemObserver(leftSideConflictEls); + + const hideOverlappedSidebars = () => { + marginScrollVisibility(toRegions(rightElementObserver.getVisibleEntries())); + sidebarScrollVisiblity(toRegions(leftElementObserver.getVisibleEntries())); + if (tocLeftScrollVisibility) { + tocLeftScrollVisibility( + toRegions(leftElementObserver.getVisibleEntries()) + ); + } + }; + + window.quartoToggleReader = () => { + // Applies a slow class (or removes it) + // to update the transition speed + const slowTransition = (slow) => { + const manageTransition = (id, slow) => { + const el = document.getElementById(id); + if (el) { + if (slow) { + el.classList.add("slow"); + } else { + el.classList.remove("slow"); + } + } + }; + + manageTransition("TOC", slow); + manageTransition("quarto-sidebar", slow); + }; + const readerMode = !isReaderMode(); + setReaderModeValue(readerMode); + + // If we're entering reader mode, slow the transition + if (readerMode) { + slowTransition(readerMode); + } + highlightReaderToggle(readerMode); + hideOverlappedSidebars(); + + // If we're exiting reader mode, restore the non-slow transition + if (!readerMode) { + slowTransition(!readerMode); + } + }; + + const highlightReaderToggle = (readerMode) => { + const els = document.querySelectorAll(".quarto-reader-toggle"); + if (els) { + els.forEach((el) => { + if (readerMode) { + el.classList.add("reader"); + } else { + el.classList.remove("reader"); + } + }); + } + }; + + const setReaderModeValue = (val) => { + if (window.location.protocol !== "file:") { + window.localStorage.setItem("quarto-reader-mode", val); + } else { + localReaderMode = val; + } + }; + + const isReaderMode = () => { + if (window.location.protocol !== "file:") { + return window.localStorage.getItem("quarto-reader-mode") === "true"; + } else { + return localReaderMode; + } + }; + let localReaderMode = null; + + const tocOpenDepthStr = tocEl?.getAttribute("data-toc-expanded"); + const tocOpenDepth = tocOpenDepthStr ? Number(tocOpenDepthStr) : 1; + + // Walk the TOC and collapse/expand nodes + // Nodes are expanded if: + // - they are top level + // - they have children that are 'active' links + // - they are directly below an link that is 'active' + const walk = (el, depth) => { + // Tick depth when we enter a UL + if (el.tagName === "UL") { + depth = depth + 1; + } + + // It this is active link + let isActiveNode = false; + if (el.tagName === "A" && el.classList.contains("active")) { + isActiveNode = true; + } + + // See if there is an active child to this element + let hasActiveChild = false; + for (child of el.children) { + hasActiveChild = walk(child, depth) || hasActiveChild; + } + + // Process the collapse state if this is an UL + if (el.tagName === "UL") { + if (tocOpenDepth === -1 && depth > 1) { + // toc-expand: false + el.classList.add("collapse"); + } else if ( + depth <= tocOpenDepth || + hasActiveChild || + prevSiblingIsActiveLink(el) + ) { + el.classList.remove("collapse"); + } else { + el.classList.add("collapse"); + } + + // untick depth when we leave a UL + depth = depth - 1; + } + return hasActiveChild || isActiveNode; + }; + + // walk the TOC and expand / collapse any items that should be shown + if (tocEl) { + updateActiveLink(); + walk(tocEl, 0); + } + + // Throttle the scroll event and walk peridiocally + window.document.addEventListener( + "scroll", + throttle(() => { + if (tocEl) { + updateActiveLink(); + walk(tocEl, 0); + } + if (!isReaderMode()) { + hideOverlappedSidebars(); + } + }, 5) + ); + window.addEventListener( + "resize", + throttle(() => { + if (tocEl) { + updateActiveLink(); + walk(tocEl, 0); + } + if (!isReaderMode()) { + hideOverlappedSidebars(); + } + }, 10) + ); + hideOverlappedSidebars(); + highlightReaderToggle(isReaderMode()); +}); + +// grouped tabsets +window.addEventListener("pageshow", (_event) => { + function getTabSettings() { + const data = localStorage.getItem("quarto-persistent-tabsets-data"); + if (!data) { + localStorage.setItem("quarto-persistent-tabsets-data", "{}"); + return {}; + } + if (data) { + return JSON.parse(data); + } + } + + function setTabSettings(data) { + localStorage.setItem( + "quarto-persistent-tabsets-data", + JSON.stringify(data) + ); + } + + function setTabState(groupName, groupValue) { + const data = getTabSettings(); + data[groupName] = groupValue; + setTabSettings(data); + } + + function toggleTab(tab, active) { + const tabPanelId = tab.getAttribute("aria-controls"); + const tabPanel = document.getElementById(tabPanelId); + if (active) { + tab.classList.add("active"); + tabPanel.classList.add("active"); + } else { + tab.classList.remove("active"); + tabPanel.classList.remove("active"); + } + } + + function toggleAll(selectedGroup, selectorsToSync) { + for (const [thisGroup, tabs] of Object.entries(selectorsToSync)) { + const active = selectedGroup === thisGroup; + for (const tab of tabs) { + toggleTab(tab, active); + } + } + } + + function 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JorgeLuizFranco Date: Sat, 14 Sep 2024 11:59:29 -0300 Subject: [PATCH 02/13] added CausalInference.jl details of implementation and possible fix for .bib cite --- profile/bib.bib | 18 + .../a-new-tool-for-explainable-ai/index.html | 12 +- profile/blog/posts/causal-recourse/bib.bib | 3464 +++++++++++++++++ .../blog/posts/causal-recourse/index copy.qmd | 127 + profile/blog/posts/causal-recourse/index.html | 139 +- profile/blog/posts/causal-recourse/index.qmd | 115 +- 6 files changed, 3855 insertions(+), 20 deletions(-) create mode 100644 profile/blog/posts/causal-recourse/bib.bib create mode 100644 profile/blog/posts/causal-recourse/index copy.qmd diff --git a/profile/bib.bib b/profile/bib.bib index 86ad05a..29127ef 100644 --- a/profile/bib.bib +++ b/profile/bib.bib @@ -1,3 +1,21 @@ +@Article{ges2003, +author = {Chickering, David Maxwell}, +title = {Optimal structure identification with greedy search}, +year = {2003}, +issue_date = {3/1/2003}, +publisher = {JMLR.org}, +volume = {3}, +number = {null}, +issn = {1532-4435}, +url = {https://doi.org/10.1162/153244303321897717}, +doi = {10.1162/153244303321897717}, +abstract = {In this paper we prove the so-called "Meek Conjecture". In particular, we show that if a DAG H is an independence map of another DAG G, then there exists a finite sequence of edge additions and covered edge reversals in G such that (1) after each edge modification H remains an independence map of G and (2) after all modifications G =H. As shown by Meek (1997), this result has an important consequence for Bayesian approaches to learning Bayesian networks from data: in the limit of large sample size, there exists a two-phase greedy search algorithm that---when applied to a particular sparsely-connected search space---provably identifies a perfect map of the generative distribution if that perfect map is a DAG. We provide a new implementation of the search space, using equivalence classes as states, for which all operators used in the greedy search can be scored efficiently using local functions of the nodes in the domain. Finally, using both synthetic and real-world datasets, we demonstrate that the two-phase greedy approach leads to good solutions when learning with finite sample sizes.}, +journal = {J. Mach. Learn. Res.}, +month = {mar}, +pages = {507–554}, +numpages = {48} +} + @InProceedings{karimi2021, author = {Karimi, Amir-Hossein and Sch\"{o}lkopf, Bernhard and Valera, Isabel}, title = {Algorithmic Recourse: from Counterfactual Explanations to Interventions}, diff --git a/profile/blog/posts/a-new-tool-for-explainable-ai/index.html b/profile/blog/posts/a-new-tool-for-explainable-ai/index.html index 5a8df92..3f0039f 100644 --- a/profile/blog/posts/a-new-tool-for-explainable-ai/index.html +++ b/profile/blog/posts/a-new-tool-for-explainable-ai/index.html @@ -170,7 +170,7 @@

To model the mapping from image inputs to labels will rely on a simple Multi-Layer Perceptron (MLP). A great Julia library for Deep Learning is Flux.jl. But wait … doesn’t ConformalPrediction.jl work with models trained in MLJ.jl? That’s right, but fortunately there exists a Flux.jl interface to MLJ.jl, namely MLJFlux.jl. The interface is still in its early stages, but already very powerful and easily accessible for anyone (like myself) who is used to building Neural Networks in Flux.jl.

In Flux.jl, you could build an MLP for this task as follows,

-
+
Code 
using Flux
@@ -347,7 +347,7 @@ 
🚧 Building the Net

where (28,28) is just the input dimension (28x28 pixel images). Since we have ten digits, our output dimension is ten.1

We can do the exact same thing in MLJFlux.jl as follows,

-
+
Code 
using MLJFlux
@@ -360,7 +360,7 @@ 
🚧 Building the Net

where here we rely on the @builder macro to make the transition from Flux.jl to MLJ.jl as seamless as possible. Finally, MLJFlux.jl already comes with a number of helper functions to define plain-vanilla networks. In this case, we will use the ImageClassifier with our custom builder and cross-entropy loss:

-
+
Code 
ImageClassifier = @load ImageClassifier
@@ -372,7 +372,7 @@ 
🚧 Building the Net

The generated instance clf is a model (in the MLJ.jl sense) so from this point on we can rely on standard MLJ.jl workflows. For example, we can wrap our model in data to create a machine and then evaluate it on a holdout set as follows:

-
+
Code 
mach = machine(clf, X, y)
@@ -390,7 +390,7 @@ 
🚧 Building the Net
 

 
🔥 Conformalizing the Network

 
Since clf is a model, it is also compatible with our package: ConformalPrediction.jl. To conformalize our MLP, we therefore only need to call conformal_model(clf). Since the generated instance conf_model is also just a model, we can still rely on standard MLJ.jl workflows. Below we first wrap it in data and then fit it. Aaaand … we’re done! Let’s look at the results in the next section.

-

+

 

 Code
 
using ConformalPrediction
@@ -404,7 +404,7 @@ 
🔥 Conformali
 
📊 Results

 
Figure 2 below presents the results. Figure 2 (a) displays highly certain predictions, now defined in the rigorous sense of Conformal Prediction: in each case, the conformal set (just beneath the image) includes only one label.

 
Figure 2 (b) and Figure 2 (c) display increasingly uncertain predictions of set size two and three, respectively. They demonstrate that CP is well equipped to deal with samples characterized by high aleatoric uncertainty: digits four (4), seven (7) and nine (9) share certain similarities. So do digits five (5) and six (6) as well as three (3) and eight (8). These may be hard to distinguish from each other even after seeing many examples (and even for a human). It is therefore unsurprising to see that these digits often end up together in conformal sets.

-

+

 

 

 

@@ -416,30 +416,27 @@ 
📊 Results

 
 
 
-  
+  
     
   
 
-
+
 
-  
+  
     
   
 
-
+
 
-  
+  
     
   
 
-
+
 📊 Results

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-📊 Results
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 " transform="translate(2518, 47)">
 
-
+
(a) Randomly selected prediction sets of size \(|C|=1\). @@ -821,31 +824,27 @@

📊 Results

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(b) Randomly selected prediction sets of size \(|C|=2\). @@ -1223,152 +1234,158 @@

📊 Results

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(c) Randomly selected prediction sets of size \(|C|=3\). @@ -1640,7 +1638,7 @@

🧐 Evaluation

To evaluate the performance of conformal models, specific performance measures can be used to assess if the model is correctly specified and well-calibrated (A. N. Angelopoulos and Bates 2022). We will look at this in some more detail in another post in the future. For now, just be aware that these measures are already available in ConformalPrediction.jl and we will briefly showcase them here.

As for many other things, ConformalPrediction.jl taps into the existing functionality of MLJ.jl for model evaluation. In particular, we will see below how we can use the generic evaluate! method on our machine. To assess the correctness of our conformal predictor, we can compute the empirical coverage rate using the custom performance measure emp_coverage. With respect to model calibration we will look at the model’s conditional coverage. For adaptive, well-calibrated conformal models, conditional coverage is high. One general go-to measure for assessing conditional coverage is size-stratified coverage. The custom measure for this purpose is just called size_stratified_coverage, aliased by ssc.

The code below implements the model evaluation using cross-validation. The Simple Inductive Classifier that we used above is not adaptive and hence the attained conditional coverage is low compared to the overall empirical coverage, which is close to \(0.95\), so in line with the desired coverage rate specified above.

-
+
Code 
_eval = evaluate!(
@@ -1653,9 +1651,13 @@ 
🧐 Evaluation

 println("Empirical coverage: $(round(_eval.measurement[1], digits=3))")
 println("SSC: $(round(_eval.measurement[2], digits=3))")
+
+
Evaluating over 6 folds:  33%[========>                ]  ETA: 0:00:05Evaluating over 6 folds:  50%[============>            ]  ETA: 0:00:03Evaluating over 6 folds:  67%[================>        ]  ETA: 0:00:02Evaluating over 6 folds:  83%[====================>    ]  ETA: 0:00:01Evaluating over 6 folds: 100%[=========================] Time: 0:00:05
+Empirical coverage: 0.959
+SSC: 0.791
+
-
-
PerformanceEvaluation object with these fields:
+
PerformanceEvaluation object with these fields:
   measure, operation, measurement, per_fold,
   per_observation, fitted_params_per_fold,
   report_per_fold, train_test_rows
@@ -1663,39 +1665,39 @@ 
🧐 Evaluation

 ┌──────────────────────────────────────────────┬───────────┬─────────────┬──────
 │ measure                                      │ operation │ measurement │ 1.9 ⋯
 ├──────────────────────────────────────────────┼───────────┼─────────────┼──────
-│ ConformalPrediction.emp_coverage             │ predict   │ 0.954       │ 0.0 ⋯
-│ ConformalPrediction.size_stratified_coverage │ predict   │ 0.661       │ 0.3 ⋯
+│ ConformalPrediction.emp_coverage             │ predict   │ 0.959       │ 0.0 ⋯
+│ ConformalPrediction.size_stratified_coverage │ predict   │ 0.791       │ 0.1 ⋯
 └──────────────────────────────────────────────┴───────────┴─────────────┴──────
-                                                               2 columns omitted
-

-
-
-
-
Empirical coverage: 0.954
-SSC: 0.661
+ 2 columns omitted

We can attain higher adaptivity (SSC) when using adaptive prediction sets:

-
+
Code -
conf_model = conformal_model(clf; method=:adaptive_inductive, coverage=.95)
-mach = machine(conf_model, X, y)
-fit!(mach)
-_eval = evaluate!(
-    mach,
-    resampling=CV(),
-    operation=predict,
-    measure=[emp_coverage, ssc]
-)
-results[:adaptive_inductive] = mach
-display(_eval)
-println("Empirical coverage: $(round(_eval.measurement[1], digits=3))")
-println("SSC: $(round(_eval.measurement[2], digits=3))")
+
conf_model = conformal_model(clf; method=:adaptive_inductive, coverage=.95)
+mach = machine(conf_model, X, y)
+fit!(mach)
+_eval = evaluate!(
+    mach,
+    resampling=CV(),
+    operation=predict,
+    measure=[emp_coverage, ssc]
+)
+results[:adaptive_inductive] = mach
+display(_eval)
+println("Empirical coverage: $(round(_eval.measurement[1], digits=3))")
+println("SSC: $(round(_eval.measurement[2], digits=3))")
+
+
[ Info: Training machine(AdaptiveInductiveClassifier(model = ImageClassifier(builder = GenericBuilder(apply = #3), …), …), …).
+Optimising neural net:  18%[====>                    ]  ETA: 0:00:00Optimising neural net:  27%[======>                  ]  ETA: 0:00:01Optimising neural net:  36%[=========>               ]  ETA: 0:00:01Optimising neural net:  45%[===========>             ]  ETA: 0:00:00Optimising neural net:  55%[=============>           ]  ETA: 0:00:00Optimising neural net:  64%[===============>         ]  ETA: 0:00:00Optimising neural net:  73%[==================>      ]  ETA: 0:00:00Optimising neural net:  82%[====================>    ]  ETA: 0:00:00Optimising neural net:  91%[======================>  ]  ETA: 0:00:00Optimising neural net: 100%[=========================] Time: 0:00:00
+Evaluating over 6 folds:  33%[========>                ]  ETA: 0:00:03Evaluating over 6 folds:  50%[============>            ]  ETA: 0:00:02Evaluating over 6 folds:  67%[================>        ]  ETA: 0:00:02Evaluating over 6 folds:  83%[====================>    ]  ETA: 0:00:01Evaluating over 6 folds: 100%[=========================] Time: 0:00:05
+Empirical coverage: 0.996
+SSC: 0.983
+
-
-
PerformanceEvaluation object with these fields:
+
PerformanceEvaluation object with these fields:
   measure, operation, measurement, per_fold,
   per_observation, fitted_params_per_fold,
   report_per_fold, train_test_rows
@@ -1703,134 +1705,121 @@ 
🧐 Evaluation

 ┌──────────────────────────────────────────────┬───────────┬─────────────┬──────
 │ measure                                      │ operation │ measurement │ 1.9 ⋯
 ├──────────────────────────────────────────────┼───────────┼─────────────┼──────
-│ ConformalPrediction.emp_coverage             │ predict   │ 0.995       │ 0.0 ⋯
-│ ConformalPrediction.size_stratified_coverage │ predict   │ 0.981       │ 0.0 ⋯
+│ ConformalPrediction.emp_coverage             │ predict   │ 0.996       │ 0.0 ⋯
+│ ConformalPrediction.size_stratified_coverage │ predict   │ 0.983       │ 0.0 ⋯
 └──────────────────────────────────────────────┴───────────┴─────────────┴──────
-                                                               2 columns omitted
-

-
-
-
-
Empirical coverage: 0.995
-SSC: 0.981
+ 2 columns omitted

We can also have a look at the resulting set size for both approaches using a custom Plots.jl recipe (fig-setsize). In line with the above, the spread is wider for the adaptive approach, which reflects that “the procedure is effectively distinguishing between easy and hard inputs” (A. N. Angelopoulos and Bates 2022).

-
+
Code -
plt_list = []
-for (_mod, mach) in results
-    push!(plt_list, bar(mach.model, mach.fitresult, X; title=String(_mod)))
-end
-plot(plt_list..., size=(800,300))
-plot(plt_list..., size=(800,300),bg_colour=:transparent)
+
plt_list = []
+for (_mod, mach) in results
+    push!(plt_list, bar(mach.model, mach.fitresult, X; title=String(_mod)))
+end
+plot(plt_list..., size=(800,300))
+plot(plt_list..., size=(800,300),bg_colour=:transparent)
-
+
- + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
@@ -2356,284 +2345,284 @@

🔁 Recap

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zz`iVPUMn%B#;=NO-3+TiRtiY;P!I9TP6bTX$fPEu3v~F~2n{XK%H~BZ#8vJCj0%&n zr68sFg?{u=4;siH5Kw7dC-er)dM2LIJ#6&Erx?u70~m+s8Rs?Tsp zqKpMaD`tkHNQtAw?o$~TrNN}=PNfHtPKcDCKvx+pR?3P*Ys?ADI`4#{g=auS=XD+q&WT@)kj@Mn18r47 zScaB@FL@$Mr5z0eFs#bD8Md7T?hu(q-UpW&sQkX?)+8Blpqyz;@A~LQvN+fJ3~u7F zs7;WFZqy5O4zPBvh8Lj)nj}rCK7?QSU(-YdX3M2a)AfYz@Fv%8j)!e-6hHs_vw35RF+F1*8zeNk&9ppxk-x1XMgR z5g%xa;RVNeVLeoW7==TUH~}t% z@GAUz4>SSvqmog~(*p{fWD^Ernzp^Y_gqQ^9ESGYxr6ncbvaWtI zFIVy||8lPSvM?93F&{HBC$lmyGcz}{Ge0vlN3%3fGc{MUHD5C}XR|hMGdFj$H-9rY NhqE}3b2tYC06SS&QLO*~ diff --git a/docs/blog/posts/new-package-energysamplers/index.html b/docs/blog/posts/new-package-energysamplers/index.html index 3ee3f26..ed97981 100644 --- a/docs/blog/posts/new-package-energysamplers/index.html +++ b/docs/blog/posts/new-package-energysamplers/index.html @@ -566,7 +566,7 @@

Energy-Based Sampler
  1. UnconditionalSampler — samples from the unconditional distribution \(p_{\theta}(x)\) as in Grathwohl et al. (2020).
  2. ConditionalSampler — samples from the conditional distribution \(p_{\theta}(x|y)\) as in Grathwohl et al. (2020).
    3. -
  3. JointSampler — samples from the joint distribution \(p_{\theta}(x,y)\) as in Kelly, Zemel, and Grathwohl (2021).
    4. +
  4. JointSampler — samples from the joint distribution \(p_{\theta}(x,y)\) as in (kelly2021directly?).

Example: Joint Energy-Based Model

@@ -2989,9 +2989,6 @@

Worked Example

Grathwohl, Will, Kuan-Chieh Wang, Joern-Henrik Jacobsen, David Duvenaud, Mohammad Norouzi, and Kevin Swersky. 2020. “Your Classifier Is Secretly an Energy Based Model and You Should Treat It Like One.” In International Conference on Learning Representations.
-
-Kelly, Jacob, Richard Zemel, and Will Grathwohl. 2021. “Directly Training Joint Energy-Based Models for Conditional Synthesis and Calibrated Prediction of Multi-Attribute Data.” https://arxiv.org/abs/2108.04227. -
Murphy, Kevin P. 2023. Probabilistic Machine Learning: Advanced Topics. MIT press.
diff --git a/docs/content/research.html b/docs/content/research.html index 5c91849..797a6f9 100644 --- a/docs/content/research.html +++ b/docs/content/research.html @@ -20,7 +20,27 @@ margin: 0 0.8em 0.2em -1em; /* quarto-specific, see https://github.com/quarto-dev/quarto-cli/issues/4556 */ vertical-align: middle; } - +/* CSS for citations */ +div.csl-bib-body { } +div.csl-entry { + clear: both; + margin-bottom: 0em; +} +.hanging-indent div.csl-entry { + margin-left:2em; + text-indent:-2em; +} +div.csl-left-margin { + min-width:2em; + float:left; +} +div.csl-right-inline { + margin-left:2em; + padding-left:1em; +} +div.csl-indent { + margin-left: 2em; +} @@ -141,18 +161,32 @@

On this page

Research using Taija

Taija has been used in the following publications:

    -
  • Conformal Intent Classification and Clarification for Fast and Accurate Intent Recognition [@hengst2024conformal] upcoming in ACL’s NAACL Findings 20241.
    • -
  • Faithful Model Explanations through Energy-Constrained Conformal Counterfactuals [@altmeyer2024faithful] published in Proceedings of the AAAI Conference on Artificial Intelligence 2024.
    • -
  • Explaining Black-Box Models through Counterfactuals [@altmeyer2023explaining] published in JuliaCon Proceedings.
    • -
  • Endogenous Macrodynamics in Algorithmic Recourse [@altmeyer2023endogenous] published in Proceedings of the 2023 IEEE Conference on Secure and Trustworthy Machine Learning (SaTML).
    • +
  • Conformal Intent Classification and Clarification for Fast and Accurate Intent Recognition (Hengst et al. 2024) upcoming in ACL’s NAACL Findings 20241.
    • +
  • Faithful Model Explanations through Energy-Constrained Conformal Counterfactuals (Altmeyer et al. 2024) published in Proceedings of the AAAI Conference on Artificial Intelligence 2024.
    • +
  • Explaining Black-Box Models through Counterfactuals (Altmeyer, Deursen, et al. 2023) published in JuliaCon Proceedings.
    • +
  • Endogenous Macrodynamics in Algorithmic Recourse (Altmeyer et al. 2023) published in Proceedings of the 2023 IEEE Conference on Secure and Trustworthy Machine Learning (SaTML).

If you have used Taija in your research, please let us know so we can add your publication to the list.

+
-

Footnotes

+

References

+
+Altmeyer, Patrick, Giovan Angela, Aleksander Buszydlik, Karol Dobiczek, Arie van Deursen, and Cynthia CS Liem. 2023. “Endogenous Macrodynamics in Algorithmic Recourse.” In 2023 IEEE Conference on Secure and Trustworthy Machine Learning (SaTML), 418–31. IEEE. +
+
+Altmeyer, Patrick, Arie van Deursen, et al. 2023. “Explaining Black-Box Models Through Counterfactuals.” In Proceedings of the JuliaCon Conferences, 1:130. 1. +
+
+Altmeyer, Patrick, Mojtaba Farmanbar, Arie van Deursen, and Cynthia CS Liem. 2024. “Faithful Model Explanations Through Energy-Constrained Conformal Counterfactuals.” In Proceedings of the AAAI Conference on Artificial Intelligence, 38:10829–37. 10. +
+
+Hengst, Floris den, Ralf Wolter, Patrick Altmeyer, and Arda Kaygan. 2024. “Conformal Intent Classification and Clarification for Fast and Accurate Intent Recognition.” https://arxiv.org/abs/2403.18973. +
+

Footnotes

  1. Experiments were run in parallel using Python’s MAPIE and ConformalPrediction.jl, in order to cross-check results. Reported results were produced using MAPIE.↩︎

    2. diff --git a/docs/listings.json b/docs/listings.json index 24f488b..9483da7 100644 --- a/docs/listings.json +++ b/docs/listings.json @@ -2,6 +2,7 @@ { "listing": "/blog/index.html", "items": [ + "/blog/posts/causal-recourse/index.html", "/blog/posts/new-package-energysamplers/index.html", "/blog/posts/conformal-llm/index.html", "/blog/posts/guest-students-laplace/index.html", diff --git a/docs/search.json b/docs/search.json index 61e3598..1864ab3 100644 --- a/docs/search.json +++ b/docs/search.json @@ -137,7 +137,7 @@ "href": "blog/posts/new-package-energysamplers/index.html#energy-based-samplers", "title": "New Package for Energy-Based Sampling", "section": "Energy-Based Samplers", - "text": "Energy-Based Samplers\nIn the context of EBM, the optimisers can be used to sample from a model posterior. To this end, the package provides the following samples:\n\nUnconditionalSampler — samples from the unconditional distribution \\(p_{\\theta}(x)\\) as in Grathwohl et al. (2020).\nConditionalSampler — samples from the conditional distribution \\(p_{\\theta}(x|y)\\) as in Grathwohl et al. (2020).\nJointSampler — samples from the joint distribution \\(p_{\\theta}(x,y)\\) as in Kelly, Zemel, and Grathwohl (2021).\n\n\nExample: Joint Energy-Based Model\nThe conditional sampler is used to draw class-conditional samples from a joint energy-based model (JEM) trained using Taija’s JointEnergyModels.jl. JEMs are explicitly trained to not only discriminate between output classes but also generate inputs. Hence, in the image below we can see that the model’s posterior conditional distributions (both over outputs and inputs) seem to approximate the true underlying distributions reasonably well: the model has learned to discriminate between the two classes (as indicated by the contours) and to generate samples from each class (as indicated by the stars).\n\n\n\nWorked Example\nNext, we will present a simple worked example involving linearly separable Gaussian blobs:\n\n\nCode\nusing Distributions\nusing MLJBase\n\n# Data:\nnobs = 2000\nX, y = make_blobs(nobs; centers=2, center_box=(-2. => 2.), cluster_std=0.1)\nXmat = Float32.(permutedims(matrix(X)))\nX = table(permutedims(Xmat))\nbatch_size = Int(round(nobs / 10))\n\n# Distributions:\n𝒟x = Normal()\n𝒟y = Categorical(ones(2) ./ 2)\n\n\nWe train a simple linear classifier to discriminate between output classes:\n\n\nCode\n# Train a simple neural network on the data (classification)\nXtrain = permutedims(MLJBase.matrix(X))\nytrain = Flux.onehotbatch(y, levels(y))\ntrain_set = zip(eachcol(Xtrain), eachcol(ytrain))\ninputdim = size(first(train_set)[1], 1)\noutputdim = size(first(train_set)[2], 1)\nnn = Chain(Dense(inputdim, outputdim))\nloss(yhat, y) = Flux.logitcrossentropy(yhat, y)\nopt_state = Flux.setup(Flux.Adam(), nn)\nepochs = 5\nfor epoch in 1:epochs\n Flux.train!(nn, train_set, opt_state) do m, x, y\n loss(m(x), y)\n end\n @info \"Epoch $epoch\"\n println(\"Accuracy: \", mean(Flux.onecold(nn(Xtrain)) .== Flux.onecold(ytrain)))\nend\n\n\nFinally, we draw conditional samples from the model. Since we used a purely discriminative model for the task, the estimated posterior conditional distributions over inputs are not very good: the conditionally drawn samples (Xhat) largely lie on the right side of the decision boundary, but they are clearly not generated by the same data generating process as the training data.\n\n\nCode\nusing EnergySamplers: ConditionalSampler, PMC\n\n# PMC\nbs = 10\nntrans = 10\nniter = 100\n# Conditionally sample from first class:\nsmpler = ConditionalSampler(\n 𝒟x, 𝒟y; input_size=size(Xmat)[1:(end - 1)], batch_size=bs\n)\nx1 = PMC(smpler, nn, ImproperSGLD(); ntransitions=ntrans, niter=niter, y=1)\n# Conditionally sample from second class:\nsmpler = ConditionalSampler(\n 𝒟x, 𝒟y; input_size=size(Xmat)[1:(end - 1)], batch_size=bs\n)\nx2 = PMC(smpler, nn, ImproperSGLD(); ntransitions=ntrans, niter=niter, y=2)\n\n# Contour plot for predictions:\nxlims = extrema(hcat(x1,x2)[1,:]) .* 1.1\nylims = extrema(hcat(x1,x2)[2,:]) .* 1.1\nxrange = range(xlims[1], xlims[2], 100)\nyrange = range(ylims[1], ylims[2], 100)\nz = [softmax(nn([x, y])) for x in xrange, y in yrange] |> z -> reduce(hcat, z)\nplt = contourf(xrange, yrange, z[1,:], lw=0.1, xlims=xlims, ylims=ylims)\n\n# Plot samples:\nscatter!(Xtrain[1, :], Xtrain[2, :], color=Int.(y.refs), group=Int.(y.refs), label=[\"X|y=0\" \"X|y=1\"], ms=2, markerstrokecolor=Int.(y.refs))\nscatter!(x1[1, :], x1[2, :], color=1, label=\"Xhat|y=0\", ms=4, alpha=0.5)\nscatter!(x2[1, :], x2[2, :], color=2, label=\"Xhat|y=1\", ms=4, alpha=0.5)\nplot(plt)\n\n\n┌ Warning: Layer with Float32 parameters got Float64 input.\n│ The input will be converted, but any earlier layers may be very slow.\n│ layer = Dense(2 => 2) # 6 parameters\n│ summary(x) = \"2-element Vector{Float64}\"\n└ @ Flux ~/.julia/packages/Flux/HBF2N/src/layers/stateless.jl:60" + "text": "Energy-Based Samplers\nIn the context of EBM, the optimisers can be used to sample from a model posterior. To this end, the package provides the following samples:\n\nUnconditionalSampler — samples from the unconditional distribution \\(p_{\\theta}(x)\\) as in Grathwohl et al. (2020).\nConditionalSampler — samples from the conditional distribution \\(p_{\\theta}(x|y)\\) as in Grathwohl et al. (2020).\nJointSampler — samples from the joint distribution \\(p_{\\theta}(x,y)\\) as in (kelly2021directly?).\n\n\nExample: Joint Energy-Based Model\nThe conditional sampler is used to draw class-conditional samples from a joint energy-based model (JEM) trained using Taija’s JointEnergyModels.jl. JEMs are explicitly trained to not only discriminate between output classes but also generate inputs. Hence, in the image below we can see that the model’s posterior conditional distributions (both over outputs and inputs) seem to approximate the true underlying distributions reasonably well: the model has learned to discriminate between the two classes (as indicated by the contours) and to generate samples from each class (as indicated by the stars).\n\n\n\nWorked Example\nNext, we will present a simple worked example involving linearly separable Gaussian blobs:\n\n\nCode\nusing Distributions\nusing MLJBase\n\n# Data:\nnobs = 2000\nX, y = make_blobs(nobs; centers=2, center_box=(-2. => 2.), cluster_std=0.1)\nXmat = Float32.(permutedims(matrix(X)))\nX = table(permutedims(Xmat))\nbatch_size = Int(round(nobs / 10))\n\n# Distributions:\n𝒟x = Normal()\n𝒟y = Categorical(ones(2) ./ 2)\n\n\nWe train a simple linear classifier to discriminate between output classes:\n\n\nCode\n# Train a simple neural network on the data (classification)\nXtrain = permutedims(MLJBase.matrix(X))\nytrain = Flux.onehotbatch(y, levels(y))\ntrain_set = zip(eachcol(Xtrain), eachcol(ytrain))\ninputdim = size(first(train_set)[1], 1)\noutputdim = size(first(train_set)[2], 1)\nnn = Chain(Dense(inputdim, outputdim))\nloss(yhat, y) = Flux.logitcrossentropy(yhat, y)\nopt_state = Flux.setup(Flux.Adam(), nn)\nepochs = 5\nfor epoch in 1:epochs\n Flux.train!(nn, train_set, opt_state) do m, x, y\n loss(m(x), y)\n end\n @info \"Epoch $epoch\"\n println(\"Accuracy: \", mean(Flux.onecold(nn(Xtrain)) .== Flux.onecold(ytrain)))\nend\n\n\nFinally, we draw conditional samples from the model. Since we used a purely discriminative model for the task, the estimated posterior conditional distributions over inputs are not very good: the conditionally drawn samples (Xhat) largely lie on the right side of the decision boundary, but they are clearly not generated by the same data generating process as the training data.\n\n\nCode\nusing EnergySamplers: ConditionalSampler, PMC\n\n# PMC\nbs = 10\nntrans = 10\nniter = 100\n# Conditionally sample from first class:\nsmpler = ConditionalSampler(\n 𝒟x, 𝒟y; input_size=size(Xmat)[1:(end - 1)], batch_size=bs\n)\nx1 = PMC(smpler, nn, ImproperSGLD(); ntransitions=ntrans, niter=niter, y=1)\n# Conditionally sample from second class:\nsmpler = ConditionalSampler(\n 𝒟x, 𝒟y; input_size=size(Xmat)[1:(end - 1)], batch_size=bs\n)\nx2 = PMC(smpler, nn, ImproperSGLD(); ntransitions=ntrans, niter=niter, y=2)\n\n# Contour plot for predictions:\nxlims = extrema(hcat(x1,x2)[1,:]) .* 1.1\nylims = extrema(hcat(x1,x2)[2,:]) .* 1.1\nxrange = range(xlims[1], xlims[2], 100)\nyrange = range(ylims[1], ylims[2], 100)\nz = [softmax(nn([x, y])) for x in xrange, y in yrange] |> z -> reduce(hcat, z)\nplt = contourf(xrange, yrange, z[1,:], lw=0.1, xlims=xlims, ylims=ylims)\n\n# Plot samples:\nscatter!(Xtrain[1, :], Xtrain[2, :], color=Int.(y.refs), group=Int.(y.refs), label=[\"X|y=0\" \"X|y=1\"], ms=2, markerstrokecolor=Int.(y.refs))\nscatter!(x1[1, :], x1[2, :], color=1, label=\"Xhat|y=0\", ms=4, alpha=0.5)\nscatter!(x2[1, :], x2[2, :], color=2, label=\"Xhat|y=1\", ms=4, alpha=0.5)\nplot(plt)\n\n\n┌ Warning: Layer with Float32 parameters got Float64 input.\n│ The input will be converted, but any earlier layers may be very slow.\n│ layer = Dense(2 => 2) # 6 parameters\n│ summary(x) = \"2-element Vector{Float64}\"\n└ @ Flux ~/.julia/packages/Flux/HBF2N/src/layers/stateless.jl:60" }, { "objectID": "blog/posts/conformal-image-classifier/index.html", @@ -179,7 +179,7 @@ "href": "blog/posts/conformal-image-classifier/index.html#evaluation", "title": "How to Conformalize a Deep Image Classifier", "section": "🧐 Evaluation", - "text": "🧐 Evaluation\nTo evaluate the performance of conformal models, specific performance measures can be used to assess if the model is correctly specified and well-calibrated (A. N. Angelopoulos and Bates 2022). We will look at this in some more detail in another post in the future. For now, just be aware that these measures are already available in ConformalPrediction.jl and we will briefly showcase them here.\nAs for many other things, ConformalPrediction.jl taps into the existing functionality of MLJ.jl for model evaluation. In particular, we will see below how we can use the generic evaluate! method on our machine. To assess the correctness of our conformal predictor, we can compute the empirical coverage rate using the custom performance measure emp_coverage. With respect to model calibration we will look at the model’s conditional coverage. For adaptive, well-calibrated conformal models, conditional coverage is high. One general go-to measure for assessing conditional coverage is size-stratified coverage. The custom measure for this purpose is just called size_stratified_coverage, aliased by ssc.\nThe code below implements the model evaluation using cross-validation. The Simple Inductive Classifier that we used above is not adaptive and hence the attained conditional coverage is low compared to the overall empirical coverage, which is close to \\(0.95\\), so in line with the desired coverage rate specified above.\n\n\nCode\n_eval = evaluate!(\n mach,\n resampling=CV(),\n operation=predict,\n measure=[emp_coverage, ssc]\n)\ndisplay(_eval)\nprintln(\"Empirical coverage: $(round(_eval.measurement[1], digits=3))\")\nprintln(\"SSC: $(round(_eval.measurement[2], digits=3))\")\n\n\n\nPerformanceEvaluation object with these fields:\n measure, operation, measurement, per_fold,\n per_observation, fitted_params_per_fold,\n report_per_fold, train_test_rows\nExtract:\n┌──────────────────────────────────────────────┬───────────┬─────────────┬──────\n│ measure │ operation │ measurement │ 1.9 ⋯\n├──────────────────────────────────────────────┼───────────┼─────────────┼──────\n│ ConformalPrediction.emp_coverage │ predict │ 0.954 │ 0.0 ⋯\n│ ConformalPrediction.size_stratified_coverage │ predict │ 0.661 │ 0.3 ⋯\n└──────────────────────────────────────────────┴───────────┴─────────────┴──────\n 2 columns omitted\n\n\n\n\nEmpirical coverage: 0.954\nSSC: 0.661\n\n\nWe can attain higher adaptivity (SSC) when using adaptive prediction sets:\n\n\nCode\nconf_model = conformal_model(clf; method=:adaptive_inductive, coverage=.95)\nmach = machine(conf_model, X, y)\nfit!(mach)\n_eval = evaluate!(\n mach,\n resampling=CV(),\n operation=predict,\n measure=[emp_coverage, ssc]\n)\nresults[:adaptive_inductive] = mach\ndisplay(_eval)\nprintln(\"Empirical coverage: $(round(_eval.measurement[1], digits=3))\")\nprintln(\"SSC: $(round(_eval.measurement[2], digits=3))\")\n\n\n\nPerformanceEvaluation object with these fields:\n measure, operation, measurement, per_fold,\n per_observation, fitted_params_per_fold,\n report_per_fold, train_test_rows\nExtract:\n┌──────────────────────────────────────────────┬───────────┬─────────────┬──────\n│ measure │ operation │ measurement │ 1.9 ⋯\n├──────────────────────────────────────────────┼───────────┼─────────────┼──────\n│ ConformalPrediction.emp_coverage │ predict │ 0.995 │ 0.0 ⋯\n│ ConformalPrediction.size_stratified_coverage │ predict │ 0.981 │ 0.0 ⋯\n└──────────────────────────────────────────────┴───────────┴─────────────┴──────\n 2 columns omitted\n\n\n\n\nEmpirical coverage: 0.995\nSSC: 0.981\n\n\nWe can also have a look at the resulting set size for both approaches using a custom Plots.jl recipe (fig-setsize). In line with the above, the spread is wider for the adaptive approach, which reflects that “the procedure is effectively distinguishing between easy and hard inputs” (A. N. Angelopoulos and Bates 2022).\n\n\nCode\nplt_list = []\nfor (_mod, mach) in results\n push!(plt_list, bar(mach.model, mach.fitresult, X; title=String(_mod)))\nend\nplot(plt_list..., size=(800,300))\nplot(plt_list..., size=(800,300),bg_colour=:transparent)\n\n\n\n\n\n\n\n \n \n \n\n\n \n \n \n\n\n \n \n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n \n \n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nFigure 3: Distribution of set sizes for both approaches." + "text": "🧐 Evaluation\nTo evaluate the performance of conformal models, specific performance measures can be used to assess if the model is correctly specified and well-calibrated (A. N. Angelopoulos and Bates 2022). We will look at this in some more detail in another post in the future. For now, just be aware that these measures are already available in ConformalPrediction.jl and we will briefly showcase them here.\nAs for many other things, ConformalPrediction.jl taps into the existing functionality of MLJ.jl for model evaluation. In particular, we will see below how we can use the generic evaluate! method on our machine. To assess the correctness of our conformal predictor, we can compute the empirical coverage rate using the custom performance measure emp_coverage. With respect to model calibration we will look at the model’s conditional coverage. For adaptive, well-calibrated conformal models, conditional coverage is high. One general go-to measure for assessing conditional coverage is size-stratified coverage. The custom measure for this purpose is just called size_stratified_coverage, aliased by ssc.\nThe code below implements the model evaluation using cross-validation. The Simple Inductive Classifier that we used above is not adaptive and hence the attained conditional coverage is low compared to the overall empirical coverage, which is close to \\(0.95\\), so in line with the desired coverage rate specified above.\n\n\nCode\n_eval = evaluate!(\n mach,\n resampling=CV(),\n operation=predict,\n measure=[emp_coverage, ssc]\n)\ndisplay(_eval)\nprintln(\"Empirical coverage: $(round(_eval.measurement[1], digits=3))\")\nprintln(\"SSC: $(round(_eval.measurement[2], digits=3))\")\n\n\nEvaluating over 6 folds: 33%[========> ] ETA: 0:00:05Evaluating over 6 folds: 50%[============> ] ETA: 0:00:03Evaluating over 6 folds: 67%[================> ] ETA: 0:00:02Evaluating over 6 folds: 83%[====================> ] ETA: 0:00:01Evaluating over 6 folds: 100%[=========================] Time: 0:00:05\nEmpirical coverage: 0.959\nSSC: 0.791\n\n\nPerformanceEvaluation object with these fields:\n measure, operation, measurement, per_fold,\n per_observation, fitted_params_per_fold,\n report_per_fold, train_test_rows\nExtract:\n┌──────────────────────────────────────────────┬───────────┬─────────────┬──────\n│ measure │ operation │ measurement │ 1.9 ⋯\n├──────────────────────────────────────────────┼───────────┼─────────────┼──────\n│ ConformalPrediction.emp_coverage │ predict │ 0.959 │ 0.0 ⋯\n│ ConformalPrediction.size_stratified_coverage │ predict │ 0.791 │ 0.1 ⋯\n└──────────────────────────────────────────────┴───────────┴─────────────┴──────\n 2 columns omitted\n\n\nWe can attain higher adaptivity (SSC) when using adaptive prediction sets:\n\n\nCode\nconf_model = conformal_model(clf; method=:adaptive_inductive, coverage=.95)\nmach = machine(conf_model, X, y)\nfit!(mach)\n_eval = evaluate!(\n mach,\n resampling=CV(),\n operation=predict,\n measure=[emp_coverage, ssc]\n)\nresults[:adaptive_inductive] = mach\ndisplay(_eval)\nprintln(\"Empirical coverage: $(round(_eval.measurement[1], digits=3))\")\nprintln(\"SSC: $(round(_eval.measurement[2], digits=3))\")\n\n\n[ Info: Training machine(AdaptiveInductiveClassifier(model = ImageClassifier(builder = GenericBuilder(apply = #3), …), …), …).\nOptimising neural net: 18%[====> ] ETA: 0:00:00Optimising neural net: 27%[======> ] ETA: 0:00:01Optimising neural net: 36%[=========> ] ETA: 0:00:01Optimising neural net: 45%[===========> ] ETA: 0:00:00Optimising neural net: 55%[=============> ] ETA: 0:00:00Optimising neural net: 64%[===============> ] ETA: 0:00:00Optimising neural net: 73%[==================> ] ETA: 0:00:00Optimising neural net: 82%[====================> ] ETA: 0:00:00Optimising neural net: 91%[======================> ] ETA: 0:00:00Optimising neural net: 100%[=========================] Time: 0:00:00\nEvaluating over 6 folds: 33%[========> ] ETA: 0:00:03Evaluating over 6 folds: 50%[============> ] ETA: 0:00:02Evaluating over 6 folds: 67%[================> ] ETA: 0:00:02Evaluating over 6 folds: 83%[====================> ] ETA: 0:00:01Evaluating over 6 folds: 100%[=========================] Time: 0:00:05\nEmpirical coverage: 0.996\nSSC: 0.983\n\n\nPerformanceEvaluation object with these fields:\n measure, operation, measurement, per_fold,\n per_observation, fitted_params_per_fold,\n report_per_fold, train_test_rows\nExtract:\n┌──────────────────────────────────────────────┬───────────┬─────────────┬──────\n│ measure │ operation │ measurement │ 1.9 ⋯\n├──────────────────────────────────────────────┼───────────┼─────────────┼──────\n│ ConformalPrediction.emp_coverage │ predict │ 0.996 │ 0.0 ⋯\n│ ConformalPrediction.size_stratified_coverage │ predict │ 0.983 │ 0.0 ⋯\n└──────────────────────────────────────────────┴───────────┴─────────────┴──────\n 2 columns omitted\n\n\nWe can also have a look at the resulting set size for both approaches using a custom Plots.jl recipe (fig-setsize). In line with the above, the spread is wider for the adaptive approach, which reflects that “the procedure is effectively distinguishing between easy and hard inputs” (A. N. Angelopoulos and Bates 2022).\n\n\nCode\nplt_list = []\nfor (_mod, mach) in results\n push!(plt_list, bar(mach.model, mach.fitresult, X; title=String(_mod)))\nend\nplot(plt_list..., size=(800,300))\nplot(plt_list..., size=(800,300),bg_colour=:transparent)\n\n\n\n\n\n\n\n \n \n \n\n\n \n \n \n\n\n \n \n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n \n \n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nFigure 3: Distribution of set sizes for both approaches." }, { "objectID": "blog/posts/conformal-image-classifier/index.html#recap", @@ -196,74 +196,116 @@ "text": "Footnotes\n\n\nFor a full tutorial on how to build an MNIST image classifier relying solely on Flux.jl, check out this tutorial.↩︎" }, { - "objectID": "hero.html", - "href": "hero.html", - "title": "Make sense of your AI models", + "objectID": "blog/posts/guest-students-laplace/index.html", + "href": "blog/posts/guest-students-laplace/index.html", + "title": "Paving the Way Towards Low-Overhead Uncertainty Calibration", "section": "", - "text": "Taija takes part in Julia Season of Contributions\n\n\n\n\n\n\n\nCounterfactual Explanations\n\n\n\n\n\n\n\nConformal Prediction\n\n\n\n\n\n\n\nBayesian Deep Learning\n\n\n\n\n\nPrevoius\n\n\n\nNext\n\n\n\n\n\n\nMake sense of your AI models\nArtificial Intelligence (AI) has been advancing rapidly in recent years. Consequently, Julia’s AI ecosystem has also been growing fast. Taija is an effort to provide users with tools to make sense of the AI models that they train and deploy. Some highlights include:\n\nModel Explainability (CounterfactualExplanations.jl)\nAlgorithmic Recourse (CounterfactualExplanations.jl, AlgorithmicRecourseDynamics.jl)\nPredictive Uncertainty Quantification (ConformalPrediction.jl, LaplaceRedux.jl)\nEffortless Bayesian Deep Learning (LaplaceRedux.jl)\nHybrid Learning (JointEnergyModels.jl)\n\nTaija is a community effort largely maintained by academics and students at TU Delft. We welcome contributions of any kind." + "text": "Guest Blog Post\n\n\n\nThis blog post was originally written by Severin Bratus and colleagues from TU Delft and published on Medium. This version of the post includes only minor edits. If you would like to contribute a guest blog post, please get in touch.\nThis post summarizes a quarter-long second-year BSc coursework project at TU Delft. Our team of five students has made multiple improvements to LaplaceRedux.jl, due to Patrick Altmeyer. Inspired by its Pythonic counterpart, laplacet-torch, this Julia library aims to provide low-overhead Bayesian uncertainty calibration to deep neural networks via Laplace Approximations (Daxberger et al. 2021).\nWe will begin by demystifying the technical terms in the last sentence, in order to explain our contributions to the library and highlight some impressions from the experience. Note that our team has begun working on this PhD-tier subject only having had some introductory courses on probability and statistics, machine learning, and computational intelligence, without any prior exposure to Julia." }, { - "objectID": "content/related.html", - "href": "content/related.html", - "title": "Taija", - "section": "", - "text": "Our packages are currently tailored towards the following larger package ecosystems for AI and machine learning in Julia:\n\nFluxML\nMLJ\n\nOther external packages and ecosystems related to Trustworthy AI in Julia include:\n\nJulia-XAI\nShapML.jl" + "objectID": "blog/posts/guest-students-laplace/index.html#bayesian-learning", + "href": "blog/posts/guest-students-laplace/index.html#bayesian-learning", + "title": "Paving the Way Towards Low-Overhead Uncertainty Calibration", + "section": "Bayesian Learning", + "text": "Bayesian Learning\nUncertainty calibration remains a crucial issue in safety-critical applications of modern AI, as, for instance, in autonomous driving. You would want your car autopilot not only to make accurate predictions but also to indicate when a model prediction is uncertain, to give control back to the human driver.\nA model is well-calibrated if the confidence of a prediction matches its true error rate. Note that you can have well-fit models that are badly calibrated, and vice versa (just like in life, you meet smart people, yet annoyingly arrogant).\nThe standard deep learning training process of gradient descent converges at a weight configuration that minimizes the loss function. The model obtained may be great, yet it is only a point estimate of what the weight parameters should look like.\nHowever, with the sheer immensity of the weight space, neural networks are probably underspecified by the data (or, overfit). As neural networks can approximate highly complex functions, many weight configurations would yield roughly the same training loss, yet with varying abilities to generalize outside the training dataset. This is why there are so many regularization methods out there, to keep the models simpler. One radical, yet effective approach is described by LeCun, Denker, and Solla (1989):\n\n… it is possible to take a perfectly reasonable network, delete half (or more) of the weights and wind up with a network that works just as well, or better.\n\n\n\n\n\n\n\nFigure 1: The loss landscape. One can imagine gradient descent as a particle, let’s say a ball, or a grain of sand, rolling to the bottom of a pit. Then for Bayesian Learning, we have as if a pile of sand poured around at that bottom point, with the pile being thicker where loss is lower. This proverbial sand pile would represent the posterior parameter distribution. Figure due to Amini et al. (2019)\n\n\n\nThe way gradient is usually illustrated is with a picture like the one shown in Figure 1 above a curved terrain of the loss function across the parameter space. Each point of the horizontal plane corresponds to some configuration of parameters. Gradient descent seeks the point at the bottom of this terrain, as the point with the lowest loss, however as the loss-curvature is highly non-convex and high-dimensional there are many directions in which we could move and still maintain a low loss. Thus instead of a singular point we would like to specify a probability distribution around that optimal point. Bayesian methods, and in particular Laplace Approximations, allow us to do this!\nFirstly, the Bayesian approach to neural network uncertainty calibration is that of modelling the posterior using Bayes’ Theorem:\n\\[\np(\\theta \\mid \\mathcal{D}) = \\tfrac{1}{Z} \\,p(\\mathcal{D} \\mid \\theta) \\, p(\\theta), \\qquad Z:= p(\\mathcal{D}) = \\textstyle\\int p(\\mathcal{D} \\mid \\theta) \\, p(\\theta) \\,d\\theta\n\\]\nHere \\(p(\\mathcal{D} \\mid \\theta)\\) is the likelihood of the data given by the parameters \\(\\theta\\). The prior distribution \\(p(\\theta)\\) specifies our beliefs about what the model parameters would be prior to observing the data. Finally, the intractable constant \\(Z\\) is called the evidence: it characterizes the probability of observing \\(\\mathcal{D}\\) as a whole, across all possible parameter settings (see here for details).\nFor models returning a probability distribution (e.g. classifiers), the loss is commonly defined as the negative log-likelihood. Thus if gradient descent minimizes loss, it maximizes the likelihood, producing the maximum likelihood estimate (MLE), which (assuming a uniform prior) also maximizes the posterior. This is why we call this point the maximum a posteriori, or the MAP. It makes sense to model this point as the mode of the posterior distribution, which could, for example, be a normal Gaussian distribution (see also the introductory post on this blog)." }, { - "objectID": "content/related.html#related-software", - "href": "content/related.html#related-software", - "title": "Taija", - "section": "", - "text": "Our packages are currently tailored towards the following larger package ecosystems for AI and machine learning in Julia:\n\nFluxML\nMLJ\n\nOther external packages and ecosystems related to Trustworthy AI in Julia include:\n\nJulia-XAI\nShapML.jl" + "objectID": "blog/posts/guest-students-laplace/index.html#laplace-approximations", + "href": "blog/posts/guest-students-laplace/index.html#laplace-approximations", + "title": "Paving the Way Towards Low-Overhead Uncertainty Calibration", + "section": "Laplace Approximations", + "text": "Laplace Approximations\nWe do this by a simple-yet-smart trick introduced back in the late 18th century by Pierre-Simon Laplace, the self-proclaimed “greatest French mathematician of his time”. In general, the Laplace Approximation (LA) aims to find a Gaussian approximation to a probability density (in our case, the posterior) defined over a set of continuous variables (in our case, the weights) (Bishop 2006). We can then estimate the loss (negative log-likelihood) as its second-order Taylor expansion:\n\\[\n\\mathcal{L}(\\mathcal{D}; \\theta) \\approx \\mathcal{L}(\\mathcal{D}; \\theta_\\text{MAP}) + \\tfrac{1}{2} (\\theta - \\theta_\\text{MAP})^\\intercal \\left( \\nabla^2 _\\theta \\mathcal{L}(\\mathcal{D}; \\theta) \\vert_{\\theta_\\text{MAP}} \\right)(\\theta - \\theta_\\text{MAP})\n\\]\nNote that the first-order Taylor term vanishes at the MAP since it contains the gradient, and the gradient is zero at MAP, since MAP is a maximum, by definition. What remains is the constant (zeroth-order) term, and the second-order term, containing the Hessian, which is a matrix of partial second-order derivatives.\nThen from this approximation, we can derive the long-sought multivariate normal distribution with the MAP as the mean, and the inverted Hessian as the covariance:\n\\[\np(\\theta \\mid \\mathcal{D}) \\approx N(\\theta; \\theta_\\text{MAP}, \\varSigma) \\qquad\\text{with}\\qquad \\varSigma := \\left( \\nabla^2_\\theta \\mathcal{L}(\\mathcal{D};\\theta) \\vert_{\\theta_\\text{MAP}} \\right)^{-1}\n\\]\nThe evidence \\(Z\\) is now also tractably approximated in closed form, allowing us to apply the Bayes’ theorem, to obtain the posterior distribution \\(p(\\theta \\mid \\mathcal{D})\\). We can then express the posterior predictive distribution, for an input \\(x_*\\), prediction \\(f(x_*)\\), to obtain the probability for an output \\(y\\).\nThe evidence \\(Z\\) is now also tractably approximated in closed form, allowing us to apply the Bayes’ theorem, to obtain the posterior distribution \\(p(\\theta \\mid \\mathcal{D})\\). We can then express the posterior predictive distribution, to obtain the probability for an output \\(y\\), given a prediction \\(f(x_*)\\) for an input \\(x_*\\).\n\\[\np(y \\mid f(x_*), \\mathcal{D}) = \\int p(y \\mid f_\\theta(x_*)) \\, p(\\theta \\mid \\mathcal{D}) \\,d\\theta\n\\]\nThis is what we are really after, after all — instead of giving one singular point-estimate prediction \\(\\widehat{y} = f(x_*)\\), we make the neural network give a distribution over \\(y\\).\nHowever, since the Hessian, a square matrix, defines the covariance between all model parameters (upon inversion), of which there may be millions or billions, the computation and storage of the Hessian (not to speak of inversion!) become intractable, as its size scales quadratically with the number of parameters involved. Thus to apply Laplace approximations to large models, we must make some simplifications — which brings us to…" }, { - "objectID": "content/about.html", - "href": "content/about.html", - "title": "Taija", - "section": "", - "text": "Taija currently covers a range of approaches towards making AI systems more trustworthy:\n\nModel Explainability (CounterfactualExplanations.jl)\nAlgorithmic Recourse (CounterfactualExplanations.jl, AlgorithmicRecourseDynamics.jl)\nPredictive Uncertainty Quantification (ConformalPrediction.jl, LaplaceRedux.jl)\nEffortless Bayesian Deep Learning (LaplaceRedux.jl)\nHybrid Learning (JointEnergyModels.jl)\n\nVarious meta packages can be used to extend the core functionality:\n\nPlotting (TaijaPlotting.jl)\nDatasets for testing and benchmarking (TaijaData.jl)\nParallelization (TaijaParallel.jl)\nInteroperability with other programming languages (TaijaInteroperability.jl)\n\nThe TaijaBase.jl package provides common symbols, types and functions that are used across all or multiple Taija packages.\n\n\n\n\n\n\n%%{\n init: {\n 'theme': 'base',\n 'themeVariables': {\n 'primaryColor': '#BB2528',\n 'primaryTextColor': '#fff',\n 'primaryBorderColor': '#7C0000',\n 'lineColor': '#F8B229',\n 'secondaryColor': '#006100',\n 'tertiaryColor': '#e9edfb',\n 'fontFamily': \"avenir\"\n }\n }\n}%%\n\nflowchart TB\n\n classDef taija fill:#389836,stroke:#333,color:#fff;\n classDef core fill:#CB3C33,stroke:#333,color:#fff;\n classDef base fill:#9558B2,stroke:#333,color:#fff;\n\n %% Base\n base[\"TaijaBase.jl\"]\n\n %% Meta\n interop[\"TaijaInteroperability.jl\"]\n data[\"TaijaData.jl\"]\n parallel[\"TaijaParallel.jl\"]\n plotting[\"TaijaPlotting.jl\"]\n\n %% Core\n ce[\"CounterfactualExplanations.jl\"]\n ar[\"AlgorithmiRecourseDynamics.jl\"]\n cp[\"ConformalPrediction.jl\"]\n lr[\"LaplaceRedux.jl\"]\n jem[\"JointEnergyModels.jl\"]\n\n class base base;\n class interop,data,parallel,plotting taija;\n class ce,cp,lr,jem,ar core;\n\n %% Graph\n subgraph \"Meta Packages\"\n data & plotting & parallel & interop\n end\n\n subgraph \"Core Packages\"\n ce & cp & lr & jem & ar\n end\n\n\n\nFigure 1: An overview of the Taija ecosystem.\n\n\n\n\n\n\nWhy Taija?\n\nTaija stands for Trustworthy Artificial Intelligence in Julia. When thinking about a logo that embodies trustworthiness, we quickly landed on 🐶." + "objectID": "blog/posts/guest-students-laplace/index.html#hessian-approximations", + "href": "blog/posts/guest-students-laplace/index.html#hessian-approximations", + "title": "Paving the Way Towards Low-Overhead Uncertainty Calibration", + "section": "Hessian approximations", + "text": "Hessian approximations\nMultiple techniques to approximate the Hessian have arisen from a field adjacent, yet distinct from Bayesian learning — that of second-order optimization, where Hessians are used to accelerate gradient descent convergence.\nOne such approximation is the Fisher information matrix, or simply the Fisher:\n\\[\nF := \\textstyle\\sum_{n=1}^N \\mathbb{E}_{\\widehat{y} \\sim p(y \\mid f_\\theta(x_n))} \\left[ gg^\\intercal \\right] \\quad\\text{with}\\quad g = \\nabla_\\theta \\log p(\\widehat{y} \\mid f_\\theta(x_n)) \\large\\vert_{\\theta_\\text{MAP}}\n\\]\nNote that if instead of sampling the prediction \\(\\widehat{y} ~ p(y \\mid f(x_n))\\) from the model-defined distribution, we take the actual training-set label \\(y_n\\), the resulting matrix is called the empirical Fisher, which is distinct from the Fisher, yet aligns with it under some conditions, and does not generally capture second-order information. See Kunstner et al. (2019) for an excellent discussion on the distinction.\nInstead of the Fisher, one can use the Generalized Gauss-Newton (GGN):\n\\[\nG := \\textstyle\\sum_{n=1}^N J(x_n) \\left( \\nabla^2_{f} \\log p(y_n \\mid f) \\Large\\vert_{f=f_{\\theta_\\text{map}}(x_n)} \\right) J(x_n)^\\intercal\n\\text{with}\\qquad J(x_n) := \\nabla_\\theta f_\\theta(x_n) \\vert_{\\theta_\\text{map}}\n\\]\nHere \\(J(x_n)\\) represents the Jacobian of the model output w.r.t. the parameters. The middle factor \\(\\nabla^2 …\\) is a Hessian of log-likelihood of \\(y_n\\) w.r.t. model output. Note that the model does not necessarily output ready target probabilities — for instance, classifiers output logits, values that define a probability distribution only after the application of the soft-max.\nUnlike the Fisher, GGN does not require the network to define a probabilistic model on its output (Botev, Ritter, and Barber 2017). For models defining an exponential family distribution over the output, the two coincide (Kunstner, Balles, and Hennig 2020). This applies to classifiers since they define a categorical distribution over the output, but not to simple regression models.\nThese matrices are quadratically large, it is infeasible to store them in full. The simplest estimation is to model the matrix as a diagonal — however one can easily contemplate how crude this approximation can be: for 100 parameters, only 1% of the full Hessian is captured.\nA more sophisticated approach, due to Martens and Grosse (2015), is inspired by the observation that in practice the covariance matrices (i.e. inverted Hessians) for neural networks are block-diagonal-dominant. Thus we can effectively model the covariance matrix (and hence the Fisher) as a block-diagonal matrix, where blocks correspond to parameters grouped by layers. Additionally, each block is decomposed into two Kronecker factors, reducing the size of data stored several magnitudes more, at a cost of another assumption.\nLastly, a novel approach is to sketch a low-rank approximation of the Fisher (Sharma, Azizan, and Pavone 2021). Figure 2 shows four Hessian approximation structures:\n\n\n\n\n\n\nFigure 2: (a) Hessian in full, intractable for large networks. (b) Low-rank. (c) Kronecker-factored Approximate Curvature, a block-diagonal method. (d) Diagonal. Source: Daxberger et al. (2021)\n\n\n\nIt is also possible to cut the costs by treating only a subset of the model parameters, i.e. a subnetwork, probabilistically, fixing the remaining parameters at their MAP-estimated values. One special case of subnetwork Laplace that was found to perform well in practice is last-layer Laplace, where the selected subnetwork contains only the weights and biases of the last layer." }, { - "objectID": "content/about.html#about", - "href": "content/about.html#about", + "objectID": "blog/posts/guest-students-laplace/index.html#our-contributions-to-laplaceredux.jl", + "href": "blog/posts/guest-students-laplace/index.html#our-contributions-to-laplaceredux.jl", + "title": "Paving the Way Towards Low-Overhead Uncertainty Calibration", + "section": "Our contributions to LaplaceRedux.jl", + "text": "Our contributions to LaplaceRedux.jl\nIn the scope of the project we have added support for: - multi-class classification, in addition to regression and binary classification; - GGN, in addition to empirical Fisher; - hardware-parallelized batched computation of both the empirical Fisher and the GGN; - subnetwork and last-layer Laplace; - KFAC for multi-class classification with Fisher; and - interfacing with MLJ, a common machine learning framework for Julia.\nWe have also made quality assurance / quality-of-life additions to the repository, adding: - a formatting check in the CI/CD pipeline; - an extensive test suite comparing the results of LaplaceRedux.jl against those of its Python counter-part package laplace-torch; and - a benchmark pipeline tracking possible downturns in performance." + }, + { + "objectID": "blog/posts/guest-students-laplace/index.html#methodology", + "href": "blog/posts/guest-students-laplace/index.html#methodology", + "title": "Paving the Way Towards Low-Overhead Uncertainty Calibration", + "section": "Methodology", + "text": "Methodology\nWe adhered to the Agile/Scrum practices, with two-week-long sprints, and weekly meetings with our formal client, Patrick Altmeyer. We have prioritized the expected requirements by the Moscow method into must-, could-, should-, and won’t-haves. This is all fairly standard for BSc software projects at TU Delft. By the end of the project, we have completed all of our self-assigned must-haves and should-haves." + }, + { + "objectID": "blog/posts/guest-students-laplace/index.html#pain-points", + "href": "blog/posts/guest-students-laplace/index.html#pain-points", + "title": "Paving the Way Towards Low-Overhead Uncertainty Calibration", + "section": "Pain Points", + "text": "Pain Points\nHere we list some obstacles we have encountered along the way: - Julia is slow to compile and load dependencies on less powerful machines. - Stack traces are sometimes rather obscure, though it seems to be the price to pay for macros. - Zygote.jl, the automatic differentiation library, is not self-autodifferentiable – it cannot differentiate its own functions. We would want this since we apply Zygote.jacobians when making predictions with the LA. - There is no accessible tool reporting branch coverage on tests – only line coverage is available. - Limited LSP and Unicode support for Jupyter Lab. - Conversion between Flux and ONNX is not yet implemented. - There is no extension library for Zygote equivalent to BackPACK or ASDL for second-order information.\n\nZygote.jl, the automatic differentiation library, is not self-autodifferentiable: issue. We would want this since we apply Zygote.jacobians when making predictions with the LA.\nThere is no accessible tool reporting branch coverage on tests – only line coverage is available.\nLimited LSP and Unicode support for Jupyter Lab.\nNo conversion between Flux and ONNX is implemented yet ONNX.jl\nThere is no extension library for Zygote equivalent to BackPACK or ASDL for second-order information." + }, + { + "objectID": "blog/posts/guest-students-laplace/index.html#highlights", + "href": "blog/posts/guest-students-laplace/index.html#highlights", + "title": "Paving the Way Towards Low-Overhead Uncertainty Calibration", + "section": "Highlights", + "text": "Highlights\nAnd here is what we found refreshing: - Metaprogramming and first-class support for macros are something completely different for students who are used to Java & Python. - The Julia standard API, and Flux/Zygote, are fairly straightforward to use, and well-thought-out for numerical computing and machine learning." + }, + { + "objectID": "blog/posts/guest-students-laplace/index.html#conclusions", + "href": "blog/posts/guest-students-laplace/index.html#conclusions", + "title": "Paving the Way Towards Low-Overhead Uncertainty Calibration", + "section": "Conclusions", + "text": "Conclusions\nWe have covered some elements of the theory behind Laplace Approximations, laid down our additions to the LaplaceRedux.jl package, and brought out some difficulties we, as complete newcomers to Julia, came across. Hope you have enjoyed the tour, and hopefully it has intrigued you enough to look deeper into Bayesian learning and/or Julia since both are developing at a lively pace. You can check out LaplaceRedux on the JuliaTrustworthyAI GitHub page here. Contributions and comments are welcome!" + }, + { + "objectID": "blog/posts/guest-students-laplace/index.html#acknowedgements", + "href": "blog/posts/guest-students-laplace/index.html#acknowedgements", + "title": "Paving the Way Towards Low-Overhead Uncertainty Calibration", + "section": "Acknowedgements", + "text": "Acknowedgements\nOur team members are Mark Ardman, Severin Bratus, Adelina Cazacu, Andrei Ionescu, and Ivan Makarov. We would like to thank Patrick Altmeyer for the opportunity to work on this unique project and for the continuous guidance throughout the development process. We are also grateful to Sebastijan Dumančić, our coach, Sven van der Voort, our TA mentor, and Antony Bartlett, our supporting advisor." + }, + { + "objectID": "index.html#trustworthy-artificial-intelligence-in-julia", + "href": "index.html#trustworthy-artificial-intelligence-in-julia", "title": "Taija", - "section": "", - "text": "Taija currently covers a range of approaches towards making AI systems more trustworthy:\n\nModel Explainability (CounterfactualExplanations.jl)\nAlgorithmic Recourse (CounterfactualExplanations.jl, AlgorithmicRecourseDynamics.jl)\nPredictive Uncertainty Quantification (ConformalPrediction.jl, LaplaceRedux.jl)\nEffortless Bayesian Deep Learning (LaplaceRedux.jl)\nHybrid Learning (JointEnergyModels.jl)\n\nVarious meta packages can be used to extend the core functionality:\n\nPlotting (TaijaPlotting.jl)\nDatasets for testing and benchmarking (TaijaData.jl)\nParallelization (TaijaParallel.jl)\nInteroperability with other programming languages (TaijaInteroperability.jl)\n\nThe TaijaBase.jl package provides common symbols, types and functions that are used across all or multiple Taija packages.\n\n\n\n\n\n\n%%{\n init: {\n 'theme': 'base',\n 'themeVariables': {\n 'primaryColor': '#BB2528',\n 'primaryTextColor': '#fff',\n 'primaryBorderColor': '#7C0000',\n 'lineColor': '#F8B229',\n 'secondaryColor': '#006100',\n 'tertiaryColor': '#e9edfb',\n 'fontFamily': \"avenir\"\n }\n }\n}%%\n\nflowchart TB\n\n classDef taija fill:#389836,stroke:#333,color:#fff;\n classDef core fill:#CB3C33,stroke:#333,color:#fff;\n classDef base fill:#9558B2,stroke:#333,color:#fff;\n\n %% Base\n base[\"TaijaBase.jl\"]\n\n %% Meta\n interop[\"TaijaInteroperability.jl\"]\n data[\"TaijaData.jl\"]\n parallel[\"TaijaParallel.jl\"]\n plotting[\"TaijaPlotting.jl\"]\n\n %% Core\n ce[\"CounterfactualExplanations.jl\"]\n ar[\"AlgorithmiRecourseDynamics.jl\"]\n cp[\"ConformalPrediction.jl\"]\n lr[\"LaplaceRedux.jl\"]\n jem[\"JointEnergyModels.jl\"]\n\n class base base;\n class interop,data,parallel,plotting taija;\n class ce,cp,lr,jem,ar core;\n\n %% Graph\n subgraph \"Meta Packages\"\n data & plotting & parallel & interop\n end\n\n subgraph \"Core Packages\"\n ce & cp & lr & jem & ar\n end\n\n\n\nFigure 1: An overview of the Taija ecosystem.\n\n\n\n\n\n\nWhy Taija?\n\nTaija stands for Trustworthy Artificial Intelligence in Julia. When thinking about a logo that embodies trustworthiness, we quickly landed on 🐶." + "section": "Trustworthy Artificial Intelligence in Julia", + "text": "Trustworthy Artificial Intelligence in Julia\nTaija is the organization that hosts software geared towards Trustworthy Artificial Intelligence in Julia." }, { - "objectID": "content/sponsors.html", - "href": "content/sponsors.html", + "objectID": "index.html#contribute", + "href": "index.html#contribute", "title": "Taija", - "section": "", - "text": "Some of Taija’s contributors have been partially or fully funded by one or more of the following entities:" + "section": "Contribute", + "text": "Contribute\nWe welcome contributions of any kind. If you want to get involved or use our software for or project, please feel free to reach out. If you have questions, comments or issues related to specific packages, please feel free to open issues or discussions on the respective repository.\n\nWorking on related projects?\nAre you working on a Julia package that would fit well into this organization? Or do you perhaps have ideas for future projects? We’d love to hear about it, so please do get in touch!" }, { - "objectID": "content/sponsors.html#sponsors", - "href": "content/sponsors.html#sponsors", + "objectID": "index.html#contact", + "href": "index.html#contact", "title": "Taija", - "section": "", - "text": "Some of Taija’s contributors have been partially or fully funded by one or more of the following entities:" + "section": "Contact", + "text": "Contact\nProbably the easiest way is to join the JuliaLang Slack and join our #taija channel. You can also post a GitHub Issue on our organization repo. You can find @pat-alt’s socials and contact details on his website: www.patalt.org." }, { - "objectID": "content/research.html", - "href": "content/research.html", + "objectID": "content/news/news.html", + "href": "content/news/news.html", "title": "Taija", "section": "", - "text": "Taija has been used in the following publications:\n\nConformal Intent Classification and Clarification for Fast and Accurate Intent Recognition [@hengst2024conformal] upcoming in ACL’s NAACL Findings 20241.\nFaithful Model Explanations through Energy-Constrained Conformal Counterfactuals [@altmeyer2024faithful] published in Proceedings of the AAAI Conference on Artificial Intelligence 2024.\nExplaining Black-Box Models through Counterfactuals [@altmeyer2023explaining] published in JuliaCon Proceedings.\nEndogenous Macrodynamics in Algorithmic Recourse [@altmeyer2023endogenous] published in Proceedings of the 2023 IEEE Conference on Secure and Trustworthy Machine Learning (SaTML).\n\nIf you have used Taija in your research, please let us know so we can add your publication to the list." + "text": "Taija takes part in Julia Season of Contributions\n\n\n\n\n\n\n\nCounterfactual Explanations\n\n\n\n\n\n\n\nConformal Prediction\n\n\n\n\n\n\n\nBayesian Deep Learning\n\n\n\n\n\nPrevoius\n\n\n\nNext" }, { - "objectID": "content/research.html#research-using-taija", - "href": "content/research.html#research-using-taija", + "objectID": "content/contribute.html", + "href": "content/contribute.html", "title": "Taija", "section": "", - "text": "Taija has been used in the following publications:\n\nConformal Intent Classification and Clarification for Fast and Accurate Intent Recognition [@hengst2024conformal] upcoming in ACL’s NAACL Findings 20241.\nFaithful Model Explanations through Energy-Constrained Conformal Counterfactuals [@altmeyer2024faithful] published in Proceedings of the AAAI Conference on Artificial Intelligence 2024.\nExplaining Black-Box Models through Counterfactuals [@altmeyer2023explaining] published in JuliaCon Proceedings.\nEndogenous Macrodynamics in Algorithmic Recourse [@altmeyer2023endogenous] published in Proceedings of the 2023 IEEE Conference on Secure and Trustworthy Machine Learning (SaTML).\n\nIf you have used Taija in your research, please let us know so we can add your publication to the list." + "text": "We welcome contributions of any kind. If you want to get involved or use our software for or project, please feel free to reach out. If you have questions, comments or issues related to specific packages, please feel free to open issues or discussions on the respective repository.\n\n\nAre you working on a Julia package that would fit well into this organization? Or do you perhaps have ideas for future projects? We’d love to hear about it, so please do get in touch!" }, { - "objectID": "content/research.html#footnotes", - "href": "content/research.html#footnotes", + "objectID": "content/contribute.html#contribute", + "href": "content/contribute.html#contribute", "title": "Taija", - "section": "Footnotes", - "text": "Footnotes\n\n\nExperiments were run in parallel using Python’s MAPIE and ConformalPrediction.jl, in order to cross-check results. Reported results were produced using MAPIE.↩︎" + "section": "", + "text": "We welcome contributions of any kind. If you want to get involved or use our software for or project, please feel free to reach out. If you have questions, comments or issues related to specific packages, please feel free to open issues or discussions on the respective repository.\n\n\nAre you working on a Julia package that would fit well into this organization? Or do you perhaps have ideas for future projects? We’d love to hear about it, so please do get in touch!" }, { "objectID": "content/contact.html", @@ -280,116 +322,109 @@ "text": "Probably the easiest way is to join the JuliaLang Slack and join our #taija channel. You can also post a GitHub Issue on our organization repo. You can find @pat-alt’s socials and contact details on his website: www.patalt.org." }, { - "objectID": "content/contribute.html", - "href": "content/contribute.html", + "objectID": "content/research.html", + "href": "content/research.html", "title": "Taija", "section": "", - "text": "We welcome contributions of any kind. If you want to get involved or use our software for or project, please feel free to reach out. If you have questions, comments or issues related to specific packages, please feel free to open issues or discussions on the respective repository.\n\n\nAre you working on a Julia package that would fit well into this organization? Or do you perhaps have ideas for future projects? We’d love to hear about it, so please do get in touch!" + "text": "Taija has been used in the following publications:\n\nConformal Intent Classification and Clarification for Fast and Accurate Intent Recognition (Hengst et al. 2024) upcoming in ACL’s NAACL Findings 20241.\nFaithful Model Explanations through Energy-Constrained Conformal Counterfactuals (Altmeyer et al. 2024) published in Proceedings of the AAAI Conference on Artificial Intelligence 2024.\nExplaining Black-Box Models through Counterfactuals (Altmeyer, Deursen, et al. 2023) published in JuliaCon Proceedings.\nEndogenous Macrodynamics in Algorithmic Recourse (Altmeyer et al. 2023) published in Proceedings of the 2023 IEEE Conference on Secure and Trustworthy Machine Learning (SaTML).\n\nIf you have used Taija in your research, please let us know so we can add your publication to the list." }, { - "objectID": "content/contribute.html#contribute", - "href": "content/contribute.html#contribute", + "objectID": "content/research.html#research-using-taija", + "href": "content/research.html#research-using-taija", "title": "Taija", "section": "", - "text": "We welcome contributions of any kind. If you want to get involved or use our software for or project, please feel free to reach out. If you have questions, comments or issues related to specific packages, please feel free to open issues or discussions on the respective repository.\n\n\nAre you working on a Julia package that would fit well into this organization? Or do you perhaps have ideas for future projects? We’d love to hear about it, so please do get in touch!" + "text": "Taija has been used in the following publications:\n\nConformal Intent Classification and Clarification for Fast and Accurate Intent Recognition (Hengst et al. 2024) upcoming in ACL’s NAACL Findings 20241.\nFaithful Model Explanations through Energy-Constrained Conformal Counterfactuals (Altmeyer et al. 2024) published in Proceedings of the AAAI Conference on Artificial Intelligence 2024.\nExplaining Black-Box Models through Counterfactuals (Altmeyer, Deursen, et al. 2023) published in JuliaCon Proceedings.\nEndogenous Macrodynamics in Algorithmic Recourse (Altmeyer et al. 2023) published in Proceedings of the 2023 IEEE Conference on Secure and Trustworthy Machine Learning (SaTML).\n\nIf you have used Taija in your research, please let us know so we can add your publication to the list." }, { - "objectID": "content/news/news.html", - "href": "content/news/news.html", + "objectID": "content/research.html#footnotes", + "href": "content/research.html#footnotes", "title": "Taija", - "section": "", - "text": "Taija takes part in Julia Season of Contributions\n\n\n\n\n\n\n\nCounterfactual Explanations\n\n\n\n\n\n\n\nConformal Prediction\n\n\n\n\n\n\n\nBayesian Deep Learning\n\n\n\n\n\nPrevoius\n\n\n\nNext" + "section": "Footnotes", + "text": "Footnotes\n\n\nExperiments were run in parallel using Python’s MAPIE and ConformalPrediction.jl, in order to cross-check results. Reported results were produced using MAPIE.↩︎" }, { - "objectID": "index.html#trustworthy-artificial-intelligence-in-julia", - "href": "index.html#trustworthy-artificial-intelligence-in-julia", + "objectID": "content/sponsors.html", + "href": "content/sponsors.html", "title": "Taija", - "section": "Trustworthy Artificial Intelligence in Julia", - "text": "Trustworthy Artificial Intelligence in Julia\nTaija is the organization that hosts software geared towards Trustworthy Artificial Intelligence in Julia." + "section": "", + "text": "Some of Taija’s contributors have been partially or fully funded by one or more of the following entities:" }, { - "objectID": "index.html#contribute", - "href": "index.html#contribute", + "objectID": "content/sponsors.html#sponsors", + "href": "content/sponsors.html#sponsors", "title": "Taija", - "section": "Contribute", - "text": "Contribute\nWe welcome contributions of any kind. If you want to get involved or use our software for or project, please feel free to reach out. If you have questions, comments or issues related to specific packages, please feel free to open issues or discussions on the respective repository.\n\nWorking on related projects?\nAre you working on a Julia package that would fit well into this organization? Or do you perhaps have ideas for future projects? We’d love to hear about it, so please do get in touch!" + "section": "", + "text": "Some of Taija’s contributors have been partially or fully funded by one or more of the following entities:" }, { - "objectID": "index.html#contact", - "href": "index.html#contact", + "objectID": "content/about.html", + "href": "content/about.html", "title": "Taija", - "section": "Contact", - "text": "Contact\nProbably the easiest way is to join the JuliaLang Slack and join our #taija channel. You can also post a GitHub Issue on our organization repo. You can find @pat-alt’s socials and contact details on his website: www.patalt.org." - }, - { - "objectID": "blog/posts/guest-students-laplace/index.html", - "href": "blog/posts/guest-students-laplace/index.html", - "title": "Paving the Way Towards Low-Overhead Uncertainty Calibration", "section": "", - "text": "Guest Blog Post\n\n\n\nThis blog post was originally written by Severin Bratus and colleagues from TU Delft and published on Medium. This version of the post includes only minor edits. If you would like to contribute a guest blog post, please get in touch.\nThis post summarizes a quarter-long second-year BSc coursework project at TU Delft. Our team of five students has made multiple improvements to LaplaceRedux.jl, due to Patrick Altmeyer. Inspired by its Pythonic counterpart, laplacet-torch, this Julia library aims to provide low-overhead Bayesian uncertainty calibration to deep neural networks via Laplace Approximations (Daxberger et al. 2021).\nWe will begin by demystifying the technical terms in the last sentence, in order to explain our contributions to the library and highlight some impressions from the experience. Note that our team has begun working on this PhD-tier subject only having had some introductory courses on probability and statistics, machine learning, and computational intelligence, without any prior exposure to Julia." + "text": "Taija currently covers a range of approaches towards making AI systems more trustworthy:\n\nModel Explainability (CounterfactualExplanations.jl)\nAlgorithmic Recourse (CounterfactualExplanations.jl, AlgorithmicRecourseDynamics.jl)\nPredictive Uncertainty Quantification (ConformalPrediction.jl, LaplaceRedux.jl)\nEffortless Bayesian Deep Learning (LaplaceRedux.jl)\nHybrid Learning (JointEnergyModels.jl)\n\nVarious meta packages can be used to extend the core functionality:\n\nPlotting (TaijaPlotting.jl)\nDatasets for testing and benchmarking (TaijaData.jl)\nParallelization (TaijaParallel.jl)\nInteroperability with other programming languages (TaijaInteroperability.jl)\n\nThe TaijaBase.jl package provides common symbols, types and functions that are used across all or multiple Taija packages.\n\n\n\n\n\n\n%%{\n init: {\n 'theme': 'base',\n 'themeVariables': {\n 'primaryColor': '#BB2528',\n 'primaryTextColor': '#fff',\n 'primaryBorderColor': '#7C0000',\n 'lineColor': '#F8B229',\n 'secondaryColor': '#006100',\n 'tertiaryColor': '#e9edfb',\n 'fontFamily': \"avenir\"\n }\n }\n}%%\n\nflowchart TB\n\n classDef taija fill:#389836,stroke:#333,color:#fff;\n classDef core fill:#CB3C33,stroke:#333,color:#fff;\n classDef base fill:#9558B2,stroke:#333,color:#fff;\n\n %% Base\n base[\"TaijaBase.jl\"]\n\n %% Meta\n interop[\"TaijaInteroperability.jl\"]\n data[\"TaijaData.jl\"]\n parallel[\"TaijaParallel.jl\"]\n plotting[\"TaijaPlotting.jl\"]\n\n %% Core\n ce[\"CounterfactualExplanations.jl\"]\n ar[\"AlgorithmiRecourseDynamics.jl\"]\n cp[\"ConformalPrediction.jl\"]\n lr[\"LaplaceRedux.jl\"]\n jem[\"JointEnergyModels.jl\"]\n\n class base base;\n class interop,data,parallel,plotting taija;\n class ce,cp,lr,jem,ar core;\n\n %% Graph\n subgraph \"Meta Packages\"\n data & plotting & parallel & interop\n end\n\n subgraph \"Core Packages\"\n ce & cp & lr & jem & ar\n end\n\n\n\nFigure 1: An overview of the Taija ecosystem.\n\n\n\n\n\n\nWhy Taija?\n\nTaija stands for Trustworthy Artificial Intelligence in Julia. When thinking about a logo that embodies trustworthiness, we quickly landed on 🐶." }, { - "objectID": "blog/posts/guest-students-laplace/index.html#bayesian-learning", - "href": "blog/posts/guest-students-laplace/index.html#bayesian-learning", - "title": "Paving the Way Towards Low-Overhead Uncertainty Calibration", - "section": "Bayesian Learning", - "text": "Bayesian Learning\nUncertainty calibration remains a crucial issue in safety-critical applications of modern AI, as, for instance, in autonomous driving. You would want your car autopilot not only to make accurate predictions but also to indicate when a model prediction is uncertain, to give control back to the human driver.\nA model is well-calibrated if the confidence of a prediction matches its true error rate. Note that you can have well-fit models that are badly calibrated, and vice versa (just like in life, you meet smart people, yet annoyingly arrogant).\nThe standard deep learning training process of gradient descent converges at a weight configuration that minimizes the loss function. The model obtained may be great, yet it is only a point estimate of what the weight parameters should look like.\nHowever, with the sheer immensity of the weight space, neural networks are probably underspecified by the data (or, overfit). As neural networks can approximate highly complex functions, many weight configurations would yield roughly the same training loss, yet with varying abilities to generalize outside the training dataset. This is why there are so many regularization methods out there, to keep the models simpler. One radical, yet effective approach is described by LeCun, Denker, and Solla (1989):\n\n… it is possible to take a perfectly reasonable network, delete half (or more) of the weights and wind up with a network that works just as well, or better.\n\n\n\n\n\n\n\nFigure 1: The loss landscape. One can imagine gradient descent as a particle, let’s say a ball, or a grain of sand, rolling to the bottom of a pit. Then for Bayesian Learning, we have as if a pile of sand poured around at that bottom point, with the pile being thicker where loss is lower. This proverbial sand pile would represent the posterior parameter distribution. Figure due to Amini et al. (2019)\n\n\n\nThe way gradient is usually illustrated is with a picture like the one shown in Figure 1 above a curved terrain of the loss function across the parameter space. Each point of the horizontal plane corresponds to some configuration of parameters. Gradient descent seeks the point at the bottom of this terrain, as the point with the lowest loss, however as the loss-curvature is highly non-convex and high-dimensional there are many directions in which we could move and still maintain a low loss. Thus instead of a singular point we would like to specify a probability distribution around that optimal point. Bayesian methods, and in particular Laplace Approximations, allow us to do this!\nFirstly, the Bayesian approach to neural network uncertainty calibration is that of modelling the posterior using Bayes’ Theorem:\n\\[\np(\\theta \\mid \\mathcal{D}) = \\tfrac{1}{Z} \\,p(\\mathcal{D} \\mid \\theta) \\, p(\\theta), \\qquad Z:= p(\\mathcal{D}) = \\textstyle\\int p(\\mathcal{D} \\mid \\theta) \\, p(\\theta) \\,d\\theta\n\\]\nHere \\(p(\\mathcal{D} \\mid \\theta)\\) is the likelihood of the data given by the parameters \\(\\theta\\). The prior distribution \\(p(\\theta)\\) specifies our beliefs about what the model parameters would be prior to observing the data. Finally, the intractable constant \\(Z\\) is called the evidence: it characterizes the probability of observing \\(\\mathcal{D}\\) as a whole, across all possible parameter settings (see here for details).\nFor models returning a probability distribution (e.g. classifiers), the loss is commonly defined as the negative log-likelihood. Thus if gradient descent minimizes loss, it maximizes the likelihood, producing the maximum likelihood estimate (MLE), which (assuming a uniform prior) also maximizes the posterior. This is why we call this point the maximum a posteriori, or the MAP. It makes sense to model this point as the mode of the posterior distribution, which could, for example, be a normal Gaussian distribution (see also the introductory post on this blog)." + "objectID": "content/about.html#about", + "href": "content/about.html#about", + "title": "Taija", + "section": "", + "text": "Taija currently covers a range of approaches towards making AI systems more trustworthy:\n\nModel Explainability (CounterfactualExplanations.jl)\nAlgorithmic Recourse (CounterfactualExplanations.jl, AlgorithmicRecourseDynamics.jl)\nPredictive Uncertainty Quantification (ConformalPrediction.jl, LaplaceRedux.jl)\nEffortless Bayesian Deep Learning (LaplaceRedux.jl)\nHybrid Learning (JointEnergyModels.jl)\n\nVarious meta packages can be used to extend the core functionality:\n\nPlotting (TaijaPlotting.jl)\nDatasets for testing and benchmarking (TaijaData.jl)\nParallelization (TaijaParallel.jl)\nInteroperability with other programming languages (TaijaInteroperability.jl)\n\nThe TaijaBase.jl package provides common symbols, types and functions that are used across all or multiple Taija packages.\n\n\n\n\n\n\n%%{\n init: {\n 'theme': 'base',\n 'themeVariables': {\n 'primaryColor': '#BB2528',\n 'primaryTextColor': '#fff',\n 'primaryBorderColor': '#7C0000',\n 'lineColor': '#F8B229',\n 'secondaryColor': '#006100',\n 'tertiaryColor': '#e9edfb',\n 'fontFamily': \"avenir\"\n }\n }\n}%%\n\nflowchart TB\n\n classDef taija fill:#389836,stroke:#333,color:#fff;\n classDef core fill:#CB3C33,stroke:#333,color:#fff;\n classDef base fill:#9558B2,stroke:#333,color:#fff;\n\n %% Base\n base[\"TaijaBase.jl\"]\n\n %% Meta\n interop[\"TaijaInteroperability.jl\"]\n data[\"TaijaData.jl\"]\n parallel[\"TaijaParallel.jl\"]\n plotting[\"TaijaPlotting.jl\"]\n\n %% Core\n ce[\"CounterfactualExplanations.jl\"]\n ar[\"AlgorithmiRecourseDynamics.jl\"]\n cp[\"ConformalPrediction.jl\"]\n lr[\"LaplaceRedux.jl\"]\n jem[\"JointEnergyModels.jl\"]\n\n class base base;\n class interop,data,parallel,plotting taija;\n class ce,cp,lr,jem,ar core;\n\n %% Graph\n subgraph \"Meta Packages\"\n data & plotting & parallel & interop\n end\n\n subgraph \"Core Packages\"\n ce & cp & lr & jem & ar\n end\n\n\n\nFigure 1: An overview of the Taija ecosystem.\n\n\n\n\n\n\nWhy Taija?\n\nTaija stands for Trustworthy Artificial Intelligence in Julia. When thinking about a logo that embodies trustworthiness, we quickly landed on 🐶." }, { - "objectID": "blog/posts/guest-students-laplace/index.html#laplace-approximations", - "href": "blog/posts/guest-students-laplace/index.html#laplace-approximations", - "title": "Paving the Way Towards Low-Overhead Uncertainty Calibration", - "section": "Laplace Approximations", - "text": "Laplace Approximations\nWe do this by a simple-yet-smart trick introduced back in the late 18th century by Pierre-Simon Laplace, the self-proclaimed “greatest French mathematician of his time”. In general, the Laplace Approximation (LA) aims to find a Gaussian approximation to a probability density (in our case, the posterior) defined over a set of continuous variables (in our case, the weights) (Bishop 2006). We can then estimate the loss (negative log-likelihood) as its second-order Taylor expansion:\n\\[\n\\mathcal{L}(\\mathcal{D}; \\theta) \\approx \\mathcal{L}(\\mathcal{D}; \\theta_\\text{MAP}) + \\tfrac{1}{2} (\\theta - \\theta_\\text{MAP})^\\intercal \\left( \\nabla^2 _\\theta \\mathcal{L}(\\mathcal{D}; \\theta) \\vert_{\\theta_\\text{MAP}} \\right)(\\theta - \\theta_\\text{MAP})\n\\]\nNote that the first-order Taylor term vanishes at the MAP since it contains the gradient, and the gradient is zero at MAP, since MAP is a maximum, by definition. What remains is the constant (zeroth-order) term, and the second-order term, containing the Hessian, which is a matrix of partial second-order derivatives.\nThen from this approximation, we can derive the long-sought multivariate normal distribution with the MAP as the mean, and the inverted Hessian as the covariance:\n\\[\np(\\theta \\mid \\mathcal{D}) \\approx N(\\theta; \\theta_\\text{MAP}, \\varSigma) \\qquad\\text{with}\\qquad \\varSigma := \\left( \\nabla^2_\\theta \\mathcal{L}(\\mathcal{D};\\theta) \\vert_{\\theta_\\text{MAP}} \\right)^{-1}\n\\]\nThe evidence \\(Z\\) is now also tractably approximated in closed form, allowing us to apply the Bayes’ theorem, to obtain the posterior distribution \\(p(\\theta \\mid \\mathcal{D})\\). We can then express the posterior predictive distribution, for an input \\(x_*\\), prediction \\(f(x_*)\\), to obtain the probability for an output \\(y\\).\nThe evidence \\(Z\\) is now also tractably approximated in closed form, allowing us to apply the Bayes’ theorem, to obtain the posterior distribution \\(p(\\theta \\mid \\mathcal{D})\\). We can then express the posterior predictive distribution, to obtain the probability for an output \\(y\\), given a prediction \\(f(x_*)\\) for an input \\(x_*\\).\n\\[\np(y \\mid f(x_*), \\mathcal{D}) = \\int p(y \\mid f_\\theta(x_*)) \\, p(\\theta \\mid \\mathcal{D}) \\,d\\theta\n\\]\nThis is what we are really after, after all — instead of giving one singular point-estimate prediction \\(\\widehat{y} = f(x_*)\\), we make the neural network give a distribution over \\(y\\).\nHowever, since the Hessian, a square matrix, defines the covariance between all model parameters (upon inversion), of which there may be millions or billions, the computation and storage of the Hessian (not to speak of inversion!) become intractable, as its size scales quadratically with the number of parameters involved. Thus to apply Laplace approximations to large models, we must make some simplifications — which brings us to…" + "objectID": "content/related.html", + "href": "content/related.html", + "title": "Taija", + "section": "", + "text": "Our packages are currently tailored towards the following larger package ecosystems for AI and machine learning in Julia:\n\nFluxML\nMLJ\n\nOther external packages and ecosystems related to Trustworthy AI in Julia include:\n\nJulia-XAI\nShapML.jl" }, { - "objectID": "blog/posts/guest-students-laplace/index.html#hessian-approximations", - "href": "blog/posts/guest-students-laplace/index.html#hessian-approximations", - "title": "Paving the Way Towards Low-Overhead Uncertainty Calibration", - "section": "Hessian approximations", - "text": "Hessian approximations\nMultiple techniques to approximate the Hessian have arisen from a field adjacent, yet distinct from Bayesian learning — that of second-order optimization, where Hessians are used to accelerate gradient descent convergence.\nOne such approximation is the Fisher information matrix, or simply the Fisher:\n\\[\nF := \\textstyle\\sum_{n=1}^N \\mathbb{E}_{\\widehat{y} \\sim p(y \\mid f_\\theta(x_n))} \\left[ gg^\\intercal \\right] \\quad\\text{with}\\quad g = \\nabla_\\theta \\log p(\\widehat{y} \\mid f_\\theta(x_n)) \\large\\vert_{\\theta_\\text{MAP}}\n\\]\nNote that if instead of sampling the prediction \\(\\widehat{y} ~ p(y \\mid f(x_n))\\) from the model-defined distribution, we take the actual training-set label \\(y_n\\), the resulting matrix is called the empirical Fisher, which is distinct from the Fisher, yet aligns with it under some conditions, and does not generally capture second-order information. See Kunstner et al. (2019) for an excellent discussion on the distinction.\nInstead of the Fisher, one can use the Generalized Gauss-Newton (GGN):\n\\[\nG := \\textstyle\\sum_{n=1}^N J(x_n) \\left( \\nabla^2_{f} \\log p(y_n \\mid f) \\Large\\vert_{f=f_{\\theta_\\text{map}}(x_n)} \\right) J(x_n)^\\intercal\n\\text{with}\\qquad J(x_n) := \\nabla_\\theta f_\\theta(x_n) \\vert_{\\theta_\\text{map}}\n\\]\nHere \\(J(x_n)\\) represents the Jacobian of the model output w.r.t. the parameters. The middle factor \\(\\nabla^2 …\\) is a Hessian of log-likelihood of \\(y_n\\) w.r.t. model output. Note that the model does not necessarily output ready target probabilities — for instance, classifiers output logits, values that define a probability distribution only after the application of the soft-max.\nUnlike the Fisher, GGN does not require the network to define a probabilistic model on its output (Botev, Ritter, and Barber 2017). For models defining an exponential family distribution over the output, the two coincide (Kunstner, Balles, and Hennig 2020). This applies to classifiers since they define a categorical distribution over the output, but not to simple regression models.\nThese matrices are quadratically large, it is infeasible to store them in full. The simplest estimation is to model the matrix as a diagonal — however one can easily contemplate how crude this approximation can be: for 100 parameters, only 1% of the full Hessian is captured.\nA more sophisticated approach, due to Martens and Grosse (2015), is inspired by the observation that in practice the covariance matrices (i.e. inverted Hessians) for neural networks are block-diagonal-dominant. Thus we can effectively model the covariance matrix (and hence the Fisher) as a block-diagonal matrix, where blocks correspond to parameters grouped by layers. Additionally, each block is decomposed into two Kronecker factors, reducing the size of data stored several magnitudes more, at a cost of another assumption.\nLastly, a novel approach is to sketch a low-rank approximation of the Fisher (Sharma, Azizan, and Pavone 2021). Figure 2 shows four Hessian approximation structures:\n\n\n\n\n\n\nFigure 2: (a) Hessian in full, intractable for large networks. (b) Low-rank. (c) Kronecker-factored Approximate Curvature, a block-diagonal method. (d) Diagonal. Source: Daxberger et al. (2021)\n\n\n\nIt is also possible to cut the costs by treating only a subset of the model parameters, i.e. a subnetwork, probabilistically, fixing the remaining parameters at their MAP-estimated values. One special case of subnetwork Laplace that was found to perform well in practice is last-layer Laplace, where the selected subnetwork contains only the weights and biases of the last layer." + "objectID": "content/related.html#related-software", + "href": "content/related.html#related-software", + "title": "Taija", + "section": "", + "text": "Our packages are currently tailored towards the following larger package ecosystems for AI and machine learning in Julia:\n\nFluxML\nMLJ\n\nOther external packages and ecosystems related to Trustworthy AI in Julia include:\n\nJulia-XAI\nShapML.jl" }, { - "objectID": "blog/posts/guest-students-laplace/index.html#our-contributions-to-laplaceredux.jl", - "href": "blog/posts/guest-students-laplace/index.html#our-contributions-to-laplaceredux.jl", - "title": "Paving the Way Towards Low-Overhead Uncertainty Calibration", - "section": "Our contributions to LaplaceRedux.jl", - "text": "Our contributions to LaplaceRedux.jl\nIn the scope of the project we have added support for: - multi-class classification, in addition to regression and binary classification; - GGN, in addition to empirical Fisher; - hardware-parallelized batched computation of both the empirical Fisher and the GGN; - subnetwork and last-layer Laplace; - KFAC for multi-class classification with Fisher; and - interfacing with MLJ, a common machine learning framework for Julia.\nWe have also made quality assurance / quality-of-life additions to the repository, adding: - a formatting check in the CI/CD pipeline; - an extensive test suite comparing the results of LaplaceRedux.jl against those of its Python counter-part package laplace-torch; and - a benchmark pipeline tracking possible downturns in performance." + "objectID": "hero.html", + "href": "hero.html", + "title": "Make sense of your AI models", + "section": "", + "text": "Taija takes part in Julia Season of Contributions\n\n\n\n\n\n\n\nCounterfactual Explanations\n\n\n\n\n\n\n\nConformal Prediction\n\n\n\n\n\n\n\nBayesian Deep Learning\n\n\n\n\n\nPrevoius\n\n\n\nNext\n\n\n\n\n\n\nMake sense of your AI models\nArtificial Intelligence (AI) has been advancing rapidly in recent years. Consequently, Julia’s AI ecosystem has also been growing fast. Taija is an effort to provide users with tools to make sense of the AI models that they train and deploy. Some highlights include:\n\nModel Explainability (CounterfactualExplanations.jl)\nAlgorithmic Recourse (CounterfactualExplanations.jl, AlgorithmicRecourseDynamics.jl)\nPredictive Uncertainty Quantification (ConformalPrediction.jl, LaplaceRedux.jl)\nEffortless Bayesian Deep Learning (LaplaceRedux.jl)\nHybrid Learning (JointEnergyModels.jl)\n\nTaija is a community effort largely maintained by academics and students at TU Delft. We welcome contributions of any kind." }, { - "objectID": "blog/posts/guest-students-laplace/index.html#methodology", - "href": "blog/posts/guest-students-laplace/index.html#methodology", - "title": "Paving the Way Towards Low-Overhead Uncertainty Calibration", - "section": "Methodology", - "text": "Methodology\nWe adhered to the Agile/Scrum practices, with two-week-long sprints, and weekly meetings with our formal client, Patrick Altmeyer. We have prioritized the expected requirements by the Moscow method into must-, could-, should-, and won’t-haves. This is all fairly standard for BSc software projects at TU Delft. By the end of the project, we have completed all of our self-assigned must-haves and should-haves." + "objectID": "blog/posts/causal-recourse/index.html", + "href": "blog/posts/causal-recourse/index.html", + "title": "When Causality meets Recourse", + "section": "", + "text": "In recent years, the need for interpretable and explainable AI has surged, particularly in high-stakes domains. Counterfactual explanations provide a means to understand how changes to input features could alter the outcomes of machine learning models. This blog post presents a new tool in the CounterfactualExplanations.jl package, developed during my JSoC (Julia Summer of Code) project, which incorporates causal reasoning into counterfactual generation." }, { - "objectID": "blog/posts/guest-students-laplace/index.html#pain-points", - "href": "blog/posts/guest-students-laplace/index.html#pain-points", - "title": "Paving the Way Towards Low-Overhead Uncertainty Calibration", - "section": "Pain Points", - "text": "Pain Points\nHere we list some obstacles we have encountered along the way: - Julia is slow to compile and load dependencies on less powerful machines. - Stack traces are sometimes rather obscure, though it seems to be the price to pay for macros. - Zygote.jl, the automatic differentiation library, is not self-autodifferentiable – it cannot differentiate its own functions. We would want this since we apply Zygote.jacobians when making predictions with the LA. - There is no accessible tool reporting branch coverage on tests – only line coverage is available. - Limited LSP and Unicode support for Jupyter Lab. - Conversion between Flux and ONNX is not yet implemented. - There is no extension library for Zygote equivalent to BackPACK or ASDL for second-order information.\n\nZygote.jl, the automatic differentiation library, is not self-autodifferentiable: issue. We would want this since we apply Zygote.jacobians when making predictions with the LA.\nThere is no accessible tool reporting branch coverage on tests – only line coverage is available.\nLimited LSP and Unicode support for Jupyter Lab.\nNo conversion between Flux and ONNX is implemented yet ONNX.jl\nThere is no extension library for Zygote equivalent to BackPACK or ASDL for second-order information." + "objectID": "blog/posts/causal-recourse/index.html#key-contributions", + "href": "blog/posts/causal-recourse/index.html#key-contributions", + "title": "When Causality meets Recourse", + "section": "Key Contributions", + "text": "Key Contributions\nDuring the project, I contributed to two key repositories:\n\nCounterfactualExplanations.jl: Developed a new tool for generating counterfactual explanations using causal information. This allows users to create smarter perturbations rather than random adjustments, ultimately providing more meaningful insights.\nCausalInference.jl: Implemented a Structural Causal Model (SCM) structure that extracts information from data, laying the groundwork for the causal reasoning capabilities in CounterfactualExplanations.jl.\n\nThis was an amazing experience, not just experience contribute to two repositories simultaneously, but also to work with the mantainers of these repos. I learned a lot about the Julia language and the Julia community. This was possible because of the mentorship of Patrick Altmeyer (CounterfactualExplanations) and Moritz Schauer (CausalInference), who guided me throughout the project and are amazing researchers." }, { - "objectID": "blog/posts/guest-students-laplace/index.html#highlights", - "href": "blog/posts/guest-students-laplace/index.html#highlights", - "title": "Paving the Way Towards Low-Overhead Uncertainty Calibration", - "section": "Highlights", - "text": "Highlights\nAnd here is what we found refreshing: - Metaprogramming and first-class support for macros are something completely different for students who are used to Java & Python. - The Julia standard API, and Flux/Zygote, are fairly straightforward to use, and well-thought-out for numerical computing and machine learning." + "objectID": "blog/posts/causal-recourse/index.html#the-mintgenerator", + "href": "blog/posts/causal-recourse/index.html#the-mintgenerator", + "title": "When Causality meets Recourse", + "section": "The MINTGenerator", + "text": "The MINTGenerator\nIn this project, we developed the MINTGenerator, a counterfactual generator based on the Recourse through Minimal Intervention (MINT) method proposed by Karimi, Schölkopf, and Valera (2021)." }, { - "objectID": "blog/posts/guest-students-laplace/index.html#conclusions", - "href": "blog/posts/guest-students-laplace/index.html#conclusions", - "title": "Paving the Way Towards Low-Overhead Uncertainty Calibration", - "section": "Conclusions", - "text": "Conclusions\nWe have covered some elements of the theory behind Laplace Approximations, laid down our additions to the LaplaceRedux.jl package, and brought out some difficulties we, as complete newcomers to Julia, came across. Hope you have enjoyed the tour, and hopefully it has intrigued you enough to look deeper into Bayesian learning and/or Julia since both are developing at a lively pace. You can check out LaplaceRedux on the JuliaTrustworthyAI GitHub page here. Contributions and comments are welcome!" + "objectID": "blog/posts/causal-recourse/index.html#description", + "href": "blog/posts/causal-recourse/index.html#description", + "title": "When Causality meets Recourse", + "section": "Description", + "text": "Description\nThe MINTGenerator incorporates causal reeasoning in algorithm recourse to achieve minimal interventions when generating a counterfactual explanation. In this sense, the main ideia is that just perturbating a black box model without taking into account the causal relations in the data can guide to misleading recommendations. Here we now shift to a perspective where every action/pertubation is an intervetion in the causal graph of the problem, thus the change is not made just in the intervened upon variable, but also in its childs in the causal structure. The generator utilizes a Structural Causal Model(SCM) to encode the variables in a way that causal effects are propagated and uses a generic gradient-based generator to create the search path, that is, any gradient-base generator (ECCo, REVISE, Watcher, …) can be used with the MINT SCM encoder to generate counterfactual samples in latent space for minimal intervetions algorithm recourse.\nThe MINT algorithm minimizes a loss function that combines the causal constraints of the SCM and the distance between the generated counterfactual and the original input. Since we want a gradient-based generator, we need to pass the constrained optimizaiton problem into an unconstrained one and we do this by using the Lagrangian. Initially, as defined in (Karimi, Schölkopf, and Valera 2021), we aim to aim to find the minimal cost set of actions \\(A\\) (in the form of structural interventions) that results in a counterfactual instance yielding the favorable output from \\(h\\),\n$$\n\\[\\begin{aligned}\n\nA^* \\in \\arg\\min_A \\text{cost}(A; \\mathbf{x}_F)\\\\\n\\textrm{s.t.} \\quad h(\\mathbf{x}_{SCF}) \\neq h(\\mathbf{x}_F) \\; \\; \\text{,}\\\\\n\n\\end{aligned}\\]\n$$\nwhere \\(\\mathbf{x}_F\\) is the original input, \\(\\mathbf{x}_{SCF}\\) is the counterfactual instance, and \\(h\\) is the black-box model. We use the \\(\\mathbf{x}_{SCF}\\) terminology because the counterfactual is derived from the SCM,\n\\[\nx_{SCF_i} =\n\\begin{cases}\nx_{F_i} + \\delta_i, & \\text{if } i \\in I \\\\\nx_{F_i} + f_i(\\text{pa}_{SCF_i}) - f_i(\\text{pa}_{F_i}), & \\text{if } i \\notin I \\; \\; \\text{,}\n\\end{cases}\n\\]\nwhere \\(I\\) is the set of intervened upon variables, \\(f_i\\) is the function that generates the value of the variable \\(i\\) given its parents, and \\(\\text{pa}_{SCF_i}\\) and \\(\\text{pa}_{F_i}\\) are the parents of the variable \\(i\\) in the counterfactual and original instance, respectively. This closed formula for the decision variable \\(\\mathbf{x}_{SCF}\\) is what makes possible to use a gradient-based generator, since with it the lagrangian is differentiable,\n\\[\n\\mathcal{L}(A ; \\lambda) = \\text{cost}(A; \\mathbf{x}_F) + \\lambda \\left(h(\\mathbf{x}_{SCF}) - h(\\mathbf{x}_F) \\right) \\; \\; \\text{,}\n\\]\nor in simple terms and more standard, since \\(\\lambda\\) is constant,\n\\[\n\\mathcal{L_{\\texttt{MINT}}}(\\mathbf{x}_{SCF}) = \\lambda \\text{cost}(\\mathbf{x}_{SCF}; \\mathbf{x}_F) + \\text{yloss}(\\mathbf{x}_{SCF},y^*) \\; \\; \\text{,}\n\\]\nwhere \\(y^*\\) is clearly \\(h(x_F)\\) and \\(\\text{yloss}\\) is :\n\\[\n\\text{yloss}(\\mathbf{x}_{SCF}, y^*) = h \\left(\\left\\{ x_{F_i} + \\delta_i [i \\in I] + \\left(f_i(\\text{pa}_{SCF_i}) - f_i(\\text{pa}_{F_i}) \\right) [i \\notin I] \\right\\}_{i=1}^n \\right) - y^* \\; \\; \\text{.}\n\\]" }, { - "objectID": "blog/posts/guest-students-laplace/index.html#acknowedgements", - "href": "blog/posts/guest-students-laplace/index.html#acknowedgements", - "title": "Paving the Way Towards Low-Overhead Uncertainty Calibration", - "section": "Acknowedgements", - "text": "Acknowedgements\nOur team members are Mark Ardman, Severin Bratus, Adelina Cazacu, Andrei Ionescu, and Ivan Makarov. We would like to thank Patrick Altmeyer for the opportunity to work on this unique project and for the continuous guidance throughout the development process. We are also grateful to Sebastijan Dumančić, our coach, Sven van der Voort, our TA mentor, and Antony Bartlett, our supporting advisor." + "objectID": "blog/posts/causal-recourse/index.html#implementation", + "href": "blog/posts/causal-recourse/index.html#implementation", + "title": "When Causality meets Recourse", + "section": "Implementation", + "text": "Implementation\n\nCausalInference.jl\nIn terms of implementation, we need to capture the causal relations from the data, that’s where CausalInference.jl comes in. However, before the project, the package did not have a SCM structure, in the sense that the methods just captured the topological Directed Acyclic Graph (DAG) that showed the causality ruling the data, that is, no causal structural equations were provided,\n\n\nCode\nusing CausalInference\nusing Plots, GraphRecipes\nusing Random\nRandom.seed!(1)\n\nN = 2000 # number of data points\n\nx = randn(N)\nv = x + randn(N)*0.25\nw = x + randn(N)*0.25\nz = v + w + randn(N)*0.25\ns = z + randn(N)*0.25\n\ndf = (x=x, v=v, w=w, z=z, s=s)\n\nest_g, score = ges(df; penalty=1.0, parallel=true)\n\nplt = graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)], size=(500,500), nodesize=0.3)\nsavefig(plt, \"www/intro.png\")\ndisplay(plt)\n\n\n┌ Warning: Only one thread available\n└ @ CausalInference ~/.julia/packages/CausalInference/ozcj8/src/ges.jl:52\n\n\n\n\n\n \n \n \n\n\n\n \n \n \n\n\n\n \n \n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nSo, our goal was given the DAG provided by the ges method in the causal discovery (Chickering 2003), generate equations that rules each of these causal relations, represented in the DAG as directed edges. The SCM is the union of the DAG and these causal equations, that is, the SCM is a tuple \\((G, \\mathbf{f})\\), where \\(G\\) is the DAG and \\(\\mathbf{f}\\) is the set of functions that generates the value of each variable given its parents.\nOur solution for constructing the structural causal equations was to assume that the data was generated by a linear model, ie, the causal relations were linear. For the DAG provided in the code example we derive\n\\[ v = \\mathcal{b}_v \\]\n\\[ x = \\mathcal{a}_{v \\to x} v + \\mathcal{b}_x \\]\n\\[ w = \\mathcal{a}_{x \\to w} x + \\mathcal{b}_w \\]\n\\[ z = \\mathcal{a}_{v \\to z} v+ \\mathcal{a}_{w \\to z} w + \\mathcal{b}_z \\]\n\\[ s = \\mathcal{a}_{z \\to s} z + \\mathcal{b}_s \\]\nand that’s the tricky thing, as we can see these causal equations are different than the ones that generated the data, but they are the ones that respect the causal system obtained from the obtained DAG. Here \\(\\mathcal{b}_i\\) and \\(\\mathcal{a}_{i \\to j}\\) are the intercept term and the coefficient obtained from the linear regression, respectively. To correctly solve the linear regression respecting the dependencies of the causal graph, we use topological_sort_by_dfs from Graphs.jl.\nNow, with the SCM structure in hand, we see that the representation could be a struct containing the DAG and the coefficients/intercepts of the causal equations, this maps exactly the tuple \\((G, \\mathbf{f})\\) that we defined. However, since we need these equations to be differentiable, we need to define a function that takes the SCM and returns the value of the variable given its parents and using just the coefficients and the DAG, lead to errors, because AutoDiff does not deal well with functions that are conditioned (if statements). So, we need to define a way to retrieve the system of causal equations in a smooth way and that’s where the causal_effects matrix comes to the rescue.\nLet the factual vector of features be denoted as:\n\\[\n\\mathbf{x}_F =\n\\begin{bmatrix}\nx_{F_1} \\\\\nx_{F_2} \\\\\nx_{F_3} \\\\\n\\vdots \\\\\nx_{F_n}\n\\end{bmatrix}\n\\]\nLet the causal_effects matrix be:\n\\[\n\\mathbf{C} =\n\\begin{bmatrix}\na_{11} & a_{12} & \\cdots & a_{1n} & b_1 \\\\\na_{21} & a_{22} & \\cdots & a_{2n} & b_2 \\\\\na_{31} & a_{32} & \\cdots & a_{3n} & b_3 \\\\\n\\vdots & \\vdots & \\ddots & \\vdots & \\vdots \\\\\na_{n1} & a_{n2} & \\cdots & a_{nn} & b_n \\\\\n\\end{bmatrix}\n\\]\nHere, \\(a_{ij}\\) represents the coefficient from the causal effect of \\(x_{F_j}\\) on \\(x_{F_i}\\), and \\(b_i\\) represents the intercept term for the variable \\(x_{F_i}\\).\nThe matrix multiplication of the causal_effects matrix with the factual vector (excluding the bias term) is given by:\n\\[\n\\mathbf{C}_{:, 1:n} \\cdot \\mathbf{x}_F =\n\\begin{bmatrix}\na_{11} & a_{12} & \\cdots & a_{1n} \\\\\na_{21} & a_{22} & \\cdots & a_{2n} \\\\\na_{31} & a_{32} & \\cdots & a_{3n} \\\\\n\\vdots & \\vdots & \\ddots & \\vdots \\\\\na_{n1} & a_{n2} & \\cdots & a_{nn}\n\\end{bmatrix}\n\\begin{bmatrix}\nx_{F_1} \\\\\nx_{F_2} \\\\\nx_{F_3} \\\\\n\\vdots \\\\\nx_{F_n}\n\\end{bmatrix}\n\\]\nFinally, we add the bias term:\n\\[\n\\mathbf{x}_{SCF} = \\mathbf{C}_{:, 1:n} \\cdot \\mathbf{x}_F +\n\\begin{bmatrix}\nb_1 \\\\\nb_2 \\\\\nb_3 \\\\\n\\vdots \\\\\nb_n\n\\end{bmatrix}\n\\]\nIn expanded form:\n\\[\n\\mathbf{x}_{SCF_i} = a_{i1} x_{F_1} + a_{i2} x_{F_2} + \\cdots + a_{in} x_{F_n} + b_i, \\quad \\forall i = 1, 2, \\dots, n\n\\]\nThis equation shows how each counterfactual variable \\(x_{SCF_i}\\) is generated as a linear combination of the factual inputs \\(x_{F_j}\\) based on the causal effects matrix, with an intercept term \\(b_i\\) added for each variable.\nOne can note that the orphan nodes, that is, the nodes that do not have parents in the DAG, are going to be equal to the intercept term \\(\\mathcal{b}_\\hat{o}\\). The intuition behind this is that when we do the linear regression, variables that have no causal parents are just equal to the unconditional mean of the variable, i.e, we get \\(x_{SCF_\\hat{o}} = \\mathbb{E}(x_\\hat{o})\\). Because of this, in some cases a better understanding of the regression is needed, so the residuals are also part of the SCM structure,\n\n\nCode\nstruct SCM\n variables::Vector{String}\n coefficients::Vector{Vector{Float64}}\n residuals::Vector{Vector{Float64}}\n dag::DiGraph\n causal_effects::Matrix{Float64}\nend\n\n\n\n\nCounterfactualExplanations.jl" }, { "objectID": "blog/posts/conformal-prediction/index.html", @@ -515,6 +550,6 @@ "href": "blog/index.html", "title": "Taija’s Blog", "section": "", - "text": "Welcome to Taija’s blog! Here you will find accessible introductions to packages, tutorials and other resources.\n\n\n\n\n\n\nInterested in contributing?\n\n\n\nHave you used one of our packages and found it useful? Or have you perhaps even contributed to one of our packages? We’d love for you to spread the word here! If you’re interested in contributing a blog post, please get in touch or open a pull request.\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nNew Package for Energy-Based Sampling\n\n\nIntroducing EnergySamplers.jl\n\n\nA short post announcing a small new package: EnergySamplers.jl for energy-based sampling.\n\n\n\n\n\nSep 6, 2024\n\n\nPatrick Altmeyer\n\n\n7 min\n\n\n9/6/24, 4:28:55 PM\n\n\n\n\n\n\n\n\n\n\n\n\nBuilding a Conformal Chatbot in Julia\n\n\nHuggingFace, Transformers, and Conformal Prediction - Part 1\n\n\nFor this year’s edition of the ING Analytics Experiment Week, we put ConformalPrediction.jl to work and built a chatbot that can be used for Conformal Intent Recognition.\n\n\n\n\n\nJul 5, 2023\n\n\nPatrick Altmeyer\n\n\n7 min\n\n\n8/28/24, 5:16:41 PM\n\n\n\n\n\n\n\n\n\n\n\n\nPaving the Way Towards Low-Overhead Uncertainty Calibration\n\n\nAn Accessible Intro to Laplace Approximations in Julia for Bayesian Deep Learning\n\n\nA guest blog post by a team of students from TU Delft, who have contributed multiple improvements to LaplaceRedux.jl.\n\n\n\n\n\nJul 4, 2023\n\n\nPatrick Altmeyer, Severin Bratus, Mark Ardman, Adelina Cazacu, Andrei Ionescu, Ivan Makarov\n\n\n11 min\n\n\n8/28/24, 4:44:08 PM\n\n\n\n\n\n\n\n\n\n\n\n\nPrediction Intervals for any Regression Model\n\n\nConformal Prediction in Julia — Part 3\n\n\nThis third post introduces conformal regression by going through a standard machine learning workflow using MLJ.jl and ConformalPrediction.jl.\n\n\n\n\n\nDec 12, 2022\n\n\nPatrick Altmeyer\n\n\n11 min\n\n\n8/28/24, 4:44:08 PM\n\n\n\n\n\n\n\n\n\n\n\n\nHow to Conformalize a Deep Image Classifier\n\n\nConformal Prediction in Julia — Part 2\n\n\nA guide demonstrating how to use ConformalPrediction.jl to conformalize a deep image classifier in a few lines of code.\n\n\n\n\n\nDec 5, 2022\n\n\nPatrick Altmeyer\n\n\n9 min\n\n\n8/28/24, 4:44:08 PM\n\n\n\n\n\n\n\n\n\n\n\n\nConformal Prediction in Julia 🟣🔴🟢\n\n\nConformal Prediction in Julia — Part 1\n\n\nA (very) gentle introduction to Conformal Prediction in Julia using my new package ConformalPrediction.jl.\n\n\n\n\n\nOct 25, 2022\n\n\nPatrick Altmeyer\n\n\n15 min\n\n\n8/28/24, 4:44:08 PM\n\n\n\n\n\n\n\n\n\n\n\n\nA new tool for explainable AI\n\n\nCounterfactual Explanations in Julia — Part I\n\n\nThis post introduces a new Julia package for generating counterfactual explanations. The package can be used to explain machine learning algorithms developed and trained in Julia as well as other popular programming languages like Python and R. \n\n\n\n\n\nApr 20, 2022\n\n\nPatrick Altmeyer\n\n\n12 min\n\n\n8/28/24, 4:44:08 PM\n\n\n\n\n\n\n\n\n\n\n\n\nGo deep, but also … go Bayesian!\n\n\nEffortless Bayesian Deep Learning in Julia — Part I\n\n\nAn introduction to effortless Bayesian deep learning through Laplace approximation coded from scratch in Julia.\n\n\n\n\n\nFeb 18, 2022\n\n\nPatrick Altmeyer\n\n\n12 min\n\n\n8/28/24, 4:44:08 PM\n\n\n\n\n\n\nNo matching items" + "text": "Welcome to Taija’s blog! Here you will find accessible introductions to packages, tutorials and other resources.\n\n\n\n\n\n\nInterested in contributing?\n\n\n\nHave you used one of our packages and found it useful? Or have you perhaps even contributed to one of our packages? We’d love for you to spread the word here! If you’re interested in contributing a blog post, please get in touch or open a pull request.\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nWhen Causality meets Recourse\n\n\nCounterfactual Explanations through Structural Causal Models\n\n\nThis post introduces a new tool in CounterfactualExplanations.jl, enhancing the package with causal reasoning to generate counterfactual explanations. \n\n\n\n\n\nSep 17, 2024\n\n\nPatrick Altmeyer, Jorge Luiz Franco\n\n\n8 min\n\n\n9/17/24, 9:07:54 AM\n\n\n\n\n\n\n\n\n\n\n\n\nNew Package for Energy-Based Sampling\n\n\nIntroducing EnergySamplers.jl\n\n\nA short post announcing a small new package: EnergySamplers.jl for energy-based sampling.\n\n\n\n\n\nSep 6, 2024\n\n\nPatrick Altmeyer\n\n\n7 min\n\n\n9/17/24, 7:52:15 AM\n\n\n\n\n\n\n\n\n\n\n\n\nBuilding a Conformal Chatbot in Julia\n\n\nHuggingFace, Transformers, and Conformal Prediction - Part 1\n\n\nFor this year’s edition of the ING Analytics Experiment Week, we put ConformalPrediction.jl to work and built a chatbot that can be used for Conformal Intent Recognition.\n\n\n\n\n\nJul 5, 2023\n\n\nPatrick Altmeyer\n\n\n7 min\n\n\n8/28/24, 5:16:41 PM\n\n\n\n\n\n\n\n\n\n\n\n\nPaving the Way Towards Low-Overhead Uncertainty Calibration\n\n\nAn Accessible Intro to Laplace Approximations in Julia for Bayesian Deep Learning\n\n\nA guest blog post by a team of students from TU Delft, who have contributed multiple improvements to LaplaceRedux.jl.\n\n\n\n\n\nJul 4, 2023\n\n\nPatrick Altmeyer, Severin Bratus, Mark Ardman, Adelina Cazacu, Andrei Ionescu, Ivan Makarov\n\n\n11 min\n\n\n8/28/24, 4:44:08 PM\n\n\n\n\n\n\n\n\n\n\n\n\nPrediction Intervals for any Regression Model\n\n\nConformal Prediction in Julia — Part 3\n\n\nThis third post introduces conformal regression by going through a standard machine learning workflow using MLJ.jl and ConformalPrediction.jl.\n\n\n\n\n\nDec 12, 2022\n\n\nPatrick Altmeyer\n\n\n11 min\n\n\n8/28/24, 4:44:08 PM\n\n\n\n\n\n\n\n\n\n\n\n\nHow to Conformalize a Deep Image Classifier\n\n\nConformal Prediction in Julia — Part 2\n\n\nA guide demonstrating how to use ConformalPrediction.jl to conformalize a deep image classifier in a few lines of code.\n\n\n\n\n\nDec 5, 2022\n\n\nPatrick Altmeyer\n\n\n9 min\n\n\n9/17/24, 8:26:22 AM\n\n\n\n\n\n\n\n\n\n\n\n\nConformal Prediction in Julia 🟣🔴🟢\n\n\nConformal Prediction in Julia — Part 1\n\n\nA (very) gentle introduction to Conformal Prediction in Julia using my new package ConformalPrediction.jl.\n\n\n\n\n\nOct 25, 2022\n\n\nPatrick Altmeyer\n\n\n15 min\n\n\n8/28/24, 4:44:08 PM\n\n\n\n\n\n\n\n\n\n\n\n\nA new tool for explainable AI\n\n\nCounterfactual Explanations in Julia — Part I\n\n\nThis post introduces a new Julia package for generating counterfactual explanations. The package can be used to explain machine learning algorithms developed and trained in Julia as well as other popular programming languages like Python and R. \n\n\n\n\n\nApr 20, 2022\n\n\nPatrick Altmeyer\n\n\n12 min\n\n\n9/17/24, 8:24:40 AM\n\n\n\n\n\n\n\n\n\n\n\n\nGo deep, but also … go Bayesian!\n\n\nEffortless Bayesian Deep Learning in Julia — Part I\n\n\nAn introduction to effortless Bayesian deep learning through Laplace approximation coded from scratch in Julia.\n\n\n\n\n\nFeb 18, 2022\n\n\nPatrick Altmeyer\n\n\n12 min\n\n\n8/28/24, 4:44:08 PM\n\n\n\n\n\n\nNo matching items" } ] \ No newline at end of file diff --git a/docs/sitemap.xml b/docs/sitemap.xml index 3366ac8..f7f8666 100644 --- a/docs/sitemap.xml +++ b/docs/sitemap.xml @@ -14,51 +14,55 @@ https://www.taija.org/blog/posts/new-package-energysamplers/index.html - 2024-09-06T14:28:55.613Z + 2024-09-17T05:52:15.620Z https://www.taija.org/blog/posts/conformal-image-classifier/index.html - 2024-08-28T14:44:08.491Z + 2024-09-17T06:26:22.958Z - https://www.taija.org/hero.html - 2024-08-29T10:29:47.950Z + https://www.taija.org/blog/posts/guest-students-laplace/index.html + 2024-08-28T14:44:08.555Z - https://www.taija.org/content/related.html - 2024-08-28T10:23:47.260Z + https://www.taija.org/index.html + 2024-08-29T10:29:59.372Z - https://www.taija.org/content/about.html - 2024-08-28T11:28:48.944Z + https://www.taija.org/content/news/news.html + 2024-08-28T12:51:08.043Z - https://www.taija.org/content/sponsors.html - 2024-08-28T10:23:07.830Z + https://www.taija.org/content/contribute.html + 2024-08-28T10:20:28.150Z + + + https://www.taija.org/content/contact.html + 2024-08-28T14:39:18.356Z https://www.taija.org/content/research.html 2024-08-28T10:21:53.352Z - https://www.taija.org/content/contact.html - 2024-08-28T14:39:18.356Z + https://www.taija.org/content/sponsors.html + 2024-08-28T10:23:07.830Z - https://www.taija.org/content/contribute.html - 2024-08-28T10:20:28.150Z + https://www.taija.org/content/about.html + 2024-08-28T11:28:48.944Z - https://www.taija.org/content/news/news.html - 2024-08-28T12:51:08.043Z + https://www.taija.org/content/related.html + 2024-08-28T10:23:47.260Z - https://www.taija.org/index.html - 2024-08-29T10:29:59.372Z + https://www.taija.org/hero.html + 2024-08-29T10:29:47.950Z - https://www.taija.org/blog/posts/guest-students-laplace/index.html - 2024-08-28T14:44:08.555Z + https://www.taija.org/blog/posts/causal-recourse/index.html + 2024-09-17T07:07:54.512Z https://www.taija.org/blog/posts/conformal-prediction/index.html @@ -66,7 +70,7 @@ https://www.taija.org/blog/posts/a-new-tool-for-explainable-ai/index.html - 2024-08-28T14:44:08.424Z + 2024-09-17T06:24:40.540Z https://www.taija.org/blog/posts/conformal-llm/index.html From 73e21358c365f51d684e3252378931d326a08416 Mon Sep 17 00:00:00 2001 From: JorgeLuizFranco Date: Tue, 17 Sep 2024 08:54:21 -0300 Subject: [PATCH 06/13] added begin of CE.jl implementatino --- .../blog/posts/causal-recourse/index copy.qmd | 127 ------------------ profile/blog/posts/causal-recourse/index.html | 26 +++- profile/blog/posts/causal-recourse/index.qmd | 29 ++++ 3 files changed, 53 insertions(+), 129 deletions(-) delete mode 100644 profile/blog/posts/causal-recourse/index copy.qmd diff --git a/profile/blog/posts/causal-recourse/index copy.qmd b/profile/blog/posts/causal-recourse/index copy.qmd deleted file mode 100644 index feef45f..0000000 --- a/profile/blog/posts/causal-recourse/index copy.qmd +++ /dev/null @@ -1,127 +0,0 @@ ---- -title: "When Causal meets Recourse" -subtitle: "Counterfactual Explanations through Structural Causal Models" -bibliography: -date: '2024-09-03' -description: | - This post introduces a new tool in CounterfactualExplanations.jl, enhancing the package with causal reasoning to generate counterfactual explanations. The functionality can be used to explain machine learning algorithms developed in Julia and other popular programming languages like Python and R. Unlike traditional counterfactual generators, this approach utilizes causal information to perturb features intelligently. -author: - - name: Jorge Luiz Franco - url: https://www.linkedin.com/in/jorgelwyz/ -categories: - - counterfactuals - - explainable AI - - causality - - Julia -image: www/intro.gif -execute: - eval: false - echo: true -draft: false ---- - -# Introduction - -In recent years, the need for interpretable and explainable AI has surged, particularly in high-stakes domains. Counterfactual explanations provide a means to understand how changes to input features could alter the outcomes of machine learning models. This blog post presents a new tool in the CounterfactualExplanations.jl package, developed during my JSoC (Julia Summer of Code) project, which incorporates causal reasoning into counterfactual generation. - -# Project Overview - -This project aimed to enhance the CounterfactualExplanations.jl package by infusing it with a robust mathematical foundation for minimal algorithmic recourse, based on the principles of causal reasoning [@karimi2021]. - -## Key Contributions - -During the project, I contributed to two key repositories: - -1. **CounterfactualExplanations.jl**: Developed a new tool for generating counterfactual explanations using causal information. This allows users to create smarter perturbations rather than random adjustments, ultimately providing more meaningful insights. - -2. **CausalInference.jl**: Implemented a Structural Causal Model (SCM) structure that extracts information from data, laying the groundwork for the causal reasoning capabilities in CounterfactualExplanations.jl. - -This was an amazing experience, not just experience contribute to two repositories simultaneously, but also to work with the mantainers of these repos. I learned a lot about the Julia language and the Julia community. This was possible because of the mentorship of Patrick Altmeyer(CounterfactualExplanations) and Moritz Schauer (CausalInference), who guided me throughout the project and are amazing researchers. - - - -## The `MINTGenerator` - -In this project, we developed the MINTGenerator, a counterfactual generator based on the Recourse through Minimal -Intervention (MINT) method proposed by @karimi2021. - -## Description - -The MINTGenerator incorporates causal reeasoning in algorithm recourse to achieve minimal interventions when generating a counterfactual explanation. In this sense, the main ideia is that just perturbating a black box model without taking into account the causal relations in the data can guide to misleading recommendations. Here we now shift to a perspective where every action/pertubation is an intervetion in the causal graph of the problem, thus the change is not made just in the intervened upon variable, but also in its childs in the causal structure. The generator utilizes a Structural Causal Model(SCM) to encode the variables in a way that causal effects are propagated and uses a generic gradient-based generator to create the search path, that is, any gradient-base generator (ECCo, REVISE, Watcher, ...) can be used with the MINT SCM encoder to generate counterfactual samples in latent space for minimal intervetions algorithm recourse. - -The MINT algorithm minimizes a loss function that combines the causal constraints of the SCM and the distance between the generated counterfactual and the original input. Since we want a gradient-based generator, we need to pass the constrained optimizaiton problem into an unconstrained one and we do this by using the Lagrangian. Initially, as defined in [@karimi2021], we aim to aim to find the minimal cost set of actions $A$ (in the form of structural interventions) that results in a counterfactual instance yielding the favorable output from $h$, - - -\begin{aligned} - -A^* \in \arg\min_A \text{cost}(A; \mathbf{x}_F)\\ -\textrm{s.t.} \quad h(\mathbf{x}_{SCF}) \neq h(\mathbf{x}_F) \; \; \text{,}\\ - -\end{aligned} - -where $\mathbf{x}_F$ is the original input, $\mathbf{x}_{SCF}$ is the counterfactual instance, and $h$ is the black-box model. We use the $\mathbf{x}_{SCF}$ terminology because the counterfactual is derived from the SCM, - -\begin{equation} - -x_{SCF_i} = -\begin{cases} -x_{F_i} + \delta_i, & \text{if } i \in I \\ -x_{F_i} + f_i(\text{pa}_{SCF_i}) - f_i(\text{pa}_{F_i}), & \text{if } i \notin I \; \; \text{,} -\end{cases} - -\end{equation} - -where $I$ is the set of intervened upon variables, $f_i$ is the function that generates the value of the variable $i$ given its parents, and $\text{pa}_{SCF_i}$ and $\text{pa}_{F_i}$ are the parents of the variable $i$ in the counterfactual and original instance, respectively. This closed formula for the decision variable $\mathbf{x}_{SCF}$ is what makes possible to use a gradient-based generator, since with it the lagrangian is differentiable, - -\begin{equation} -\mathcal{L}(A ; \lambda) = \text{cost}(A; \mathbf{x}_F) + \lambda \left(h(\mathbf{x}_{SCF}) - h(\mathbf{x}_F) \right) \; \; \text{,} -\end{equation} - -or in simple terms and more standard, since $\lambda$ is constant, - -\begin{equation} -\mathcal{L_{\texttt{MINT}}}(\mathbf{x}_{SCF}) = \lambda \text{cost}(\mathbf{x}_{SCF}; \mathbf{x}_F) + \text{yloss}(\mathbf{x}_{SCF},y^*) \; \; \text{,} -\end{equation} - -where $y^*$ is clearly $h(x_F)$ and $\text{yloss}$ is : - -\begin{equation} -\text{yloss}(\mathbf{x}_{SCF}, y^*) = h \left(\left\{ x_{F_i} + \delta_i [i \in I] + \left(f_i(\text{pa}_{SCF_i}) - f_i(\text{pa}_{F_i}) \right) [i \notin I] \right\}_{i=1}^n \right) - y^* \; \; \text{.} -\end{equation} - - - -## Implementation - -In terms of implementation, we need to capture the causal relations from the data, that's where `CausalInference.jl` comes in. However, before the project, the package did not have a SCM structure, in the sense that the methods just captured the topological Directed Acyclic Graph (DAG) that generated the data, that is, no causal structural equations were provided, - -```{julia} -using CausalInference -using Plots, GraphRecipes -using Random -Random.seed!(1) - -N = 2000 # number of data points - -x = randn(N) -v = x + randn(N)*0.25 -w = x + randn(N)*0.25 -z = v + w + randn(N)*0.25 -s = z + randn(N)*0.25 - -df = (x=x, v=v, w=w, z=z, s=s) - -est_g, score = ges(df; penalty=1.0, parallel=true) - -graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)]) -``` - -So, our goal was given the DAG provided by the `ges` method in the causal discovery [@ges2003], generate equations that rules each of these causal relations, represented in the DAG as directed edges. The SCM is the union of the DAG and these causal equations, that is, the SCM is a tuple $(G, \mathbf{f})$, where $G$ is the DAG and $\mathbf{f}$ is the set of functions that generates the value of each variable given its parents. - -Our solution for constructing the structural causal equations was to assume that the data was generated by a linear model, ie, the causal relations were linear. For the data provided in the code example we have $ v = \mathcal{b}_v $ , $` x = v + \mathcal{b}_v `$, $` w = \epsilon_w + x `$, $` z = \epsilon_z + v + w `$, $s = \epsilon_s + z$, where $\epsilon_i$ is the noise term. - -# Conclusion - - - -# References diff --git a/profile/blog/posts/causal-recourse/index.html b/profile/blog/posts/causal-recourse/index.html index 1597120..6a09123 100644 --- a/profile/blog/posts/causal-recourse/index.html +++ b/profile/blog/posts/causal-recourse/index.html @@ -230,7 +230,7 @@

    Implementation

    CausalInference.jl

    In terms of implementation, we need to capture the causal relations from the data, that’s where CausalInference.jl comes in. However, before the project, the package did not have a SCM structure, in the sense that the methods just captured the topological Directed Acyclic Graph (DAG) that showed the causality ruling the data, that is, no causal structural equations were provided,

    -
    +
    using CausalInference
 using Plots, GraphRecipes
 using Random
@@ -317,7 +317,7 @@ 
    CausalInference.j
 \]
    
 
    This equation shows how each counterfactual variable \(x_{SCF_i}\) is generated as a linear combination of the factual inputs \(x_{F_j}\) based on the causal effects matrix, with an intercept term \(b_i\) added for each variable.
    
 
    One can note that the orphan nodes, that is, the nodes that do not have parents in the DAG, are going to be equal to the intercept term \(\mathcal{b}_\hat{o}\). The intuition behind this is that when we do the linear regression, variables that have no causal parents are just equal to the unconditional mean of the variable, i.e, we get \(x_{SCF_\hat{o}} = \mathbb{E}(x_\hat{o})\). Because of this, in some cases a better understanding of the regression is needed, so the residuals are also part of the SCM structure,
    
-
    
+
    
 
    struct SCM
     variables::Vector{String}
     coefficients::Vector{Vector{Float64}}
@@ -329,6 +329,28 @@ 
    CausalInference.j

    CounterfactualExplanations.jl

    +

    Now, we need to go into the optimization problem previously described. We seek to minimize the lagrangian function we defined where now we have a differentiable function. The standard way to implement generators in CounterfactualExplanations.jl is to use AutoDiff exactly using composable functions in the lagrangian. The definition of \(\mathcal{L_{\texttt{MINT}}}\) is in the same shape of the the others gradient-based generators in the package, so the optimization is straightforward. However, we needed some way to pass the \(x_F\) into the \(x_{SCF}\) and that’s where transformer.jl comes in. This is where InputTransformers are defined in the package and in some way this is what we are doing, we are passing our factual to the “latent” causal space of the counterfactual. Our first step is to create a new kind of InputTransformer that is the SCM itself,

    +
    +
    const TypedInputTransformer = Union{
+    Type{<:StatsBase.AbstractDataTransform},
+    Type{<:MultivariateStats.AbstractDimensionalityReduction},
+    Type{<:GenerativeModels.AbstractGenerativeModel},
+    Type{<:CausalInference.SCM} # The SCM transfromer
+}
    +
    +

    and then we need a way to create this transformer, that’s where we “overload” fit_transformer using CausalInferece.jl,

    +
    +
    function fit_transformer(
+    data::CounterfactualData, input_encoder::Type{<:CausalInference.SCM}; kwargs...
+)
+    t = Tables.table(transpose(data.X))
+    est_g, score = CausalInference.ges(t; penalty=1.0, parallel=true)
+    est_dag = CausalInference.pdag2dag!(est_g)
+    scm = CausalInference.estimate_equations(t, est_dag)
+    return scm
+end
    +
    +

    .

diff --git a/profile/blog/posts/causal-recourse/index.qmd b/profile/blog/posts/causal-recourse/index.qmd index cc2bb1d..ad68e8e 100644 --- a/profile/blog/posts/causal-recourse/index.qmd +++ b/profile/blog/posts/causal-recourse/index.qmd @@ -220,6 +220,35 @@ end ### `CounterfactualExplanations.jl` +Now, we need to go into the optimization problem previously described. We seek to minimize the lagrangian function we defined where now we have a differentiable function. The standard way to implement generators in `CounterfactualExplanations.jl` is to use `AutoDiff` exactly using composable functions in the lagrangian. The definition of $\mathcal{L_{\texttt{MINT}}}$ is in the same shape of the the others gradient-based generators in the package, so the optimization is straightforward. However, we needed some way to pass the $x_F$ into the $x_{SCF}$ and that's where `transformer.jl` comes in. This is where `InputTransformer`s are defined in the package and in some way this is what we are doing, we are passing our factual to the "latent" causal space of the counterfactual. Our first step is to create a new kind of `InputTransformer` that is the SCM itself, + +```{julia} +const TypedInputTransformer = Union{ + Type{<:StatsBase.AbstractDataTransform}, + Type{<:MultivariateStats.AbstractDimensionalityReduction}, + Type{<:GenerativeModels.AbstractGenerativeModel}, + Type{<:CausalInference.SCM} # The SCM transfromer +} +``` + +and then we need a way to create this transformer, that's where we "overload" `fit_transformer` using `CausalInferece.jl`, + +```{julia} +function fit_transformer( + data::CounterfactualData, input_encoder::Type{<:CausalInference.SCM}; kwargs... +) + t = Tables.table(transpose(data.X)) + est_g, score = CausalInference.ges(t; penalty=1.0, parallel=true) + est_dag = CausalInference.pdag2dag!(est_g) + scm = CausalInference.estimate_equations(t, est_dag) + return scm +end +``` +... We are getting there! However, now comes the hardest part, where this is placed? + + + + # Conclusion From 36adbbfb699d11f1ad2d8ea2b2592fa1067b0d73 Mon Sep 17 00:00:00 2001 From: pat-alt Date: Tue, 17 Sep 2024 14:02:18 +0200 Subject: [PATCH 07/13] rerendered --- .../index/execute-results/html.json | 4 ++-- profile/blog/posts/causal-recourse/index.qmd | 2 +- .../blog/posts/causal-recourse/www/intro.png | Bin 20746 -> 12517 bytes 3 files changed, 3 insertions(+), 3 deletions(-) diff --git a/profile/_freeze/blog/posts/causal-recourse/index/execute-results/html.json b/profile/_freeze/blog/posts/causal-recourse/index/execute-results/html.json index d24ec6f..d347bce 100644 --- a/profile/_freeze/blog/posts/causal-recourse/index/execute-results/html.json +++ b/profile/_freeze/blog/posts/causal-recourse/index/execute-results/html.json @@ -1,8 +1,8 @@ { - "hash": "72a0783834c8c2c8385acb8b156a59f3", + "hash": "cc0cc232d9ce1a91f7c42084f0162fdc", "result": { "engine": "julia", - "markdown": "---\ntitle: \"When Causality meets Recourse\"\nsubtitle: \"Counterfactual Explanations through Structural Causal Models\"\ndate: '2024-09-17'\ndescription: |\n This post introduces a new tool in CounterfactualExplanations.jl, enhancing the package with causal reasoning to generate counterfactual explanations.\nauthor: \n - name: Jorge Luiz Franco \n url: https://www.linkedin.com/in/jorgelwyz/\ncategories:\n - counterfactuals\n - explainable AI\n - causality\n - Julia\nimage: www/intro.png\nexecute:\n eval: true\n echo: true\nengine: julia\njulia: \n exeflags: [\"--project=./\"]\ncode-fold: show\n---\n\n\n\n# Introduction\n\nIn recent years, the need for interpretable and explainable AI has surged, particularly in high-stakes domains. Counterfactual explanations provide a means to understand how changes to input features could alter the outcomes of machine learning models. This blog post presents a new tool in the CounterfactualExplanations.jl package, developed during my JSoC (Julia Summer of Code) project, which incorporates causal reasoning into counterfactual generation.\n\n# Project Overview\n\nThis project aimed to enhance the CounterfactualExplanations.jl package by infusing it with a robust mathematical foundation for minimal algorithmic recourse, based on the principles of causal reasoning [@karimi2021algorithmic]. \n\n## Key Contributions\n\nDuring the project, I contributed to two key repositories:\n\n1. **CounterfactualExplanations.jl**: Developed a new tool for generating counterfactual explanations using causal information. This allows users to create smarter perturbations rather than random adjustments, ultimately providing more meaningful insights.\n\n2. **CausalInference.jl**: Implemented a Structural Causal Model (SCM) structure that extracts information from data, laying the groundwork for the causal reasoning capabilities in CounterfactualExplanations.jl.\n\nThis was an amazing experience, not just experience contribute to two repositories simultaneously, but also to work with the mantainers of these repos. I learned a lot about the Julia language and the Julia community. This was possible because of the mentorship of Patrick Altmeyer (CounterfactualExplanations) and Moritz Schauer (CausalInference), who guided me throughout the project and are amazing researchers.\n\n## The `MINTGenerator`\n\nIn this project, we developed the MINTGenerator, a counterfactual generator based on the Recourse through Minimal\nIntervention (MINT) method proposed by @karimi2021algorithmic.\n\n## Description\n\nThe MINTGenerator incorporates causal reeasoning in algorithm recourse to achieve minimal interventions when generating a counterfactual explanation. In this sense, the main ideia is that just perturbating a black box model without taking into account the causal relations in the data can guide to misleading recommendations. Here we now shift to a perspective where every action/pertubation is an intervetion in the causal graph of the problem, thus the change is not made just in the intervened upon variable, but also in its childs in the causal structure. The generator utilizes a Structural Causal Model(SCM) to encode the variables in a way that causal effects are propagated and uses a generic gradient-based generator to create the search path, that is, any gradient-base generator (ECCo, REVISE, Watcher, ...) can be used with the MINT SCM encoder to generate counterfactual samples in latent space for minimal intervetions algorithm recourse.\n\nThe MINT algorithm minimizes a loss function that combines the causal constraints of the SCM and the distance between the generated counterfactual and the original input. Since we want a gradient-based generator, we need to pass the constrained optimizaiton problem into an unconstrained one and we do this by using the Lagrangian. Initially, as defined in [@karimi2021algorithmic], we aim to aim to find the minimal cost set of actions $A$ (in the form of structural interventions) that results in a counterfactual instance yielding the favorable output from $h$,\n\n$$\n\\begin{aligned}\n\nA^* \\in \\arg\\min_A \\text{cost}(A; \\mathbf{x}_F)\\\\\n\\textrm{s.t.} \\quad h(\\mathbf{x}_{SCF}) \\neq h(\\mathbf{x}_F) \\; \\; \\text{,}\\\\\n\n\\end{aligned} \n$$\n\nwhere $\\mathbf{x}_F$ is the original input, $\\mathbf{x}_{SCF}$ is the counterfactual instance, and $h$ is the black-box model. We use the $\\mathbf{x}_{SCF}$ terminology because the counterfactual is derived from the SCM,\n\n$$\nx_{SCF_i} = \n\\begin{cases}\nx_{F_i} + \\delta_i, & \\text{if } i \\in I \\\\\nx_{F_i} + f_i(\\text{pa}_{SCF_i}) - f_i(\\text{pa}_{F_i}), & \\text{if } i \\notin I \\; \\; \\text{,}\n\\end{cases} \n$$\n\nwhere $I$ is the set of intervened upon variables, $f_i$ is the function that generates the value of the variable $i$ given its parents, and $\\text{pa}_{SCF_i}$ and $\\text{pa}_{F_i}$ are the parents of the variable $i$ in the counterfactual and original instance, respectively. This closed formula for the decision variable $\\mathbf{x}_{SCF}$ is what makes possible to use a gradient-based generator, since with it the lagrangian is differentiable,\n\n$$\n\\mathcal{L}(A ; \\lambda) = \\text{cost}(A; \\mathbf{x}_F) + \\lambda \\left(h(\\mathbf{x}_{SCF}) - h(\\mathbf{x}_F) \\right) \\; \\; \\text{,}\n$$\n\nor in simple terms and more standard, since $\\lambda$ is constant,\n\n$$\n\\mathcal{L_{\\texttt{MINT}}}(\\mathbf{x}_{SCF}) = \\lambda \\text{cost}(\\mathbf{x}_{SCF}; \\mathbf{x}_F) + \\text{yloss}(\\mathbf{x}_{SCF},y^*) \\; \\; \\text{,}\n$$\n\nwhere $y^*$ is clearly $h(x_F)$ and $\\text{yloss}$ is : \n\n$$\n\\text{yloss}(\\mathbf{x}_{SCF}, y^*) = h \\left(\\left\\{ x_{F_i} + \\delta_i [i \\in I] + \\left(f_i(\\text{pa}_{SCF_i}) - f_i(\\text{pa}_{F_i}) \\right) [i \\notin I] \\right\\}_{i=1}^n \\right) - y^* \\; \\; \\text{.} \n$$\n\n## Implementation\n\n### `CausalInference.jl`\n\nIn terms of implementation, we need to capture the causal relations from the data, that's where `CausalInference.jl` comes in. However, before the project, the package did not have a SCM structure, in the sense that the methods just captured the topological Directed Acyclic Graph (DAG) that showed the causality ruling the data, that is, no causal structural equations were provided,\n\n\n\n::: {#2 .cell execution_count=1}\n``` {.julia .cell-code}\nusing CausalInference\nusing Plots, GraphRecipes\nusing Random\nRandom.seed!(1)\n\nN = 2000 # number of data points\n\nx = randn(N)\nv = x + randn(N)*0.25\nw = x + randn(N)*0.25\nz = v + w + randn(N)*0.25\ns = z + randn(N)*0.25\n\ndf = (x=x, v=v, w=w, z=z, s=s)\n\nest_g, score = ges(df; penalty=1.0, parallel=true)\n\nplt = graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)], size=(500,500), nodesize=0.3)\nsavefig(plt, \"www/intro.png\")\ndisplay(plt)\n```\n\n::: {.cell-output .cell-output-stdout}\n```\n┌ Warning: Only one thread available\n└ @ CausalInference ~/.julia/packages/CausalInference/ozcj8/src/ges.jl:52\n```\n:::\n\n::: {.cell-output .cell-output-display}\n```{=html}\n\n\n\n \n \n \n\n\n\n \n \n \n\n\n\n \n \n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n```\n:::\n:::\n\n\n\n\n\nSo, our goal was given the DAG provided by the `ges` method in the causal discovery [@chickering2003optimal], generate equations that rules each of these causal relations, represented in the DAG as directed edges. The SCM is the union of the DAG and these causal equations, that is, the SCM is a tuple $(G, \\mathbf{f})$, where $G$ is the DAG and $\\mathbf{f}$ is the set of functions that generates the value of each variable given its parents. \n\nOur solution for constructing the structural causal equations was to assume that the data was generated by a linear model, ie, the causal relations were linear. For the DAG provided in the code example we derive\n\n$$ v = \\mathcal{b}_v $$\n\n$$ x = \\mathcal{a}_{v \\to x} v + \\mathcal{b}_x $$\n\n$$ w = \\mathcal{a}_{x \\to w} x + \\mathcal{b}_w $$\n\n$$ z = \\mathcal{a}_{v \\to z} v+ \\mathcal{a}_{w \\to z} w + \\mathcal{b}_z $$\n\n$$ s = \\mathcal{a}_{z \\to s} z + \\mathcal{b}_s $$\n\nand that's the tricky thing, as we can see these causal equations are different than the ones that generated the data, but they are the ones that respect the causal system obtained from the obtained DAG. Here $\\mathcal{b}_i$ and $\\mathcal{a}_{i \\to j}$ are the intercept term and the coefficient obtained from the linear regression, respectively. To correctly solve the linear regression respecting the dependencies of the causal graph, we use `topological_sort_by_dfs` from `Graphs.jl`.\n\nNow, with the SCM structure in hand, we see that the representation could be a struct containing the DAG and the coefficients/intercepts of the causal equations, this maps exactly the tuple $(G, \\mathbf{f})$ that we defined. However, since we need these equations to be differentiable, we need to define a function that takes the SCM and returns the value of the variable given its parents and using just the coefficients and the DAG, lead to errors, because `AutoDiff` does not deal well with functions that are conditioned (`if` statements). So, we need to define a way to retrieve the system of causal equations in a smooth way and that's where the `causal_effects` matrix comes to the rescue.\n\nLet the factual vector of features be denoted as:\n\n$$\n\\mathbf{x}_F = \n\\begin{bmatrix}\nx_{F_1} \\\\\nx_{F_2} \\\\\nx_{F_3} \\\\\n\\vdots \\\\\nx_{F_n}\n\\end{bmatrix}\n$$\n\nLet the `causal_effects` matrix be:\n\n$$\n\\mathbf{C} =\n\\begin{bmatrix}\na_{11} & a_{12} & \\cdots & a_{1n} & b_1 \\\\\na_{21} & a_{22} & \\cdots & a_{2n} & b_2 \\\\\na_{31} & a_{32} & \\cdots & a_{3n} & b_3 \\\\\n\\vdots & \\vdots & \\ddots & \\vdots & \\vdots \\\\\na_{n1} & a_{n2} & \\cdots & a_{nn} & b_n \\\\\n\\end{bmatrix}\n$$\n\nHere, $a_{ij}$ represents the coefficient from the causal effect of $x_{F_j}$ on $x_{F_i}$, and $b_i$ represents the intercept term for the variable $x_{F_i}$.\n\nThe matrix multiplication of the `causal_effects` matrix with the factual vector (excluding the bias term) is given by:\n\n$$\n\\mathbf{C}_{:, 1:n} \\cdot \\mathbf{x}_F =\n\\begin{bmatrix}\na_{11} & a_{12} & \\cdots & a_{1n} \\\\\na_{21} & a_{22} & \\cdots & a_{2n} \\\\\na_{31} & a_{32} & \\cdots & a_{3n} \\\\\n\\vdots & \\vdots & \\ddots & \\vdots \\\\\na_{n1} & a_{n2} & \\cdots & a_{nn}\n\\end{bmatrix}\n\\begin{bmatrix}\nx_{F_1} \\\\\nx_{F_2} \\\\\nx_{F_3} \\\\\n\\vdots \\\\\nx_{F_n}\n\\end{bmatrix}\n$$\n\nFinally, we add the bias term:\n\n$$\n\\mathbf{x}_{SCF} = \\mathbf{C}_{:, 1:n} \\cdot \\mathbf{x}_F + \n\\begin{bmatrix}\nb_1 \\\\\nb_2 \\\\\nb_3 \\\\\n\\vdots \\\\\nb_n\n\\end{bmatrix}\n$$\n\nIn expanded form:\n\n$$\n\\mathbf{x}_{SCF_i} = a_{i1} x_{F_1} + a_{i2} x_{F_2} + \\cdots + a_{in} x_{F_n} + b_i, \\quad \\forall i = 1, 2, \\dots, n\n$$\n\nThis equation shows how each counterfactual variable $x_{SCF_i}$ is generated as a linear combination of the factual inputs $x_{F_j}$ based on the causal effects matrix, with an intercept term $b_i$ added for each variable.\n\nOne can note that the `orphan` nodes, that is, the nodes that do not have parents in the DAG, are going to be equal to the intercept term $\\mathcal{b}_\\hat{o}$. The intuition behind this is that when we do the linear regression, variables that have no causal parents are just equal to the unconditional mean of the variable, i.e, we get $x_{SCF_\\hat{o}} = \\mathbb{E}(x_\\hat{o})$. Because of this, in some cases a better understanding of the regression is needed, so the residuals are also part of the SCM structure,\n\n\n\n::: {#4 .cell execution_count=0}\n``` {.julia .cell-code}\nstruct SCM\n variables::Vector{String}\n coefficients::Vector{Vector{Float64}}\n residuals::Vector{Vector{Float64}}\n dag::DiGraph\n causal_effects::Matrix{Float64}\nend\n```\n:::\n\n\n\n\n\n### `CounterfactualExplanations.jl` \n\n\n# Conclusion\n\n\n\n# References\n\n", + "markdown": "---\ntitle: \"When Causality meets Recourse\"\nsubtitle: \"Counterfactual Explanations through Structural Causal Models\"\ndate: '2024-09-17'\ndescription: |\n This post introduces a new tool in CounterfactualExplanations.jl, enhancing the package with causal reasoning to generate counterfactual explanations.\nauthor: \n - name: Jorge Luiz Franco \n url: https://www.linkedin.com/in/jorgelwyz/\ncategories:\n - counterfactuals\n - explainable AI\n - causality\n - Julia\nimage: www/intro.png\nexecute:\n eval: true\n echo: true\nengine: julia\njulia: \n exeflags: [\"--project=./\"]\ncode-fold: show\n---\n\n\n\n# Introduction\n\nIn recent years, the need for interpretable and explainable AI has surged, particularly in high-stakes domains. Counterfactual explanations provide a means to understand how changes to input features could alter the outcomes of machine learning models. This blog post presents a new tool in the CounterfactualExplanations.jl package, developed during my JSoC (Julia Summer of Code) project, which incorporates causal reasoning into counterfactual generation.\n\n# Project Overview\n\nThis project aimed to enhance the CounterfactualExplanations.jl package by infusing it with a robust mathematical foundation for minimal algorithmic recourse, based on the principles of causal reasoning [@karimi2021algorithmic]. \n\n## Key Contributions\n\nDuring the project, I contributed to two key repositories:\n\n1. **CounterfactualExplanations.jl**: Developed a new tool for generating counterfactual explanations using causal information. This allows users to create smarter perturbations rather than random adjustments, ultimately providing more meaningful insights.\n\n2. **CausalInference.jl**: Implemented a Structural Causal Model (SCM) structure that extracts information from data, laying the groundwork for the causal reasoning capabilities in CounterfactualExplanations.jl.\n\nThis was an amazing experience, not just experience contribute to two repositories simultaneously, but also to work with the mantainers of these repos. I learned a lot about the Julia language and the Julia community. This was possible because of the mentorship of Patrick Altmeyer (CounterfactualExplanations) and Moritz Schauer (CausalInference), who guided me throughout the project and are amazing researchers.\n\n## The `MINTGenerator`\n\nIn this project, we developed the MINTGenerator, a counterfactual generator based on the Recourse through Minimal\nIntervention (MINT) method proposed by @karimi2021algorithmic.\n\n## Description\n\nThe MINTGenerator incorporates causal reeasoning in algorithm recourse to achieve minimal interventions when generating a counterfactual explanation. In this sense, the main ideia is that just perturbating a black box model without taking into account the causal relations in the data can guide to misleading recommendations. Here we now shift to a perspective where every action/pertubation is an intervetion in the causal graph of the problem, thus the change is not made just in the intervened upon variable, but also in its childs in the causal structure. The generator utilizes a Structural Causal Model(SCM) to encode the variables in a way that causal effects are propagated and uses a generic gradient-based generator to create the search path, that is, any gradient-base generator (ECCo, REVISE, Watcher, ...) can be used with the MINT SCM encoder to generate counterfactual samples in latent space for minimal intervetions algorithm recourse.\n\nThe MINT algorithm minimizes a loss function that combines the causal constraints of the SCM and the distance between the generated counterfactual and the original input. Since we want a gradient-based generator, we need to pass the constrained optimizaiton problem into an unconstrained one and we do this by using the Lagrangian. Initially, as defined in [@karimi2021algorithmic], we aim to aim to find the minimal cost set of actions $A$ (in the form of structural interventions) that results in a counterfactual instance yielding the favorable output from $h$,\n\n$$\n\\begin{aligned}\n\nA^* \\in \\arg\\min_A \\text{cost}(A; \\mathbf{x}_F)\\\\\n\\textrm{s.t.} \\quad h(\\mathbf{x}_{SCF}) \\neq h(\\mathbf{x}_F) \\; \\; \\text{,}\\\\\n\n\\end{aligned} \n$$\n\nwhere $\\mathbf{x}_F$ is the original input, $\\mathbf{x}_{SCF}$ is the counterfactual instance, and $h$ is the black-box model. We use the $\\mathbf{x}_{SCF}$ terminology because the counterfactual is derived from the SCM,\n\n$$\nx_{SCF_i} = \n\\begin{cases}\nx_{F_i} + \\delta_i, & \\text{if } i \\in I \\\\\nx_{F_i} + f_i(\\text{pa}_{SCF_i}) - f_i(\\text{pa}_{F_i}), & \\text{if } i \\notin I \\; \\; \\text{,}\n\\end{cases} \n$$\n\nwhere $I$ is the set of intervened upon variables, $f_i$ is the function that generates the value of the variable $i$ given its parents, and $\\text{pa}_{SCF_i}$ and $\\text{pa}_{F_i}$ are the parents of the variable $i$ in the counterfactual and original instance, respectively. This closed formula for the decision variable $\\mathbf{x}_{SCF}$ is what makes possible to use a gradient-based generator, since with it the lagrangian is differentiable,\n\n$$\n\\mathcal{L}(A ; \\lambda) = \\text{cost}(A; \\mathbf{x}_F) + \\lambda \\left(h(\\mathbf{x}_{SCF}) - h(\\mathbf{x}_F) \\right) \\; \\; \\text{,}\n$$\n\nor in simple terms and more standard, since $\\lambda$ is constant,\n\n$$\n\\mathcal{L_{\\texttt{MINT}}}(\\mathbf{x}_{SCF}) = \\lambda \\text{cost}(\\mathbf{x}_{SCF}; \\mathbf{x}_F) + \\text{yloss}(\\mathbf{x}_{SCF},y^*) \\; \\; \\text{,}\n$$\n\nwhere $y^*$ is clearly $h(x_F)$ and $\\text{yloss}$ is : \n\n$$\n\\text{yloss}(\\mathbf{x}_{SCF}, y^*) = h \\left(\\left\\{ x_{F_i} + \\delta_i [i \\in I] + \\left(f_i(\\text{pa}_{SCF_i}) - f_i(\\text{pa}_{F_i}) \\right) [i \\notin I] \\right\\}_{i=1}^n \\right) - y^* \\; \\; \\text{.} \n$$\n\n## Implementation\n\n### `CausalInference.jl`\n\nIn terms of implementation, we need to capture the causal relations from the data, that's where `CausalInference.jl` comes in. However, before the project, the package did not have a SCM structure, in the sense that the methods just captured the topological Directed Acyclic Graph (DAG) that showed the causality ruling the data, that is, no causal structural equations were provided,\n\n\n\n::: {#2 .cell execution_count=1}\n``` {.julia .cell-code}\nusing CausalInference\nusing Plots, GraphRecipes\nusing Random\nRandom.seed!(1)\n\nN = 2000 # number of data points\n\nx = randn(N)\nv = x + randn(N)*0.25\nw = x + randn(N)*0.25\nz = v + w + randn(N)*0.25\ns = z + randn(N)*0.25\n\ndf = (x=x, v=v, w=w, z=z, s=s)\n\nest_g, score = ges(df; penalty=1.0, parallel=true)\n\nplt = graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)], size=(500,500), nodesize=0.1, fontsize=2)\nsavefig(plt, \"www/intro.png\")\ndisplay(plt)\n```\n\n::: {.cell-output .cell-output-stdout}\n```\n┌ Warning: Only one thread available\n└ @ CausalInference ~/.julia/packages/CausalInference/ozcj8/src/ges.jl:52\n```\n:::\n\n::: {.cell-output .cell-output-display}\n```{=html}\n\n\n\n \n \n \n\n\n\n \n \n \n\n\n\n \n \n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n```\n:::\n:::\n\n\n\n\n\nSo, our goal was given the DAG provided by the `ges` method in the causal discovery [@chickering2003optimal], generate equations that rules each of these causal relations, represented in the DAG as directed edges. The SCM is the union of the DAG and these causal equations, that is, the SCM is a tuple $(G, \\mathbf{f})$, where $G$ is the DAG and $\\mathbf{f}$ is the set of functions that generates the value of each variable given its parents. \n\nOur solution for constructing the structural causal equations was to assume that the data was generated by a linear model, ie, the causal relations were linear. For the DAG provided in the code example we derive\n\n$$ v = \\mathcal{b}_v $$\n\n$$ x = \\mathcal{a}_{v \\to x} v + \\mathcal{b}_x $$\n\n$$ w = \\mathcal{a}_{x \\to w} x + \\mathcal{b}_w $$\n\n$$ z = \\mathcal{a}_{v \\to z} v+ \\mathcal{a}_{w \\to z} w + \\mathcal{b}_z $$\n\n$$ s = \\mathcal{a}_{z \\to s} z + \\mathcal{b}_s $$\n\nand that's the tricky thing, as we can see these causal equations are different than the ones that generated the data, but they are the ones that respect the causal system obtained from the obtained DAG. Here $\\mathcal{b}_i$ and $\\mathcal{a}_{i \\to j}$ are the intercept term and the coefficient obtained from the linear regression, respectively. To correctly solve the linear regression respecting the dependencies of the causal graph, we use `topological_sort_by_dfs` from `Graphs.jl`.\n\nNow, with the SCM structure in hand, we see that the representation could be a struct containing the DAG and the coefficients/intercepts of the causal equations, this maps exactly the tuple $(G, \\mathbf{f})$ that we defined. However, since we need these equations to be differentiable, we need to define a function that takes the SCM and returns the value of the variable given its parents and using just the coefficients and the DAG, lead to errors, because `AutoDiff` does not deal well with functions that are conditioned (`if` statements). So, we need to define a way to retrieve the system of causal equations in a smooth way and that's where the `causal_effects` matrix comes to the rescue.\n\nLet the factual vector of features be denoted as:\n\n$$\n\\mathbf{x}_F = \n\\begin{bmatrix}\nx_{F_1} \\\\\nx_{F_2} \\\\\nx_{F_3} \\\\\n\\vdots \\\\\nx_{F_n}\n\\end{bmatrix}\n$$\n\nLet the `causal_effects` matrix be:\n\n$$\n\\mathbf{C} =\n\\begin{bmatrix}\na_{11} & a_{12} & \\cdots & a_{1n} & b_1 \\\\\na_{21} & a_{22} & \\cdots & a_{2n} & b_2 \\\\\na_{31} & a_{32} & \\cdots & a_{3n} & b_3 \\\\\n\\vdots & \\vdots & \\ddots & \\vdots & \\vdots \\\\\na_{n1} & a_{n2} & \\cdots & a_{nn} & b_n \\\\\n\\end{bmatrix}\n$$\n\nHere, $a_{ij}$ represents the coefficient from the causal effect of $x_{F_j}$ on $x_{F_i}$, and $b_i$ represents the intercept term for the variable $x_{F_i}$.\n\nThe matrix multiplication of the `causal_effects` matrix with the factual vector (excluding the bias term) is given by:\n\n$$\n\\mathbf{C}_{:, 1:n} \\cdot \\mathbf{x}_F =\n\\begin{bmatrix}\na_{11} & a_{12} & \\cdots & a_{1n} \\\\\na_{21} & a_{22} & \\cdots & a_{2n} \\\\\na_{31} & a_{32} & \\cdots & a_{3n} \\\\\n\\vdots & \\vdots & \\ddots & \\vdots \\\\\na_{n1} & a_{n2} & \\cdots & a_{nn}\n\\end{bmatrix}\n\\begin{bmatrix}\nx_{F_1} \\\\\nx_{F_2} \\\\\nx_{F_3} \\\\\n\\vdots \\\\\nx_{F_n}\n\\end{bmatrix}\n$$\n\nFinally, we add the bias term:\n\n$$\n\\mathbf{x}_{SCF} = \\mathbf{C}_{:, 1:n} \\cdot \\mathbf{x}_F + \n\\begin{bmatrix}\nb_1 \\\\\nb_2 \\\\\nb_3 \\\\\n\\vdots \\\\\nb_n\n\\end{bmatrix}\n$$\n\nIn expanded form:\n\n$$\n\\mathbf{x}_{SCF_i} = a_{i1} x_{F_1} + a_{i2} x_{F_2} + \\cdots + a_{in} x_{F_n} + b_i, \\quad \\forall i = 1, 2, \\dots, n\n$$\n\nThis equation shows how each counterfactual variable $x_{SCF_i}$ is generated as a linear combination of the factual inputs $x_{F_j}$ based on the causal effects matrix, with an intercept term $b_i$ added for each variable.\n\nOne can note that the `orphan` nodes, that is, the nodes that do not have parents in the DAG, are going to be equal to the intercept term $\\mathcal{b}_\\hat{o}$. The intuition behind this is that when we do the linear regression, variables that have no causal parents are just equal to the unconditional mean of the variable, i.e, we get $x_{SCF_\\hat{o}} = \\mathbb{E}(x_\\hat{o})$. Because of this, in some cases a better understanding of the regression is needed, so the residuals are also part of the SCM structure,\n\n\n\n::: {#4 .cell execution_count=0}\n``` {.julia .cell-code}\nstruct SCM\n variables::Vector{String}\n coefficients::Vector{Vector{Float64}}\n residuals::Vector{Vector{Float64}}\n dag::DiGraph\n causal_effects::Matrix{Float64}\nend\n```\n:::\n\n\n\n\n\n### `CounterfactualExplanations.jl` \n\n\n# Conclusion\n\n\n\n# References\n\n", "supporting": [ "index_files/figure-html" ], diff --git a/profile/blog/posts/causal-recourse/index.qmd b/profile/blog/posts/causal-recourse/index.qmd index 8aa42f3..f92a37d 100644 --- a/profile/blog/posts/causal-recourse/index.qmd +++ b/profile/blog/posts/causal-recourse/index.qmd @@ -114,7 +114,7 @@ df = (x=x, v=v, w=w, z=z, s=s) est_g, score = ges(df; penalty=1.0, parallel=true) -plt = graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)], size=(500,500), nodesize=0.3) +plt = graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)], size=(500,500), nodesize=0.1, fontsize=2) savefig(plt, "www/intro.png") display(plt) ``` diff --git a/profile/blog/posts/causal-recourse/www/intro.png b/profile/blog/posts/causal-recourse/www/intro.png index db4d335ed11189b2f351481d3f8f1d2b3373a44d..226a52830d533edd1e3d0ac2b7acdf36cf244d1c 100644 GIT binary patch literal 12517 zcmeHu`9GBH`~DbXUn3L}67>jW$p*v%5NhIF9prF73A7F2F0vOCS&gc9@&l z5(sQP_+K|S5ub3Sq?X}doQEy8n-P{+|IjLPt`i8dgdJukdjeB`cb;`hWG*d@k37;Q z^1ey9n#+Chp1Ue}+11_ZD|L+r6s$Hro&CDK$tY2A`Qg#TjMHl`r<|9S&0Tl#or%Mf z=qK?Fe-})uXZ!14=nPVv2c166t?qgtd?(3>az4$M$4q`1JAu%#X1gKA;37!nB=oE! zNfN>`gxv{*Yg=e+1RdW0|Ka~>Kx}C;1jgxO$Bx<9*vQ9UJalu%b;XrZQg&*@gSTl5 z+5|$2B_oaU%uIIZm|XsbfP;U$ovSS?xx-HBn6OJYKR>-z_3xqYgC#4^ZQZ7@bLsQK z(BmU^-NDHe3BrA!a8A{f{=v{~!OM>ve80TocnsG@tz!{Q0iBnhn^p3K?G20*F3o!O zOl$4hteou29p40E?g|_ksGHPmiRpZD`0bYA69ms%9?7A^0d@$Ud;HR`G$+RRC_mTwah(zKnbEG7AF5t`==HC1JR2+-e zDJj+0)gA4gYLFTXbXOc*2+4nc$&@SiI8nHUNAlvAmX`bZ`Re>lU%wVpn8OiVLaGi= 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zOHSD3PTA)DfEz=+rul%1(rv|B#Qf75D5*NFL(E{M2lEMWje#pJ#nw!F!g%UPg+zAW z(I8TLobR9z<(@`l{xay0ZC1tL7z3van*;@D<;e4%mApEgf|}t$=^J%##t3P%L&3%~ zUh+}hggN2Yr@Hq>N5+ijO|2cnp+8bARrO88rIdwY7+N1`7q{cRa<2I6U|V9y*1seP zJu0(!7?cXYVP_tabu;?$xY?5Mo5x)HtDp4nFL~=%H{|pAS2ye|4v5Wx&07Z`Gc~Y! zBHDX38H*B`D4oSAXzEd6VPn+y=z$u0;@9b{uP%LO?=~IQ)kj*#X&OV5EPW1sUNs`)@-A;d7jd+t{n+CqY63lz0T-hVRiDe0`0jVT1>)l3nm|FeynDZ~e zoT>$|e%3KE5;gc?`cQe|bb5^jDe!8k7C`Fg8n>Cvil+Mj++yWtb Date: Tue, 17 Sep 2024 14:02:37 +0200 Subject: [PATCH 08/13] rerendered --- docs/blog/index.html | 4 +- docs/blog/index.xml | 78 +++++++++--------- docs/blog/posts/causal-recourse/index.html | 76 ++++++++--------- docs/blog/posts/causal-recourse/www/intro.png | Bin 20746 -> 12517 bytes docs/search.json | 4 +- docs/sitemap.xml | 2 +- 6 files changed, 84 insertions(+), 80 deletions(-) diff --git a/docs/blog/index.html b/docs/blog/index.html index ff22fcd..a28df7a 100644 --- a/docs/blog/index.html +++ b/docs/blog/index.html @@ -227,7 +227,7 @@

Taija’s Blog

So, our goal was given the DAG provided by the ges method in the causal discovery (Chickering 2003), generate equations that rules each of these causal relations, represented in the DAG as directed edges. The SCM is the union of the DAG and these causal equations, that is, the SCM is a tuple , where is the DAG and is the set of functions that generates the value of each variable given its parents.

diff --git a/docs/blog/posts/causal-recourse/index.html b/docs/blog/posts/causal-recourse/index.html index f3745a3..0b264c4 100644 --- a/docs/blog/posts/causal-recourse/index.html +++ b/docs/blog/posts/causal-recourse/index.html @@ -358,7 +358,7 @@

CausalInference.j est_g, score = ges(df; penalty=1.0, parallel=true) -plt = graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)], size=(500,500), nodesize=0.3) +plt = graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)], size=(500,500), nodesize=0.1, fontsize=2) savefig(plt, "www/intro.png") display(plt)

-
+

@@ -256,7 +256,7 @@

8 min

-9/17/24, 9:07:54 AM +9/17/24, 1:51:51 PM
diff --git a/docs/blog/index.xml b/docs/blog/index.xml index c9f0d3a..12366da 100644 --- a/docs/blog/index.xml +++ b/docs/blog/index.xml @@ -203,7 +203,11 @@ font-style: inherit;">500), nodesize=0.3) +font-style: inherit;">0.1, fontsize=2) savefig(plt, display(plt)
- + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

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@@ -370,53 +370,53 @@

CausalInference.j - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

So, our goal was given the DAG provided by the ges method in the causal discovery (Chickering 2003), generate equations that rules each of these causal relations, represented in the DAG as directed edges. The SCM is the union of the DAG and these causal equations, that is, the SCM is a tuple \((G, \mathbf{f})\), where \(G\) is the DAG and \(\mathbf{f}\) is the set of functions that generates the value of each variable given its parents.

@@ -1124,7 +1124,7 @@

Conclusion

est_g, score = ges(df; penalty=1.0, parallel=true) -plt = graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)], size=(500,500), nodesize=0.3) +plt = graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)], size=(500,500), nodesize=0.1, fontsize=2) savefig(plt, "www/intro.png") display(plt) ``` diff --git a/docs/blog/posts/causal-recourse/www/intro.png b/docs/blog/posts/causal-recourse/www/intro.png index db4d335ed11189b2f351481d3f8f1d2b3373a44d..226a52830d533edd1e3d0ac2b7acdf36cf244d1c 100644 GIT binary patch literal 12517 zcmeHu`9GBH`~DbXUn3L}67>jW$p*v%5NhIF9prF73A7F2F0vOCS&gc9@&l z5(sQP_+K|S5ub3Sq?X}doQEy8n-P{+|IjLPt`i8dgdJukdjeB`cb;`hWG*d@k37;Q z^1ey9n#+Chp1Ue}+11_ZD|L+r6s$Hro&CDK$tY2A`Qg#TjMHl`r<|9S&0Tl#or%Mf z=qK?Fe-})uXZ!14=nPVv2c166t?qgtd?(3>az4$M$4q`1JAu%#X1gKA;37!nB=oE! zNfN>`gxv{*Yg=e+1RdW0|Ka~>Kx}C;1jgxO$Bx<9*vQ9UJalu%b;XrZQg&*@gSTl5 z+5|$2B_oaU%uIIZm|XsbfP;U$ovSS?xx-HBn6OJYKR>-z_3xqYgC#4^ZQZ7@bLsQK 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zOHSD3PTA)DfEz=+rul%1(rv|B#Qf75D5*NFL(E{M2lEMWje#pJ#nw!F!g%UPg+zAW z(I8TLobR9z<(@`l{xay0ZC1tL7z3van*;@D<;e4%mApEgf|}t$=^J%##t3P%L&3%~ zUh+}hggN2Yr@Hq>N5+ijO|2cnp+8bARrO88rIdwY7+N1`7q{cRa<2I6U|V9y*1seP zJu0(!7?cXYVP_tabu;?$xY?5Mo5x)HtDp4nFL~=%H{|pAS2ye|4v5Wx&07Z`Gc~Y! zBHDX38H*B`D4oSAXzEd6VPn+y=z$u0;@9b{uP%LO?=~IQ)kj*#X&OV5EPW1sUNs`)@-A;d7jd+t{n+CqY63lz0T-hVRiDe0`0jVT1>)l3nm|FeynDZ~e zoT>$|e%3KE5;gc?`cQe|bb5^jDe!8k7C`Fg8n>Cvil+Mj++yWtb https://www.taija.org/blog/posts/causal-recourse/index.html - 2024-09-17T07:07:54.512Z + 2024-09-17T11:51:51.700Z https://www.taija.org/blog/posts/conformal-prediction/index.html From 23813727577c6fd8cdd4275afe3cb9a4e836853c Mon Sep 17 00:00:00 2001 From: pat-alt Date: Tue, 17 Sep 2024 14:22:42 +0200 Subject: [PATCH 09/13] small things --- docs/blog/index.html | 7 +- docs/blog/index.xml | 252 ++++-- docs/blog/posts/causal-recourse/index.html | 647 +++++++------- docs/blog/posts/causal-recourse/www/intro.png | Bin 12517 -> 19542 bytes docs/search.json | 6 +- docs/site_libs/bootstrap/bootstrap.min.css | 6 +- .../quarto-syntax-highlighting.css | 2 +- docs/sitemap.xml | 2 +- .../index/execute-results/html.json | 4 +- profile/blog/posts/_metadata.yml | 2 +- .../blog/posts/causal-recourse/Manifest.toml | 504 ++++++++++- .../blog/posts/causal-recourse/Project.toml | 4 + profile/blog/posts/causal-recourse/index.html | 800 ------------------ profile/blog/posts/causal-recourse/index.qmd | 12 +- .../blog/posts/causal-recourse/www/intro.png | Bin 12517 -> 19542 bytes 15 files changed, 1069 insertions(+), 1179 deletions(-) delete mode 100644 profile/blog/posts/causal-recourse/index.html diff --git a/docs/blog/index.html b/docs/blog/index.html index a28df7a..a962a1b 100644 --- a/docs/blog/index.html +++ b/docs/blog/index.html @@ -129,7 +129,6 @@ }; - @@ -227,7 +226,7 @@

Taija’s Blog

-
+

@@ -253,10 +252,10 @@

Patrick Altmeyer, Jorge Luiz Franco

-8 min +9 min
-9/17/24, 1:51:51 PM +9/17/24, 2:22:00 PM
diff --git a/docs/blog/index.xml b/docs/blog/index.xml index 12366da..c45f089 100644 --- a/docs/blog/index.xml +++ b/docs/blog/index.xml @@ -45,9 +45,7 @@

Description

The MINTGenerator incorporates causal reeasoning in algorithm recourse to achieve minimal interventions when generating a counterfactual explanation. In this sense, the main ideia is that just perturbating a black box model without taking into account the causal relations in the data can guide to misleading recommendations. Here we now shift to a perspective where every action/pertubation is an intervetion in the causal graph of the problem, thus the change is not made just in the intervened upon variable, but also in its childs in the causal structure. The generator utilizes a Structural Causal Model(SCM) to encode the variables in a way that causal effects are propagated and uses a generic gradient-based generator to create the search path, that is, any gradient-base generator (ECCo, REVISE, Watcher, …) can be used with the MINT SCM encoder to generate counterfactual samples in latent space for minimal intervetions algorithm recourse.

The MINT algorithm minimizes a loss function that combines the causal constraints of the SCM and the distance between the generated counterfactual and the original input. Since we want a gradient-based generator, we need to pass the constrained optimizaiton problem into an unconstrained one and we do this by using the Lagrangian. Initially, as defined in (Karimi, Schölkopf, and Valera 2021), we aim to aim to find the minimal cost set of actions (in the form of structural interventions) that results in a counterfactual instance yielding the favorable output from ,

-$$ - -

$$

+

where is the original input, is the counterfactual instance, and is the black-box model. We use the terminology because the counterfactual is derived from the SCM,

where is the set of intervened upon variables, is the function that generates the value of the variable given its parents, and and are the parents of the variable in the counterfactual and original instance, respectively. This closed formula for the decision variable is what makes possible to use a gradient-based generator, since with it the lagrangian is differentiable,

@@ -74,36 +72,64 @@ font-style: inherit;">CausalInference background-color: null; font-style: inherit;">using Plots, CounterfactualExplanations +using CounterfactualExplanations.GenerativeModels +using Graphs +using GraphRecipes -using MultivariateStats +using Plots +using Random -Random.seed!(1) - -N using StatsBase + +N = 2000 # number of data points - -x +x = randn(N) -v v = x *0.25 -w w = x *0.25 -z z = v *0.25 -s s = z *0.25 - -df +df = (x=z, s=s) - -est_g, score +est_g, score = =true) - -plt +plt = 0.1, fontsize=2) -25) +savefig(plt, "www/intro.png") -display(plt)
@@ -225,53 +251,53 @@ font-style: inherit;">display(plt)
- + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

So, our goal was given the DAG provided by the ges method in the causal discovery (Chickering 2003), generate equations that rules each of these causal relations, represented in the DAG as directed edges. The SCM is the union of the DAG and these causal equations, that is, the SCM is a tuple , where is the DAG and is the set of functions that generates the value of each variable given its parents.

@@ -337,6 +363,114 @@ font-style: inherit;">end

CounterfactualExplanations.jl

+

Now, we need to go into the optimization problem previously described. We seek to minimize the lagrangian function we defined where now we have a differentiable function. The standard way to implement generators in CounterfactualExplanations.jl is to use AutoDiff exactly using composable functions in the lagrangian. The definition of is in the same shape of the the others gradient-based generators in the package, so the optimization is straightforward. However, we needed some way to pass the into the and that’s where transformer.jl comes in. This is where InputTransformers are defined in the package and in some way this is what we are doing, we are passing our factual to the “latent” causal space of the counterfactual. Our first step is to create a new kind of InputTransformer that is the SCM itself,

+
+
+Code +
const TypedInputTransformer = Union{
+    Type{<:StatsBase.AbstractDataTransform},
+    Type{<:MultivariateStats.AbstractDimensionalityReduction},
+    Type{<:GenerativeModels.AbstractGenerativeModel},
+    Type{<:CausalInference.SCM} # The SCM transfromer
+}
+
+
+

and then we need a way to create this transformer, that’s where we “overload” fit_transformer using CausalInferece.jl,

+
+
+Code +
function fit_transformer(
+    data::CounterfactualData, input_encoder::Type{<:CausalInference.SCM}; kwargs...
+)
+    t = Tables.table(transpose(data.X))
+    est_g, score = CausalInference.ges(t; penalty=1.0, parallel=true)
+    est_dag = CausalInference.pdag2dag!(est_g)
+    scm = CausalInference.estimate_equations(t, est_dag)
+    return scm
+end
+
+
+

… We are getting there! However, now comes the hardest part, where this is placed?

diff --git a/docs/blog/posts/causal-recourse/index.html b/docs/blog/posts/causal-recourse/index.html index 0b264c4..7b1005f 100644 --- a/docs/blog/posts/causal-recourse/index.html +++ b/docs/blog/posts/causal-recourse/index.html @@ -304,14 +304,12 @@

The MINTGenerator<

Description

The MINTGenerator incorporates causal reeasoning in algorithm recourse to achieve minimal interventions when generating a counterfactual explanation. In this sense, the main ideia is that just perturbating a black box model without taking into account the causal relations in the data can guide to misleading recommendations. Here we now shift to a perspective where every action/pertubation is an intervetion in the causal graph of the problem, thus the change is not made just in the intervened upon variable, but also in its childs in the causal structure. The generator utilizes a Structural Causal Model(SCM) to encode the variables in a way that causal effects are propagated and uses a generic gradient-based generator to create the search path, that is, any gradient-base generator (ECCo, REVISE, Watcher, …) can be used with the MINT SCM encoder to generate counterfactual samples in latent space for minimal intervetions algorithm recourse.

The MINT algorithm minimizes a loss function that combines the causal constraints of the SCM and the distance between the generated counterfactual and the original input. Since we want a gradient-based generator, we need to pass the constrained optimizaiton problem into an unconstrained one and we do this by using the Lagrangian. Initially, as defined in (Karimi, Schölkopf, and Valera 2021), we aim to aim to find the minimal cost set of actions \(A\) (in the form of structural interventions) that results in a counterfactual instance yielding the favorable output from \(h\),

-$$ -\[\begin{aligned} - +

\[ +\begin{aligned} A^* \in \arg\min_A \text{cost}(A; \mathbf{x}_F)\\ \textrm{s.t.} \quad h(\mathbf{x}_{SCF}) \neq h(\mathbf{x}_F) \; \; \text{,}\\ - -\end{aligned}\] -

$$

+\end{aligned} +\]

where \(\mathbf{x}_F\) is the original input, \(\mathbf{x}_{SCF}\) is the counterfactual instance, and \(h\) is the black-box model. We use the \(\mathbf{x}_{SCF}\) terminology because the counterfactual is derived from the SCM,

\[ x_{SCF_i} = @@ -342,25 +340,31 @@

CausalInference.j
Code 
using CausalInference
-using Plots, GraphRecipes
-using Random
-Random.seed!(1)
-
-N = 2000 # number of data points
-
-x = randn(N)
-v = x + randn(N)*0.25
-w = x + randn(N)*0.25
-z = v + w + randn(N)*0.25
-s = z + randn(N)*0.25
+using CounterfactualExplanations
+using CounterfactualExplanations.GenerativeModels
+using Graphs
+using GraphRecipes
+using MultivariateStats
+using Plots
+using Random
+Random.seed!(1)
+using StatsBase
+
+N = 2000 # number of data points
 
-df = (x=x, v=v, w=w, z=z, s=s)
-
-est_g, score = ges(df; penalty=1.0, parallel=true)
-
-plt = graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)], size=(500,500), nodesize=0.1, fontsize=2)
-savefig(plt, "www/intro.png")
-display(plt)
+x = randn(N) +v = x + randn(N)*0.25 +w = x + randn(N)*0.25 +z = v + w + randn(N)*0.25 +s = z + randn(N)*0.25 + +df = (x=x, v=v, w=w, z=z, s=s) + +est_g, score = ges(df; penalty=1.0, parallel=true) + +plt = graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)], size=(500,500), nodesize=0.1, fontsize=25) +savefig(plt, "www/intro.png") +display(plt) 
┌ Warning: Only one thread available
@@ -370,53 +374,53 @@ 
CausalInference.j
 
 
 
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So, our goal was given the DAG provided by the ges method in the causal discovery (Chickering 2003), generate equations that rules each of these causal relations, represented in the DAG as directed edges. The SCM is the union of the DAG and these causal equations, that is, the SCM is a tuple \((G, \mathbf{f})\), where \(G\) is the DAG and \(\mathbf{f}\) is the set of functions that generates the value of each variable given its parents.

@@ -501,6 +505,34 @@

CausalInference.j

CounterfactualExplanations.jl

+

Now, we need to go into the optimization problem previously described. We seek to minimize the lagrangian function we defined where now we have a differentiable function. The standard way to implement generators in CounterfactualExplanations.jl is to use AutoDiff exactly using composable functions in the lagrangian. The definition of \(\mathcal{L_{\texttt{MINT}}}\) is in the same shape of the the others gradient-based generators in the package, so the optimization is straightforward. However, we needed some way to pass the \(x_F\) into the \(x_{SCF}\) and that’s where transformer.jl comes in. This is where InputTransformers are defined in the package and in some way this is what we are doing, we are passing our factual to the “latent” causal space of the counterfactual. Our first step is to create a new kind of InputTransformer that is the SCM itself,

+
+
+Code +
const TypedInputTransformer = Union{
+    Type{<:StatsBase.AbstractDataTransform},
+    Type{<:MultivariateStats.AbstractDimensionalityReduction},
+    Type{<:GenerativeModels.AbstractGenerativeModel},
+    Type{<:CausalInference.SCM} # The SCM transfromer
+}
+
+
+

and then we need a way to create this transformer, that’s where we “overload” fit_transformer using CausalInferece.jl,

+
+
+Code +
function fit_transformer(
+    data::CounterfactualData, input_encoder::Type{<:CausalInference.SCM}; kwargs...
+)
+    t = Tables.table(transpose(data.X))
+    est_g, score = CausalInference.ges(t; penalty=1.0, parallel=true)
+    est_dag = CausalInference.pdag2dag!(est_g)
+    scm = CausalInference.estimate_equations(t, est_dag)
+    return scm
+end
+
+
+

… We are getting there! However, now comes the hardest part, where this is placed?

@@ -1006,238 +1038,271 @@

Conclusion

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z7*k8dNwe|aCEZEM$@Y8p6onqJv5`|!nyz^4&_5HtlkgKm5ECS)_dUD;9njz2xm=U0=^-20_RhYXo6 zJCLa4lR*=mv);RMnyaSS?G%nuruVvz1SySPW^oqP|GuHArFE-aU|k7QWL+NbA6p}a zPsa+yr}f7=Ovmk%+6$@_#=? jDE|M4|JMOo5;6~r=sW#kas>a)0Aa^gYqN)24u=0f<=|l9 diff --git a/docs/search.json b/docs/search.json index 14c2948..b6689e7 100644 --- a/docs/search.json +++ b/docs/search.json @@ -417,14 +417,14 @@ "href": "blog/posts/causal-recourse/index.html#description", "title": "When Causality meets Recourse", "section": "Description", - "text": "Description\nThe MINTGenerator incorporates causal reeasoning in algorithm recourse to achieve minimal interventions when generating a counterfactual explanation. In this sense, the main ideia is that just perturbating a black box model without taking into account the causal relations in the data can guide to misleading recommendations. Here we now shift to a perspective where every action/pertubation is an intervetion in the causal graph of the problem, thus the change is not made just in the intervened upon variable, but also in its childs in the causal structure. The generator utilizes a Structural Causal Model(SCM) to encode the variables in a way that causal effects are propagated and uses a generic gradient-based generator to create the search path, that is, any gradient-base generator (ECCo, REVISE, Watcher, …) can be used with the MINT SCM encoder to generate counterfactual samples in latent space for minimal intervetions algorithm recourse.\nThe MINT algorithm minimizes a loss function that combines the causal constraints of the SCM and the distance between the generated counterfactual and the original input. Since we want a gradient-based generator, we need to pass the constrained optimizaiton problem into an unconstrained one and we do this by using the Lagrangian. Initially, as defined in (Karimi, Schölkopf, and Valera 2021), we aim to aim to find the minimal cost set of actions \\(A\\) (in the form of structural interventions) that results in a counterfactual instance yielding the favorable output from \\(h\\),\n$$\n\\[\\begin{aligned}\n\nA^* \\in \\arg\\min_A \\text{cost}(A; \\mathbf{x}_F)\\\\\n\\textrm{s.t.} \\quad h(\\mathbf{x}_{SCF}) \\neq h(\\mathbf{x}_F) \\; \\; \\text{,}\\\\\n\n\\end{aligned}\\]\n$$\nwhere \\(\\mathbf{x}_F\\) is the original input, \\(\\mathbf{x}_{SCF}\\) is the counterfactual instance, and \\(h\\) is the black-box model. We use the \\(\\mathbf{x}_{SCF}\\) terminology because the counterfactual is derived from the SCM,\n\\[\nx_{SCF_i} =\n\\begin{cases}\nx_{F_i} + \\delta_i, & \\text{if } i \\in I \\\\\nx_{F_i} + f_i(\\text{pa}_{SCF_i}) - f_i(\\text{pa}_{F_i}), & \\text{if } i \\notin I \\; \\; \\text{,}\n\\end{cases}\n\\]\nwhere \\(I\\) is the set of intervened upon variables, \\(f_i\\) is the function that generates the value of the variable \\(i\\) given its parents, and \\(\\text{pa}_{SCF_i}\\) and \\(\\text{pa}_{F_i}\\) are the parents of the variable \\(i\\) in the counterfactual and original instance, respectively. This closed formula for the decision variable \\(\\mathbf{x}_{SCF}\\) is what makes possible to use a gradient-based generator, since with it the lagrangian is differentiable,\n\\[\n\\mathcal{L}(A ; \\lambda) = \\text{cost}(A; \\mathbf{x}_F) + \\lambda \\left(h(\\mathbf{x}_{SCF}) - h(\\mathbf{x}_F) \\right) \\; \\; \\text{,}\n\\]\nor in simple terms and more standard, since \\(\\lambda\\) is constant,\n\\[\n\\mathcal{L_{\\texttt{MINT}}}(\\mathbf{x}_{SCF}) = \\lambda \\text{cost}(\\mathbf{x}_{SCF}; \\mathbf{x}_F) + \\text{yloss}(\\mathbf{x}_{SCF},y^*) \\; \\; \\text{,}\n\\]\nwhere \\(y^*\\) is clearly \\(h(x_F)\\) and \\(\\text{yloss}\\) is :\n\\[\n\\text{yloss}(\\mathbf{x}_{SCF}, y^*) = h \\left(\\left\\{ x_{F_i} + \\delta_i [i \\in I] + \\left(f_i(\\text{pa}_{SCF_i}) - f_i(\\text{pa}_{F_i}) \\right) [i \\notin I] \\right\\}_{i=1}^n \\right) - y^* \\; \\; \\text{.}\n\\]" + "text": "Description\nThe MINTGenerator incorporates causal reeasoning in algorithm recourse to achieve minimal interventions when generating a counterfactual explanation. In this sense, the main ideia is that just perturbating a black box model without taking into account the causal relations in the data can guide to misleading recommendations. Here we now shift to a perspective where every action/pertubation is an intervetion in the causal graph of the problem, thus the change is not made just in the intervened upon variable, but also in its childs in the causal structure. The generator utilizes a Structural Causal Model(SCM) to encode the variables in a way that causal effects are propagated and uses a generic gradient-based generator to create the search path, that is, any gradient-base generator (ECCo, REVISE, Watcher, …) can be used with the MINT SCM encoder to generate counterfactual samples in latent space for minimal intervetions algorithm recourse.\nThe MINT algorithm minimizes a loss function that combines the causal constraints of the SCM and the distance between the generated counterfactual and the original input. Since we want a gradient-based generator, we need to pass the constrained optimizaiton problem into an unconstrained one and we do this by using the Lagrangian. Initially, as defined in (Karimi, Schölkopf, and Valera 2021), we aim to aim to find the minimal cost set of actions \\(A\\) (in the form of structural interventions) that results in a counterfactual instance yielding the favorable output from \\(h\\),\n\\[\n\\begin{aligned}\nA^* \\in \\arg\\min_A \\text{cost}(A; \\mathbf{x}_F)\\\\\n\\textrm{s.t.} \\quad h(\\mathbf{x}_{SCF}) \\neq h(\\mathbf{x}_F) \\; \\; \\text{,}\\\\\n\\end{aligned}\n\\]\nwhere \\(\\mathbf{x}_F\\) is the original input, \\(\\mathbf{x}_{SCF}\\) is the counterfactual instance, and \\(h\\) is the black-box model. We use the \\(\\mathbf{x}_{SCF}\\) terminology because the counterfactual is derived from the SCM,\n\\[\nx_{SCF_i} =\n\\begin{cases}\nx_{F_i} + \\delta_i, & \\text{if } i \\in I \\\\\nx_{F_i} + f_i(\\text{pa}_{SCF_i}) - f_i(\\text{pa}_{F_i}), & \\text{if } i \\notin I \\; \\; \\text{,}\n\\end{cases}\n\\]\nwhere \\(I\\) is the set of intervened upon variables, \\(f_i\\) is the function that generates the value of the variable \\(i\\) given its parents, and \\(\\text{pa}_{SCF_i}\\) and \\(\\text{pa}_{F_i}\\) are the parents of the variable \\(i\\) in the counterfactual and original instance, respectively. This closed formula for the decision variable \\(\\mathbf{x}_{SCF}\\) is what makes possible to use a gradient-based generator, since with it the lagrangian is differentiable,\n\\[\n\\mathcal{L}(A ; \\lambda) = \\text{cost}(A; \\mathbf{x}_F) + \\lambda \\left(h(\\mathbf{x}_{SCF}) - h(\\mathbf{x}_F) \\right) \\; \\; \\text{,}\n\\]\nor in simple terms and more standard, since \\(\\lambda\\) is constant,\n\\[\n\\mathcal{L_{\\texttt{MINT}}}(\\mathbf{x}_{SCF}) = \\lambda \\text{cost}(\\mathbf{x}_{SCF}; \\mathbf{x}_F) + \\text{yloss}(\\mathbf{x}_{SCF},y^*) \\; \\; \\text{,}\n\\]\nwhere \\(y^*\\) is clearly \\(h(x_F)\\) and \\(\\text{yloss}\\) is :\n\\[\n\\text{yloss}(\\mathbf{x}_{SCF}, y^*) = h \\left(\\left\\{ x_{F_i} + \\delta_i [i \\in I] + \\left(f_i(\\text{pa}_{SCF_i}) - f_i(\\text{pa}_{F_i}) \\right) [i \\notin I] \\right\\}_{i=1}^n \\right) - y^* \\; \\; \\text{.}\n\\]" }, { "objectID": "blog/posts/causal-recourse/index.html#implementation", "href": "blog/posts/causal-recourse/index.html#implementation", "title": "When Causality meets Recourse", "section": "Implementation", - "text": "Implementation\n\nCausalInference.jl\nIn terms of implementation, we need to capture the causal relations from the data, that’s where CausalInference.jl comes in. However, before the project, the package did not have a SCM structure, in the sense that the methods just captured the topological Directed Acyclic Graph (DAG) that showed the causality ruling the data, that is, no causal structural equations were provided,\n\n\nCode\nusing CausalInference\nusing Plots, GraphRecipes\nusing Random\nRandom.seed!(1)\n\nN = 2000 # number of data points\n\nx = randn(N)\nv = x + randn(N)*0.25\nw = x + randn(N)*0.25\nz = v + w + randn(N)*0.25\ns = z + randn(N)*0.25\n\ndf = (x=x, v=v, w=w, z=z, s=s)\n\nest_g, score = ges(df; penalty=1.0, parallel=true)\n\nplt = graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)], size=(500,500), nodesize=0.1, fontsize=2)\nsavefig(plt, \"www/intro.png\")\ndisplay(plt)\n\n\n┌ Warning: Only one thread available\n└ @ CausalInference ~/.julia/packages/CausalInference/ozcj8/src/ges.jl:52\n\n\n\n\n\n \n \n \n\n\n\n \n \n \n\n\n\n \n \n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nSo, our goal was given the DAG provided by the ges method in the causal discovery (Chickering 2003), generate equations that rules each of these causal relations, represented in the DAG as directed edges. The SCM is the union of the DAG and these causal equations, that is, the SCM is a tuple \\((G, \\mathbf{f})\\), where \\(G\\) is the DAG and \\(\\mathbf{f}\\) is the set of functions that generates the value of each variable given its parents.\nOur solution for constructing the structural causal equations was to assume that the data was generated by a linear model, ie, the causal relations were linear. For the DAG provided in the code example we derive\n\\[ v = \\mathcal{b}_v \\]\n\\[ x = \\mathcal{a}_{v \\to x} v + \\mathcal{b}_x \\]\n\\[ w = \\mathcal{a}_{x \\to w} x + \\mathcal{b}_w \\]\n\\[ z = \\mathcal{a}_{v \\to z} v+ \\mathcal{a}_{w \\to z} w + \\mathcal{b}_z \\]\n\\[ s = \\mathcal{a}_{z \\to s} z + \\mathcal{b}_s \\]\nand that’s the tricky thing, as we can see these causal equations are different than the ones that generated the data, but they are the ones that respect the causal system obtained from the obtained DAG. Here \\(\\mathcal{b}_i\\) and \\(\\mathcal{a}_{i \\to j}\\) are the intercept term and the coefficient obtained from the linear regression, respectively. To correctly solve the linear regression respecting the dependencies of the causal graph, we use topological_sort_by_dfs from Graphs.jl.\nNow, with the SCM structure in hand, we see that the representation could be a struct containing the DAG and the coefficients/intercepts of the causal equations, this maps exactly the tuple \\((G, \\mathbf{f})\\) that we defined. However, since we need these equations to be differentiable, we need to define a function that takes the SCM and returns the value of the variable given its parents and using just the coefficients and the DAG, lead to errors, because AutoDiff does not deal well with functions that are conditioned (if statements). So, we need to define a way to retrieve the system of causal equations in a smooth way and that’s where the causal_effects matrix comes to the rescue.\nLet the factual vector of features be denoted as:\n\\[\n\\mathbf{x}_F =\n\\begin{bmatrix}\nx_{F_1} \\\\\nx_{F_2} \\\\\nx_{F_3} \\\\\n\\vdots \\\\\nx_{F_n}\n\\end{bmatrix}\n\\]\nLet the causal_effects matrix be:\n\\[\n\\mathbf{C} =\n\\begin{bmatrix}\na_{11} & a_{12} & \\cdots & a_{1n} & b_1 \\\\\na_{21} & a_{22} & \\cdots & a_{2n} & b_2 \\\\\na_{31} & a_{32} & \\cdots & a_{3n} & b_3 \\\\\n\\vdots & \\vdots & \\ddots & \\vdots & \\vdots \\\\\na_{n1} & a_{n2} & \\cdots & a_{nn} & b_n \\\\\n\\end{bmatrix}\n\\]\nHere, \\(a_{ij}\\) represents the coefficient from the causal effect of \\(x_{F_j}\\) on \\(x_{F_i}\\), and \\(b_i\\) represents the intercept term for the variable \\(x_{F_i}\\).\nThe matrix multiplication of the causal_effects matrix with the factual vector (excluding the bias term) is given by:\n\\[\n\\mathbf{C}_{:, 1:n} \\cdot \\mathbf{x}_F =\n\\begin{bmatrix}\na_{11} & a_{12} & \\cdots & a_{1n} \\\\\na_{21} & a_{22} & \\cdots & a_{2n} \\\\\na_{31} & a_{32} & \\cdots & a_{3n} \\\\\n\\vdots & \\vdots & \\ddots & \\vdots \\\\\na_{n1} & a_{n2} & \\cdots & a_{nn}\n\\end{bmatrix}\n\\begin{bmatrix}\nx_{F_1} \\\\\nx_{F_2} \\\\\nx_{F_3} \\\\\n\\vdots \\\\\nx_{F_n}\n\\end{bmatrix}\n\\]\nFinally, we add the bias term:\n\\[\n\\mathbf{x}_{SCF} = \\mathbf{C}_{:, 1:n} \\cdot \\mathbf{x}_F +\n\\begin{bmatrix}\nb_1 \\\\\nb_2 \\\\\nb_3 \\\\\n\\vdots \\\\\nb_n\n\\end{bmatrix}\n\\]\nIn expanded form:\n\\[\n\\mathbf{x}_{SCF_i} = a_{i1} x_{F_1} + a_{i2} x_{F_2} + \\cdots + a_{in} x_{F_n} + b_i, \\quad \\forall i = 1, 2, \\dots, n\n\\]\nThis equation shows how each counterfactual variable \\(x_{SCF_i}\\) is generated as a linear combination of the factual inputs \\(x_{F_j}\\) based on the causal effects matrix, with an intercept term \\(b_i\\) added for each variable.\nOne can note that the orphan nodes, that is, the nodes that do not have parents in the DAG, are going to be equal to the intercept term \\(\\mathcal{b}_\\hat{o}\\). The intuition behind this is that when we do the linear regression, variables that have no causal parents are just equal to the unconditional mean of the variable, i.e, we get \\(x_{SCF_\\hat{o}} = \\mathbb{E}(x_\\hat{o})\\). Because of this, in some cases a better understanding of the regression is needed, so the residuals are also part of the SCM structure,\n\n\nCode\nstruct SCM\n variables::Vector{String}\n coefficients::Vector{Vector{Float64}}\n residuals::Vector{Vector{Float64}}\n dag::DiGraph\n causal_effects::Matrix{Float64}\nend\n\n\n\n\nCounterfactualExplanations.jl" + "text": "Implementation\n\nCausalInference.jl\nIn terms of implementation, we need to capture the causal relations from the data, that’s where CausalInference.jl comes in. However, before the project, the package did not have a SCM structure, in the sense that the methods just captured the topological Directed Acyclic Graph (DAG) that showed the causality ruling the data, that is, no causal structural equations were provided,\n\n\nCode\nusing CausalInference\nusing CounterfactualExplanations\nusing CounterfactualExplanations.GenerativeModels\nusing Graphs\nusing GraphRecipes\nusing MultivariateStats\nusing Plots\nusing Random\nRandom.seed!(1)\nusing StatsBase\n\nN = 2000 # number of data points\n\nx = randn(N)\nv = x + randn(N)*0.25\nw = x + randn(N)*0.25\nz = v + w + randn(N)*0.25\ns = z + randn(N)*0.25\n\ndf = (x=x, v=v, w=w, z=z, s=s)\n\nest_g, score = ges(df; penalty=1.0, parallel=true)\n\nplt = graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)], size=(500,500), nodesize=0.1, fontsize=25)\nsavefig(plt, \"www/intro.png\")\ndisplay(plt)\n\n\n┌ Warning: Only one thread available\n└ @ CausalInference ~/.julia/packages/CausalInference/ozcj8/src/ges.jl:52\n\n\n\n\n\n \n \n \n\n\n\n \n \n \n\n\n\n \n \n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nSo, our goal was given the DAG provided by the ges method in the causal discovery (Chickering 2003), generate equations that rules each of these causal relations, represented in the DAG as directed edges. The SCM is the union of the DAG and these causal equations, that is, the SCM is a tuple \\((G, \\mathbf{f})\\), where \\(G\\) is the DAG and \\(\\mathbf{f}\\) is the set of functions that generates the value of each variable given its parents.\nOur solution for constructing the structural causal equations was to assume that the data was generated by a linear model, ie, the causal relations were linear. For the DAG provided in the code example we derive\n\\[ v = \\mathcal{b}_v \\]\n\\[ x = \\mathcal{a}_{v \\to x} v + \\mathcal{b}_x \\]\n\\[ w = \\mathcal{a}_{x \\to w} x + \\mathcal{b}_w \\]\n\\[ z = \\mathcal{a}_{v \\to z} v+ \\mathcal{a}_{w \\to z} w + \\mathcal{b}_z \\]\n\\[ s = \\mathcal{a}_{z \\to s} z + \\mathcal{b}_s \\]\nand that’s the tricky thing, as we can see these causal equations are different than the ones that generated the data, but they are the ones that respect the causal system obtained from the obtained DAG. Here \\(\\mathcal{b}_i\\) and \\(\\mathcal{a}_{i \\to j}\\) are the intercept term and the coefficient obtained from the linear regression, respectively. To correctly solve the linear regression respecting the dependencies of the causal graph, we use topological_sort_by_dfs from Graphs.jl.\nNow, with the SCM structure in hand, we see that the representation could be a struct containing the DAG and the coefficients/intercepts of the causal equations, this maps exactly the tuple \\((G, \\mathbf{f})\\) that we defined. However, since we need these equations to be differentiable, we need to define a function that takes the SCM and returns the value of the variable given its parents and using just the coefficients and the DAG, lead to errors, because AutoDiff does not deal well with functions that are conditioned (if statements). So, we need to define a way to retrieve the system of causal equations in a smooth way and that’s where the causal_effects matrix comes to the rescue.\nLet the factual vector of features be denoted as:\n\\[\n\\mathbf{x}_F =\n\\begin{bmatrix}\nx_{F_1} \\\\\nx_{F_2} \\\\\nx_{F_3} \\\\\n\\vdots \\\\\nx_{F_n}\n\\end{bmatrix}\n\\]\nLet the causal_effects matrix be:\n\\[\n\\mathbf{C} =\n\\begin{bmatrix}\na_{11} & a_{12} & \\cdots & a_{1n} & b_1 \\\\\na_{21} & a_{22} & \\cdots & a_{2n} & b_2 \\\\\na_{31} & a_{32} & \\cdots & a_{3n} & b_3 \\\\\n\\vdots & \\vdots & \\ddots & \\vdots & \\vdots \\\\\na_{n1} & a_{n2} & \\cdots & a_{nn} & b_n \\\\\n\\end{bmatrix}\n\\]\nHere, \\(a_{ij}\\) represents the coefficient from the causal effect of \\(x_{F_j}\\) on \\(x_{F_i}\\), and \\(b_i\\) represents the intercept term for the variable \\(x_{F_i}\\).\nThe matrix multiplication of the causal_effects matrix with the factual vector (excluding the bias term) is given by:\n\\[\n\\mathbf{C}_{:, 1:n} \\cdot \\mathbf{x}_F =\n\\begin{bmatrix}\na_{11} & a_{12} & \\cdots & a_{1n} \\\\\na_{21} & a_{22} & \\cdots & a_{2n} \\\\\na_{31} & a_{32} & \\cdots & a_{3n} \\\\\n\\vdots & \\vdots & \\ddots & \\vdots \\\\\na_{n1} & a_{n2} & \\cdots & a_{nn}\n\\end{bmatrix}\n\\begin{bmatrix}\nx_{F_1} \\\\\nx_{F_2} \\\\\nx_{F_3} \\\\\n\\vdots \\\\\nx_{F_n}\n\\end{bmatrix}\n\\]\nFinally, we add the bias term:\n\\[\n\\mathbf{x}_{SCF} = \\mathbf{C}_{:, 1:n} \\cdot \\mathbf{x}_F +\n\\begin{bmatrix}\nb_1 \\\\\nb_2 \\\\\nb_3 \\\\\n\\vdots \\\\\nb_n\n\\end{bmatrix}\n\\]\nIn expanded form:\n\\[\n\\mathbf{x}_{SCF_i} = a_{i1} x_{F_1} + a_{i2} x_{F_2} + \\cdots + a_{in} x_{F_n} + b_i, \\quad \\forall i = 1, 2, \\dots, n\n\\]\nThis equation shows how each counterfactual variable \\(x_{SCF_i}\\) is generated as a linear combination of the factual inputs \\(x_{F_j}\\) based on the causal effects matrix, with an intercept term \\(b_i\\) added for each variable.\nOne can note that the orphan nodes, that is, the nodes that do not have parents in the DAG, are going to be equal to the intercept term \\(\\mathcal{b}_\\hat{o}\\). The intuition behind this is that when we do the linear regression, variables that have no causal parents are just equal to the unconditional mean of the variable, i.e, we get \\(x_{SCF_\\hat{o}} = \\mathbb{E}(x_\\hat{o})\\). Because of this, in some cases a better understanding of the regression is needed, so the residuals are also part of the SCM structure,\n\n\nCode\nstruct SCM\n variables::Vector{String}\n coefficients::Vector{Vector{Float64}}\n residuals::Vector{Vector{Float64}}\n dag::DiGraph\n causal_effects::Matrix{Float64}\nend\n\n\n\n\nCounterfactualExplanations.jl\nNow, we need to go into the optimization problem previously described. We seek to minimize the lagrangian function we defined where now we have a differentiable function. The standard way to implement generators in CounterfactualExplanations.jl is to use AutoDiff exactly using composable functions in the lagrangian. The definition of \\(\\mathcal{L_{\\texttt{MINT}}}\\) is in the same shape of the the others gradient-based generators in the package, so the optimization is straightforward. However, we needed some way to pass the \\(x_F\\) into the \\(x_{SCF}\\) and that’s where transformer.jl comes in. This is where InputTransformers are defined in the package and in some way this is what we are doing, we are passing our factual to the “latent” causal space of the counterfactual. Our first step is to create a new kind of InputTransformer that is the SCM itself,\n\n\nCode\nconst TypedInputTransformer = Union{\n Type{<:StatsBase.AbstractDataTransform},\n Type{<:MultivariateStats.AbstractDimensionalityReduction},\n Type{<:GenerativeModels.AbstractGenerativeModel},\n Type{<:CausalInference.SCM} # The SCM transfromer\n}\n\n\nand then we need a way to create this transformer, that’s where we “overload” fit_transformer using CausalInferece.jl,\n\n\nCode\nfunction fit_transformer(\n data::CounterfactualData, input_encoder::Type{<:CausalInference.SCM}; kwargs...\n)\n t = Tables.table(transpose(data.X))\n est_g, score = CausalInference.ges(t; penalty=1.0, parallel=true)\n est_dag = CausalInference.pdag2dag!(est_g)\n scm = CausalInference.estimate_equations(t, est_dag)\n return scm\nend\n\n\n… We are getting there! However, now comes the hardest part, where this is placed?" }, { "objectID": "blog/posts/conformal-prediction/index.html", @@ -550,6 +550,6 @@ "href": "blog/index.html", "title": "Taija’s Blog", "section": "", - "text": "Welcome to Taija’s blog! Here you will find accessible introductions to packages, tutorials and other resources.\n\n\n\n\n\n\nInterested in contributing?\n\n\n\nHave you used one of our packages and found it useful? Or have you perhaps even contributed to one of our packages? We’d love for you to spread the word here! If you’re interested in contributing a blog post, please get in touch or open a pull request.\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nWhen Causality meets Recourse\n\n\nCounterfactual Explanations through Structural Causal Models\n\n\nThis post introduces a new tool in CounterfactualExplanations.jl, enhancing the package with causal reasoning to generate counterfactual explanations. \n\n\n\n\n\nSep 17, 2024\n\n\nPatrick Altmeyer, Jorge Luiz Franco\n\n\n8 min\n\n\n9/17/24, 1:51:51 PM\n\n\n\n\n\n\n\n\n\n\n\n\nNew Package for Energy-Based Sampling\n\n\nIntroducing EnergySamplers.jl\n\n\nA short post announcing a small new package: EnergySamplers.jl for energy-based sampling.\n\n\n\n\n\nSep 6, 2024\n\n\nPatrick Altmeyer\n\n\n7 min\n\n\n9/17/24, 7:52:15 AM\n\n\n\n\n\n\n\n\n\n\n\n\nBuilding a Conformal Chatbot in Julia\n\n\nHuggingFace, Transformers, and Conformal Prediction - Part 1\n\n\nFor this year’s edition of the ING Analytics Experiment Week, we put ConformalPrediction.jl to work and built a chatbot that can be used for Conformal Intent Recognition.\n\n\n\n\n\nJul 5, 2023\n\n\nPatrick Altmeyer\n\n\n7 min\n\n\n8/28/24, 5:16:41 PM\n\n\n\n\n\n\n\n\n\n\n\n\nPaving the Way Towards Low-Overhead Uncertainty Calibration\n\n\nAn Accessible Intro to Laplace Approximations in Julia for Bayesian Deep Learning\n\n\nA guest blog post by a team of students from TU Delft, who have contributed multiple improvements to LaplaceRedux.jl.\n\n\n\n\n\nJul 4, 2023\n\n\nPatrick Altmeyer, Severin Bratus, Mark Ardman, Adelina Cazacu, Andrei Ionescu, Ivan Makarov\n\n\n11 min\n\n\n8/28/24, 4:44:08 PM\n\n\n\n\n\n\n\n\n\n\n\n\nPrediction Intervals for any Regression Model\n\n\nConformal Prediction in Julia — Part 3\n\n\nThis third post introduces conformal regression by going through a standard machine learning workflow using MLJ.jl and ConformalPrediction.jl.\n\n\n\n\n\nDec 12, 2022\n\n\nPatrick Altmeyer\n\n\n11 min\n\n\n8/28/24, 4:44:08 PM\n\n\n\n\n\n\n\n\n\n\n\n\nHow to Conformalize a Deep Image Classifier\n\n\nConformal Prediction in Julia — Part 2\n\n\nA guide demonstrating how to use ConformalPrediction.jl to conformalize a deep image classifier in a few lines of code.\n\n\n\n\n\nDec 5, 2022\n\n\nPatrick Altmeyer\n\n\n9 min\n\n\n9/17/24, 8:26:22 AM\n\n\n\n\n\n\n\n\n\n\n\n\nConformal Prediction in Julia 🟣🔴🟢\n\n\nConformal Prediction in Julia — Part 1\n\n\nA (very) gentle introduction to Conformal Prediction in Julia using my new package ConformalPrediction.jl.\n\n\n\n\n\nOct 25, 2022\n\n\nPatrick Altmeyer\n\n\n15 min\n\n\n8/28/24, 4:44:08 PM\n\n\n\n\n\n\n\n\n\n\n\n\nA new tool for explainable AI\n\n\nCounterfactual Explanations in Julia — Part I\n\n\nThis post introduces a new Julia package for generating counterfactual explanations. The package can be used to explain machine learning algorithms developed and trained in Julia as well as other popular programming languages like Python and R. \n\n\n\n\n\nApr 20, 2022\n\n\nPatrick Altmeyer\n\n\n12 min\n\n\n9/17/24, 8:24:40 AM\n\n\n\n\n\n\n\n\n\n\n\n\nGo deep, but also … go Bayesian!\n\n\nEffortless Bayesian Deep Learning in Julia — Part I\n\n\nAn introduction to effortless Bayesian deep learning through Laplace approximation coded from scratch in Julia.\n\n\n\n\n\nFeb 18, 2022\n\n\nPatrick Altmeyer\n\n\n12 min\n\n\n8/28/24, 4:44:08 PM\n\n\n\n\n\n\nNo matching items" + "text": "Welcome to Taija’s blog! Here you will find accessible introductions to packages, tutorials and other resources.\n\n\n\n\n\n\nInterested in contributing?\n\n\n\nHave you used one of our packages and found it useful? Or have you perhaps even contributed to one of our packages? We’d love for you to spread the word here! If you’re interested in contributing a blog post, please get in touch or open a pull request.\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nWhen Causality meets Recourse\n\n\nCounterfactual Explanations through Structural Causal Models\n\n\nThis post introduces a new tool in CounterfactualExplanations.jl, enhancing the package with causal reasoning to generate counterfactual explanations. \n\n\n\n\n\nSep 17, 2024\n\n\nPatrick Altmeyer, Jorge Luiz Franco\n\n\n9 min\n\n\n9/17/24, 2:22:00 PM\n\n\n\n\n\n\n\n\n\n\n\n\nNew Package for Energy-Based Sampling\n\n\nIntroducing EnergySamplers.jl\n\n\nA short post announcing a small new package: EnergySamplers.jl for energy-based sampling.\n\n\n\n\n\nSep 6, 2024\n\n\nPatrick Altmeyer\n\n\n7 min\n\n\n9/17/24, 7:52:15 AM\n\n\n\n\n\n\n\n\n\n\n\n\nBuilding a Conformal Chatbot in Julia\n\n\nHuggingFace, Transformers, and Conformal Prediction - Part 1\n\n\nFor this year’s edition of the ING Analytics Experiment Week, we put ConformalPrediction.jl to work and built a chatbot that can be used for Conformal Intent Recognition.\n\n\n\n\n\nJul 5, 2023\n\n\nPatrick Altmeyer\n\n\n7 min\n\n\n8/28/24, 5:16:41 PM\n\n\n\n\n\n\n\n\n\n\n\n\nPaving the Way Towards Low-Overhead Uncertainty Calibration\n\n\nAn Accessible Intro to Laplace Approximations in Julia for Bayesian Deep Learning\n\n\nA guest blog post by a team of students from TU Delft, who have contributed multiple improvements to LaplaceRedux.jl.\n\n\n\n\n\nJul 4, 2023\n\n\nPatrick Altmeyer, Severin Bratus, Mark Ardman, Adelina Cazacu, Andrei Ionescu, Ivan Makarov\n\n\n11 min\n\n\n8/28/24, 4:44:08 PM\n\n\n\n\n\n\n\n\n\n\n\n\nPrediction Intervals for any Regression Model\n\n\nConformal Prediction in Julia — Part 3\n\n\nThis third post introduces conformal regression by going through a standard machine learning workflow using MLJ.jl and ConformalPrediction.jl.\n\n\n\n\n\nDec 12, 2022\n\n\nPatrick Altmeyer\n\n\n11 min\n\n\n8/28/24, 4:44:08 PM\n\n\n\n\n\n\n\n\n\n\n\n\nHow to Conformalize a Deep Image Classifier\n\n\nConformal Prediction in Julia — Part 2\n\n\nA guide demonstrating how to use ConformalPrediction.jl to conformalize a deep image classifier in a few lines of code.\n\n\n\n\n\nDec 5, 2022\n\n\nPatrick Altmeyer\n\n\n9 min\n\n\n9/17/24, 8:26:22 AM\n\n\n\n\n\n\n\n\n\n\n\n\nConformal Prediction in Julia 🟣🔴🟢\n\n\nConformal Prediction in Julia — Part 1\n\n\nA (very) gentle introduction to Conformal Prediction in Julia using my new package ConformalPrediction.jl.\n\n\n\n\n\nOct 25, 2022\n\n\nPatrick Altmeyer\n\n\n15 min\n\n\n8/28/24, 4:44:08 PM\n\n\n\n\n\n\n\n\n\n\n\n\nA new tool for explainable AI\n\n\nCounterfactual Explanations in Julia — Part I\n\n\nThis post introduces a new Julia package for generating counterfactual explanations. The package can be used to explain machine learning algorithms developed and trained in Julia as well as other popular programming languages like Python and R. \n\n\n\n\n\nApr 20, 2022\n\n\nPatrick Altmeyer\n\n\n12 min\n\n\n9/17/24, 8:24:40 AM\n\n\n\n\n\n\n\n\n\n\n\n\nGo deep, but also … go Bayesian!\n\n\nEffortless Bayesian Deep Learning in Julia — Part I\n\n\nAn introduction to effortless Bayesian deep learning through Laplace approximation coded from scratch in Julia.\n\n\n\n\n\nFeb 18, 2022\n\n\nPatrick Altmeyer\n\n\n12 min\n\n\n8/28/24, 4:44:08 PM\n\n\n\n\n\n\nNo matching items" } ] \ No newline at end of file diff --git a/docs/site_libs/bootstrap/bootstrap.min.css b/docs/site_libs/bootstrap/bootstrap.min.css index e142eb2..cd977db 100644 --- a/docs/site_libs/bootstrap/bootstrap.min.css +++ b/docs/site_libs/bootstrap/bootstrap.min.css @@ -1,12 +1,12 @@ 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.offcanvas{position:static;z-index:auto;flex-grow:1;-webkit-flex-grow:1;width:auto !important;height:auto !important;visibility:visible !important;background-color:rgba(0,0,0,0) !important;border:0 !important;transform:none !important;transition:none}.navbar-expand-xxl .offcanvas .offcanvas-header{display:none}.navbar-expand-xxl .offcanvas .offcanvas-body{display:flex;display:-webkit-flex;flex-grow:0;-webkit-flex-grow:0;padding:0;overflow-y:visible}}.navbar-expand{flex-wrap:nowrap;-webkit-flex-wrap:nowrap;justify-content:flex-start;-webkit-justify-content:flex-start}.navbar-expand .navbar-nav{flex-direction:row;-webkit-flex-direction:row}.navbar-expand .navbar-nav .dropdown-menu{position:absolute}.navbar-expand .navbar-nav .nav-link{padding-right:var(--bs-navbar-nav-link-padding-x);padding-left:var(--bs-navbar-nav-link-padding-x)}.navbar-expand .navbar-nav-scroll{overflow:visible}.navbar-expand .navbar-collapse{display:flex !important;display:-webkit-flex 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0.75rem;position:relative;display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;min-width:0;height:var(--bs-card-height);color:var(--bs-body-color);word-wrap:break-word;background-color:var(--bs-card-bg);background-clip:border-box;border:var(--bs-card-border-width) solid var(--bs-card-border-color);border-radius:var(--bs-card-border-radius)}.card>hr{margin-right:0;margin-left:0}.card>.list-group{border-top:inherit;border-bottom:inherit}.card>.list-group:first-child{border-top-width:0;border-top-left-radius:var(--bs-card-inner-border-radius);border-top-right-radius:var(--bs-card-inner-border-radius)}.card>.list-group:last-child{border-bottom-width:0;border-bottom-right-radius:var(--bs-card-inner-border-radius);border-bottom-left-radius:var(--bs-card-inner-border-radius)}.card>.card-header+.list-group,.card>.list-group+.card-footer{border-top:0}.card-body{flex:1 1 auto;-webkit-flex:1 1 auto;padding:var(--bs-card-spacer-y) var(--bs-card-spacer-x);color:var(--bs-card-color)}.card-title{margin-bottom:var(--bs-card-title-spacer-y);color:var(--bs-card-title-color)}.card-subtitle{margin-top:calc(-0.5*var(--bs-card-title-spacer-y));margin-bottom:0;color:var(--bs-card-subtitle-color)}.card-text:last-child{margin-bottom:0}.card-link+.card-link{margin-left:var(--bs-card-spacer-x)}.card-header{padding:var(--bs-card-cap-padding-y) var(--bs-card-cap-padding-x);margin-bottom:0;color:var(--bs-card-cap-color);background-color:var(--bs-card-cap-bg);border-bottom:var(--bs-card-border-width) solid var(--bs-card-border-color)}.card-header:first-child{border-radius:var(--bs-card-inner-border-radius) var(--bs-card-inner-border-radius) 0 0}.card-footer{padding:var(--bs-card-cap-padding-y) var(--bs-card-cap-padding-x);color:var(--bs-card-cap-color);background-color:var(--bs-card-cap-bg);border-top:var(--bs-card-border-width) solid var(--bs-card-border-color)}.card-footer:last-child{border-radius:0 0 var(--bs-card-inner-border-radius) var(--bs-card-inner-border-radius)}.card-header-tabs{margin-right:calc(-0.5*var(--bs-card-cap-padding-x));margin-bottom:calc(-1*var(--bs-card-cap-padding-y));margin-left:calc(-0.5*var(--bs-card-cap-padding-x));border-bottom:0}.card-header-tabs .nav-link.active{background-color:var(--bs-card-bg);border-bottom-color:var(--bs-card-bg)}.card-header-pills{margin-right:calc(-0.5*var(--bs-card-cap-padding-x));margin-left:calc(-0.5*var(--bs-card-cap-padding-x))}.card-img-overlay{position:absolute;top:0;right:0;bottom:0;left:0;padding:var(--bs-card-img-overlay-padding);border-radius:var(--bs-card-inner-border-radius)}.card-img,.card-img-top,.card-img-bottom{width:100%}.card-img,.card-img-top{border-top-left-radius:var(--bs-card-inner-border-radius);border-top-right-radius:var(--bs-card-inner-border-radius)}.card-img,.card-img-bottom{border-bottom-right-radius:var(--bs-card-inner-border-radius);border-bottom-left-radius:var(--bs-card-inner-border-radius)}.card-group>.card{margin-bottom:var(--bs-card-group-margin)}@media(min-width: 576px){.card-group{display:flex;display:-webkit-flex;flex-flow:row wrap;-webkit-flex-flow:row wrap}.card-group>.card{flex:1 0 0%;-webkit-flex:1 0 0%;margin-bottom:0}.card-group>.card+.card{margin-left:0;border-left:0}.card-group>.card:not(:last-child){border-top-right-radius:0;border-bottom-right-radius:0}.card-group>.card:not(:last-child) .card-img-top,.card-group>.card:not(:last-child) .card-header{border-top-right-radius:0}.card-group>.card:not(:last-child) .card-img-bottom,.card-group>.card:not(:last-child) .card-footer{border-bottom-right-radius:0}.card-group>.card:not(:first-child){border-top-left-radius:0;border-bottom-left-radius:0}.card-group>.card:not(:first-child) .card-img-top,.card-group>.card:not(:first-child) .card-header{border-top-left-radius:0}.card-group>.card:not(:first-child) .card-img-bottom,.card-group>.card:not(:first-child) .card-footer{border-bottom-left-radius:0}}.accordion{--bs-accordion-color: #0a1432;--bs-accordion-bg: #f6f8fd;--bs-accordion-transition: color 0.15s ease-in-out, background-color 0.15s ease-in-out, border-color 0.15s ease-in-out, box-shadow 0.15s ease-in-out, border-radius 0.15s ease;--bs-accordion-border-color: #dee2e6;--bs-accordion-border-width: 1px;--bs-accordion-border-radius: 0.25rem;--bs-accordion-inner-border-radius: calc(0.25rem - 1px);--bs-accordion-btn-padding-x: 1.25rem;--bs-accordion-btn-padding-y: 1rem;--bs-accordion-btn-color: #0a1432;--bs-accordion-btn-bg: #f6f8fd;--bs-accordion-btn-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%230a1432'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-icon-width: 1.25rem;--bs-accordion-btn-icon-transform: rotate(-180deg);--bs-accordion-btn-icon-transition: transform 0.2s ease-in-out;--bs-accordion-btn-active-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%231a2856'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-focus-border-color: #a0b1ec;--bs-accordion-btn-focus-box-shadow: 0 0 0 0.25rem rgba(64, 99, 216, 0.25);--bs-accordion-body-padding-x: 1.25rem;--bs-accordion-body-padding-y: 1rem;--bs-accordion-active-color: #1a2856;--bs-accordion-active-bg: #d9e0f7}.accordion-button{position:relative;display:flex;display:-webkit-flex;align-items:center;-webkit-align-items:center;width:100%;padding:var(--bs-accordion-btn-padding-y) var(--bs-accordion-btn-padding-x);font-size:1rem;color:var(--bs-accordion-btn-color);text-align:left;background-color:var(--bs-accordion-btn-bg);border:0;border-radius:0;overflow-anchor:none;transition:var(--bs-accordion-transition)}@media(prefers-reduced-motion: reduce){.accordion-button{transition:none}}.accordion-button:not(.collapsed){color:var(--bs-accordion-active-color);background-color:var(--bs-accordion-active-bg);box-shadow:inset 0 calc(-1*var(--bs-accordion-border-width)) 0 var(--bs-accordion-border-color)}.accordion-button:not(.collapsed)::after{background-image:var(--bs-accordion-btn-active-icon);transform:var(--bs-accordion-btn-icon-transform)}.accordion-button::after{flex-shrink:0;-webkit-flex-shrink:0;width:var(--bs-accordion-btn-icon-width);height:var(--bs-accordion-btn-icon-width);margin-left:auto;content:"";background-image:var(--bs-accordion-btn-icon);background-repeat:no-repeat;background-size:var(--bs-accordion-btn-icon-width);transition:var(--bs-accordion-btn-icon-transition)}@media(prefers-reduced-motion: reduce){.accordion-button::after{transition:none}}.accordion-button:hover{z-index:2}.accordion-button:focus{z-index:3;border-color:var(--bs-accordion-btn-focus-border-color);outline:0;box-shadow:var(--bs-accordion-btn-focus-box-shadow)}.accordion-header{margin-bottom:0}.accordion-item{color:var(--bs-accordion-color);background-color:var(--bs-accordion-bg);border:var(--bs-accordion-border-width) solid var(--bs-accordion-border-color)}.accordion-item:first-of-type{border-top-left-radius:var(--bs-accordion-border-radius);border-top-right-radius:var(--bs-accordion-border-radius)}.accordion-item:first-of-type .accordion-button{border-top-left-radius:var(--bs-accordion-inner-border-radius);border-top-right-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:not(:first-of-type){border-top:0}.accordion-item:last-of-type{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-item:last-of-type .accordion-button.collapsed{border-bottom-right-radius:var(--bs-accordion-inner-border-radius);border-bottom-left-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:last-of-type .accordion-collapse{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-body{padding:var(--bs-accordion-body-padding-y) var(--bs-accordion-body-padding-x)}.accordion-flush .accordion-collapse{border-width:0}.accordion-flush .accordion-item{border-right:0;border-left:0;border-radius:0}.accordion-flush .accordion-item:first-child{border-top:0}.accordion-flush .accordion-item:last-child{border-bottom:0}.accordion-flush .accordion-item .accordion-button,.accordion-flush .accordion-item .accordion-button.collapsed{border-radius:0}[data-bs-theme=dark] .accordion-button::after{--bs-accordion-btn-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%238ca1e8'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-active-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%238ca1e8'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e")}.breadcrumb{--bs-breadcrumb-padding-x: 0;--bs-breadcrumb-padding-y: 0;--bs-breadcrumb-margin-bottom: 1rem;--bs-breadcrumb-bg: ;--bs-breadcrumb-border-radius: ;--bs-breadcrumb-divider-color: rgba(10, 20, 50, 0.75);--bs-breadcrumb-item-padding-x: 0.5rem;--bs-breadcrumb-item-active-color: rgba(10, 20, 50, 0.75);display:flex;display:-webkit-flex;flex-wrap:wrap;-webkit-flex-wrap:wrap;padding:var(--bs-breadcrumb-padding-y) var(--bs-breadcrumb-padding-x);margin-bottom:var(--bs-breadcrumb-margin-bottom);font-size:var(--bs-breadcrumb-font-size);list-style:none;background-color:var(--bs-breadcrumb-bg);border-radius:var(--bs-breadcrumb-border-radius)}.breadcrumb-item+.breadcrumb-item{padding-left:var(--bs-breadcrumb-item-padding-x)}.breadcrumb-item+.breadcrumb-item::before{float:left;padding-right:var(--bs-breadcrumb-item-padding-x);color:var(--bs-breadcrumb-divider-color);content:var(--bs-breadcrumb-divider, ">") /* rtl: var(--bs-breadcrumb-divider, ">") */}.breadcrumb-item.active{color:var(--bs-breadcrumb-item-active-color)}.pagination{--bs-pagination-padding-x: 0.75rem;--bs-pagination-padding-y: 0.375rem;--bs-pagination-font-size:1rem;--bs-pagination-color: #4063D8;--bs-pagination-bg: #f6f8fd;--bs-pagination-border-width: 1px;--bs-pagination-border-color: #dee2e6;--bs-pagination-border-radius: 0.25rem;--bs-pagination-hover-color: #334fad;--bs-pagination-hover-bg: #f8f9fa;--bs-pagination-hover-border-color: #dee2e6;--bs-pagination-focus-color: #334fad;--bs-pagination-focus-bg: #e9ecef;--bs-pagination-focus-box-shadow: 0 0 0 0.25rem rgba(64, 99, 216, 0.25);--bs-pagination-active-color: #ffffff;--bs-pagination-active-bg: #4063D8;--bs-pagination-active-border-color: #4063D8;--bs-pagination-disabled-color: rgba(10, 20, 50, 0.75);--bs-pagination-disabled-bg: #e9ecef;--bs-pagination-disabled-border-color: #dee2e6;display:flex;display:-webkit-flex;padding-left:0;list-style:none}.page-link{position:relative;display:block;padding:var(--bs-pagination-padding-y) var(--bs-pagination-padding-x);font-size:var(--bs-pagination-font-size);color:var(--bs-pagination-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-pagination-bg);border:var(--bs-pagination-border-width) solid var(--bs-pagination-border-color);transition:color .15s ease-in-out,background-color .15s ease-in-out,border-color .15s ease-in-out,box-shadow .15s ease-in-out}@media(prefers-reduced-motion: reduce){.page-link{transition:none}}.page-link:hover{z-index:2;color:var(--bs-pagination-hover-color);background-color:var(--bs-pagination-hover-bg);border-color:var(--bs-pagination-hover-border-color)}.page-link:focus{z-index:3;color:var(--bs-pagination-focus-color);background-color:var(--bs-pagination-focus-bg);outline:0;box-shadow:var(--bs-pagination-focus-box-shadow)}.page-link.active,.active>.page-link{z-index:3;color:var(--bs-pagination-active-color);background-color:var(--bs-pagination-active-bg);border-color:var(--bs-pagination-active-border-color)}.page-link.disabled,.disabled>.page-link{color:var(--bs-pagination-disabled-color);pointer-events:none;background-color:var(--bs-pagination-disabled-bg);border-color:var(--bs-pagination-disabled-border-color)}.page-item:not(:first-child) .page-link{margin-left:calc(1px*-1)}.page-item:first-child .page-link{border-top-left-radius:var(--bs-pagination-border-radius);border-bottom-left-radius:var(--bs-pagination-border-radius)}.page-item:last-child .page-link{border-top-right-radius:var(--bs-pagination-border-radius);border-bottom-right-radius:var(--bs-pagination-border-radius)}.pagination-lg{--bs-pagination-padding-x: 1.5rem;--bs-pagination-padding-y: 0.75rem;--bs-pagination-font-size:1.25rem;--bs-pagination-border-radius: 0.5rem}.pagination-sm{--bs-pagination-padding-x: 0.5rem;--bs-pagination-padding-y: 0.25rem;--bs-pagination-font-size:0.875rem;--bs-pagination-border-radius: 0.2em}.badge{--bs-badge-padding-x: 0.65em;--bs-badge-padding-y: 0.35em;--bs-badge-font-size:0.75em;--bs-badge-font-weight: 700;--bs-badge-color: #ffffff;--bs-badge-border-radius: 0.25rem;display:inline-block;padding:var(--bs-badge-padding-y) var(--bs-badge-padding-x);font-size:var(--bs-badge-font-size);font-weight:var(--bs-badge-font-weight);line-height:1;color:var(--bs-badge-color);text-align:center;white-space:nowrap;vertical-align:baseline;border-radius:var(--bs-badge-border-radius)}.badge:empty{display:none}.btn .badge{position:relative;top:-1px}.alert{--bs-alert-bg: transparent;--bs-alert-padding-x: 1rem;--bs-alert-padding-y: 1rem;--bs-alert-margin-bottom: 1rem;--bs-alert-color: inherit;--bs-alert-border-color: transparent;--bs-alert-border: 1px solid var(--bs-alert-border-color);--bs-alert-border-radius: 0.25rem;--bs-alert-link-color: inherit;position:relative;padding:var(--bs-alert-padding-y) var(--bs-alert-padding-x);margin-bottom:var(--bs-alert-margin-bottom);color:var(--bs-alert-color);background-color:var(--bs-alert-bg);border:var(--bs-alert-border);border-radius:var(--bs-alert-border-radius)}.alert-heading{color:inherit}.alert-link{font-weight:700;color:var(--bs-alert-link-color)}.alert-dismissible{padding-right:3rem}.alert-dismissible .btn-close{position:absolute;top:0;right:0;z-index:2;padding:1.25rem 1rem}.alert-default{--bs-alert-color: var(--bs-default-text-emphasis);--bs-alert-bg: var(--bs-default-bg-subtle);--bs-alert-border-color: var(--bs-default-border-subtle);--bs-alert-link-color: var(--bs-default-text-emphasis)}.alert-primary{--bs-alert-color: var(--bs-primary-text-emphasis);--bs-alert-bg: var(--bs-primary-bg-subtle);--bs-alert-border-color: var(--bs-primary-border-subtle);--bs-alert-link-color: var(--bs-primary-text-emphasis)}.alert-secondary{--bs-alert-color: var(--bs-secondary-text-emphasis);--bs-alert-bg: var(--bs-secondary-bg-subtle);--bs-alert-border-color: var(--bs-secondary-border-subtle);--bs-alert-link-color: var(--bs-secondary-text-emphasis)}.alert-success{--bs-alert-color: var(--bs-success-text-emphasis);--bs-alert-bg: var(--bs-success-bg-subtle);--bs-alert-border-color: var(--bs-success-border-subtle);--bs-alert-link-color: var(--bs-success-text-emphasis)}.alert-info{--bs-alert-color: var(--bs-info-text-emphasis);--bs-alert-bg: var(--bs-info-bg-subtle);--bs-alert-border-color: var(--bs-info-border-subtle);--bs-alert-link-color: var(--bs-info-text-emphasis)}.alert-warning{--bs-alert-color: var(--bs-warning-text-emphasis);--bs-alert-bg: var(--bs-warning-bg-subtle);--bs-alert-border-color: var(--bs-warning-border-subtle);--bs-alert-link-color: var(--bs-warning-text-emphasis)}.alert-danger{--bs-alert-color: var(--bs-danger-text-emphasis);--bs-alert-bg: var(--bs-danger-bg-subtle);--bs-alert-border-color: var(--bs-danger-border-subtle);--bs-alert-link-color: var(--bs-danger-text-emphasis)}.alert-light{--bs-alert-color: var(--bs-light-text-emphasis);--bs-alert-bg: var(--bs-light-bg-subtle);--bs-alert-border-color: var(--bs-light-border-subtle);--bs-alert-link-color: var(--bs-light-text-emphasis)}.alert-dark{--bs-alert-color: var(--bs-dark-text-emphasis);--bs-alert-bg: var(--bs-dark-bg-subtle);--bs-alert-border-color: var(--bs-dark-border-subtle);--bs-alert-link-color: var(--bs-dark-text-emphasis)}@keyframes progress-bar-stripes{0%{background-position-x:1rem}}.progress,.progress-stacked{--bs-progress-height: 1rem;--bs-progress-font-size:0.75rem;--bs-progress-bg: #e9ecef;--bs-progress-border-radius: 0.25rem;--bs-progress-box-shadow: inset 0 1px 2px rgba(0, 0, 0, 0.075);--bs-progress-bar-color: #ffffff;--bs-progress-bar-bg: #4063D8;--bs-progress-bar-transition: width 0.6s ease;display:flex;display:-webkit-flex;height:var(--bs-progress-height);overflow:hidden;font-size:var(--bs-progress-font-size);background-color:var(--bs-progress-bg);border-radius:var(--bs-progress-border-radius)}.progress-bar{display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;justify-content:center;-webkit-justify-content:center;overflow:hidden;color:var(--bs-progress-bar-color);text-align:center;white-space:nowrap;background-color:var(--bs-progress-bar-bg);transition:var(--bs-progress-bar-transition)}@media(prefers-reduced-motion: reduce){.progress-bar{transition:none}}.progress-bar-striped{background-image:linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);background-size:var(--bs-progress-height) var(--bs-progress-height)}.progress-stacked>.progress{overflow:visible}.progress-stacked>.progress>.progress-bar{width:100%}.progress-bar-animated{animation:1s linear infinite progress-bar-stripes}@media(prefers-reduced-motion: reduce){.progress-bar-animated{animation:none}}.list-group{--bs-list-group-color: #0a1432;--bs-list-group-bg: #f6f8fd;--bs-list-group-border-color: #dee2e6;--bs-list-group-border-width: 1px;--bs-list-group-border-radius: 0.25rem;--bs-list-group-item-padding-x: 1rem;--bs-list-group-item-padding-y: 0.5rem;--bs-list-group-action-color: rgba(10, 20, 50, 0.75);--bs-list-group-action-hover-color: #000;--bs-list-group-action-hover-bg: #f8f9fa;--bs-list-group-action-active-color: #0a1432;--bs-list-group-action-active-bg: #e9ecef;--bs-list-group-disabled-color: rgba(10, 20, 50, 0.75);--bs-list-group-disabled-bg: #f6f8fd;--bs-list-group-active-color: #ffffff;--bs-list-group-active-bg: #4063D8;--bs-list-group-active-border-color: #4063D8;display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;padding-left:0;margin-bottom:0;border-radius:var(--bs-list-group-border-radius)}.list-group-numbered{list-style-type:none;counter-reset:section}.list-group-numbered>.list-group-item::before{content:counters(section, ".") ". ";counter-increment:section}.list-group-item-action{width:100%;color:var(--bs-list-group-action-color);text-align:inherit}.list-group-item-action:hover,.list-group-item-action:focus{z-index:1;color:var(--bs-list-group-action-hover-color);text-decoration:none;background-color:var(--bs-list-group-action-hover-bg)}.list-group-item-action:active{color:var(--bs-list-group-action-active-color);background-color:var(--bs-list-group-action-active-bg)}.list-group-item{position:relative;display:block;padding:var(--bs-list-group-item-padding-y) var(--bs-list-group-item-padding-x);color:var(--bs-list-group-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-list-group-bg);border:var(--bs-list-group-border-width) solid var(--bs-list-group-border-color)}.list-group-item:first-child{border-top-left-radius:inherit;border-top-right-radius:inherit}.list-group-item:last-child{border-bottom-right-radius:inherit;border-bottom-left-radius:inherit}.list-group-item.disabled,.list-group-item:disabled{color:var(--bs-list-group-disabled-color);pointer-events:none;background-color:var(--bs-list-group-disabled-bg)}.list-group-item.active{z-index:2;color:var(--bs-list-group-active-color);background-color:var(--bs-list-group-active-bg);border-color:var(--bs-list-group-active-border-color)}.list-group-item+.list-group-item{border-top-width:0}.list-group-item+.list-group-item.active{margin-top:calc(-1*var(--bs-list-group-border-width));border-top-width:var(--bs-list-group-border-width)}.list-group-horizontal{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal>.list-group-item.active{margin-top:0}.list-group-horizontal>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}@media(min-width: 576px){.list-group-horizontal-sm{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-sm>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-sm>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-sm>.list-group-item.active{margin-top:0}.list-group-horizontal-sm>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-sm>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 768px){.list-group-horizontal-md{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-md>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-md>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-md>.list-group-item.active{margin-top:0}.list-group-horizontal-md>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-md>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 992px){.list-group-horizontal-lg{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-lg>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-lg>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-lg>.list-group-item.active{margin-top:0}.list-group-horizontal-lg>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-lg>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 1200px){.list-group-horizontal-xl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xl>.list-group-item.active{margin-top:0}.list-group-horizontal-xl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xl>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 1400px){.list-group-horizontal-xxl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xxl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xxl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xxl>.list-group-item.active{margin-top:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}.list-group-flush{border-radius:0}.list-group-flush>.list-group-item{border-width:0 0 var(--bs-list-group-border-width)}.list-group-flush>.list-group-item:last-child{border-bottom-width:0}.list-group-item-default{--bs-list-group-color: var(--bs-default-text-emphasis);--bs-list-group-bg: var(--bs-default-bg-subtle);--bs-list-group-border-color: var(--bs-default-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-default-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-default-border-subtle);--bs-list-group-active-color: var(--bs-default-bg-subtle);--bs-list-group-active-bg: var(--bs-default-text-emphasis);--bs-list-group-active-border-color: var(--bs-default-text-emphasis)}.list-group-item-primary{--bs-list-group-color: var(--bs-primary-text-emphasis);--bs-list-group-bg: var(--bs-primary-bg-subtle);--bs-list-group-border-color: var(--bs-primary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-primary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-primary-border-subtle);--bs-list-group-active-color: var(--bs-primary-bg-subtle);--bs-list-group-active-bg: var(--bs-primary-text-emphasis);--bs-list-group-active-border-color: var(--bs-primary-text-emphasis)}.list-group-item-secondary{--bs-list-group-color: var(--bs-secondary-text-emphasis);--bs-list-group-bg: var(--bs-secondary-bg-subtle);--bs-list-group-border-color: var(--bs-secondary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-secondary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-secondary-border-subtle);--bs-list-group-active-color: var(--bs-secondary-bg-subtle);--bs-list-group-active-bg: var(--bs-secondary-text-emphasis);--bs-list-group-active-border-color: var(--bs-secondary-text-emphasis)}.list-group-item-success{--bs-list-group-color: var(--bs-success-text-emphasis);--bs-list-group-bg: var(--bs-success-bg-subtle);--bs-list-group-border-color: var(--bs-success-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-success-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-success-border-subtle);--bs-list-group-active-color: var(--bs-success-bg-subtle);--bs-list-group-active-bg: var(--bs-success-text-emphasis);--bs-list-group-active-border-color: var(--bs-success-text-emphasis)}.list-group-item-info{--bs-list-group-color: var(--bs-info-text-emphasis);--bs-list-group-bg: var(--bs-info-bg-subtle);--bs-list-group-border-color: var(--bs-info-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-info-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-info-border-subtle);--bs-list-group-active-color: var(--bs-info-bg-subtle);--bs-list-group-active-bg: var(--bs-info-text-emphasis);--bs-list-group-active-border-color: var(--bs-info-text-emphasis)}.list-group-item-warning{--bs-list-group-color: var(--bs-warning-text-emphasis);--bs-list-group-bg: var(--bs-warning-bg-subtle);--bs-list-group-border-color: var(--bs-warning-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-warning-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-warning-border-subtle);--bs-list-group-active-color: var(--bs-warning-bg-subtle);--bs-list-group-active-bg: var(--bs-warning-text-emphasis);--bs-list-group-active-border-color: var(--bs-warning-text-emphasis)}.list-group-item-danger{--bs-list-group-color: var(--bs-danger-text-emphasis);--bs-list-group-bg: var(--bs-danger-bg-subtle);--bs-list-group-border-color: var(--bs-danger-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-danger-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-danger-border-subtle);--bs-list-group-active-color: var(--bs-danger-bg-subtle);--bs-list-group-active-bg: var(--bs-danger-text-emphasis);--bs-list-group-active-border-color: var(--bs-danger-text-emphasis)}.list-group-item-light{--bs-list-group-color: var(--bs-light-text-emphasis);--bs-list-group-bg: var(--bs-light-bg-subtle);--bs-list-group-border-color: var(--bs-light-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-light-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-light-border-subtle);--bs-list-group-active-color: var(--bs-light-bg-subtle);--bs-list-group-active-bg: var(--bs-light-text-emphasis);--bs-list-group-active-border-color: var(--bs-light-text-emphasis)}.list-group-item-dark{--bs-list-group-color: var(--bs-dark-text-emphasis);--bs-list-group-bg: var(--bs-dark-bg-subtle);--bs-list-group-border-color: var(--bs-dark-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-dark-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-dark-border-subtle);--bs-list-group-active-color: var(--bs-dark-bg-subtle);--bs-list-group-active-bg: var(--bs-dark-text-emphasis);--bs-list-group-active-border-color: var(--bs-dark-text-emphasis)}.btn-close{--bs-btn-close-color: #000;--bs-btn-close-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%23000'%3e%3cpath d='M.293.293a1 1 0 0 1 1.414 0L8 6.586 14.293.293a1 1 0 1 1 1.414 1.414L9.414 8l6.293 6.293a1 1 0 0 1-1.414 1.414L8 9.414l-6.293 6.293a1 1 0 0 1-1.414-1.414L6.586 8 .293 1.707a1 1 0 0 1 0-1.414z'/%3e%3c/svg%3e");--bs-btn-close-opacity: 0.5;--bs-btn-close-hover-opacity: 0.75;--bs-btn-close-focus-shadow: 0 0 0 0.25rem rgba(64, 99, 216, 0.25);--bs-btn-close-focus-opacity: 1;--bs-btn-close-disabled-opacity: 0.25;--bs-btn-close-white-filter: invert(1) grayscale(100%) brightness(200%);box-sizing:content-box;width:1em;height:1em;padding:.25em .25em;color:var(--bs-btn-close-color);background:rgba(0,0,0,0) var(--bs-btn-close-bg) center/1em auto no-repeat;border:0;border-radius:.25rem;opacity:var(--bs-btn-close-opacity)}.btn-close:hover{color:var(--bs-btn-close-color);text-decoration:none;opacity:var(--bs-btn-close-hover-opacity)}.btn-close:focus{outline:0;box-shadow:var(--bs-btn-close-focus-shadow);opacity:var(--bs-btn-close-focus-opacity)}.btn-close:disabled,.btn-close.disabled{pointer-events:none;user-select:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;-o-user-select:none;opacity:var(--bs-btn-close-disabled-opacity)}.btn-close-white{filter:var(--bs-btn-close-white-filter)}[data-bs-theme=dark] .btn-close{filter:var(--bs-btn-close-white-filter)}.toast{--bs-toast-zindex: 1090;--bs-toast-padding-x: 0.75rem;--bs-toast-padding-y: 0.5rem;--bs-toast-spacing: 1.5rem;--bs-toast-max-width: 350px;--bs-toast-font-size:0.875rem;--bs-toast-color: ;--bs-toast-bg: rgba(246, 248, 253, 0.85);--bs-toast-border-width: 1px;--bs-toast-border-color: rgba(0, 0, 0, 0.175);--bs-toast-border-radius: 0.25rem;--bs-toast-box-shadow: 0 0.5rem 1rem rgba(0, 0, 0, 0.15);--bs-toast-header-color: rgba(10, 20, 50, 0.75);--bs-toast-header-bg: rgba(246, 248, 253, 0.85);--bs-toast-header-border-color: rgba(0, 0, 0, 0.175);width:var(--bs-toast-max-width);max-width:100%;font-size:var(--bs-toast-font-size);color:var(--bs-toast-color);pointer-events:auto;background-color:var(--bs-toast-bg);background-clip:padding-box;border:var(--bs-toast-border-width) solid var(--bs-toast-border-color);box-shadow:var(--bs-toast-box-shadow);border-radius:var(--bs-toast-border-radius)}.toast.showing{opacity:0}.toast:not(.show){display:none}.toast-container{--bs-toast-zindex: 1090;position:absolute;z-index:var(--bs-toast-zindex);width:max-content;width:-webkit-max-content;width:-moz-max-content;width:-ms-max-content;width:-o-max-content;max-width:100%;pointer-events:none}.toast-container>:not(:last-child){margin-bottom:var(--bs-toast-spacing)}.toast-header{display:flex;display:-webkit-flex;align-items:center;-webkit-align-items:center;padding:var(--bs-toast-padding-y) var(--bs-toast-padding-x);color:var(--bs-toast-header-color);background-color:var(--bs-toast-header-bg);background-clip:padding-box;border-bottom:var(--bs-toast-border-width) solid var(--bs-toast-header-border-color);border-top-left-radius:calc(var(--bs-toast-border-radius) - var(--bs-toast-border-width));border-top-right-radius:calc(var(--bs-toast-border-radius) - var(--bs-toast-border-width))}.toast-header .btn-close{margin-right:calc(-0.5*var(--bs-toast-padding-x));margin-left:var(--bs-toast-padding-x)}.toast-body{padding:var(--bs-toast-padding-x);word-wrap:break-word}.modal{--bs-modal-zindex: 1055;--bs-modal-width: 500px;--bs-modal-padding: 1rem;--bs-modal-margin: 0.5rem;--bs-modal-color: ;--bs-modal-bg: #f6f8fd;--bs-modal-border-color: rgba(0, 0, 0, 0.175);--bs-modal-border-width: 1px;--bs-modal-border-radius: 0.5rem;--bs-modal-box-shadow: 0 0.125rem 0.25rem rgba(0, 0, 0, 0.075);--bs-modal-inner-border-radius: calc(0.5rem - 1px);--bs-modal-header-padding-x: 1rem;--bs-modal-header-padding-y: 1rem;--bs-modal-header-padding: 1rem 1rem;--bs-modal-header-border-color: #dee2e6;--bs-modal-header-border-width: 1px;--bs-modal-title-line-height: 1.5;--bs-modal-footer-gap: 0.5rem;--bs-modal-footer-bg: ;--bs-modal-footer-border-color: #dee2e6;--bs-modal-footer-border-width: 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.value-box-title:empty::after{content:" "}.bslib-value-box .value-box-value{font-size:calc(1.29rem + 0.48vw);margin-top:0;margin-bottom:.5rem;font-weight:500;line-height:1.2}@media(min-width: 1200px){.bslib-value-box .value-box-value{font-size:1.65rem}}.bslib-value-box .value-box-value:empty::after{content:" "}.bslib-value-box .value-box-showcase{align-items:center;justify-content:center;margin-top:auto;margin-bottom:auto;padding:1rem}.bslib-value-box .value-box-showcase .bi,.bslib-value-box .value-box-showcase .fa,.bslib-value-box .value-box-showcase .fab,.bslib-value-box .value-box-showcase .fas,.bslib-value-box .value-box-showcase .far{opacity:.85;min-width:50px;max-width:125%}.bslib-value-box .value-box-showcase .bi,.bslib-value-box .value-box-showcase .fa,.bslib-value-box .value-box-showcase .fab,.bslib-value-box .value-box-showcase .fas,.bslib-value-box .value-box-showcase .far{font-size:4rem}.bslib-value-box.showcase-top-right .value-box-grid{grid-template-columns:1fr 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.value-box-grid{grid-template-columns:var(---bslib-value-box-showcase-w-fs, 1fr) auto}.bslib-value-box.showcase-left-center:not([data-fill-screen=true]) .value-box-grid .value-box-showcase{grid-area:left}.bslib-value-box.showcase-left-center:not([data-fill-screen=true]) .value-box-grid .value-box-area{grid-area:right}.bslib-value-box.showcase-bottom .value-box-grid{grid-template-columns:1fr;grid-template-rows:1fr var(---bslib-value-box-showcase-h, auto);grid-template-areas:"top" "bottom";overflow:hidden}.bslib-value-box.showcase-bottom .value-box-grid .value-box-showcase{grid-area:bottom;padding:0;margin:0}.bslib-value-box.showcase-bottom .value-box-grid .value-box-area{grid-area:top}.bslib-value-box.showcase-bottom[data-full-screen=true] .value-box-grid{grid-template-rows:1fr var(---bslib-value-box-showcase-h-fs, 2fr)}.bslib-value-box.showcase-bottom[data-full-screen=true] .value-box-grid .value-box-showcase{padding:1rem}[data-bs-theme=dark] .bslib-value-box{--bslib-value-box-shadow: 0 0.5rem 1rem rgb(0 0 0 / 50%)}@media(min-width: 576px){.nav:not(.nav-hidden){display:flex !important;display:-webkit-flex !important}.nav:not(.nav-hidden):not(.nav-stacked):not(.flex-column){float:none !important}.nav:not(.nav-hidden):not(.nav-stacked):not(.flex-column)>.bslib-nav-spacer{margin-left:auto !important}.nav:not(.nav-hidden):not(.nav-stacked):not(.flex-column)>.form-inline{margin-top:auto;margin-bottom:auto}.nav:not(.nav-hidden).nav-stacked{flex-direction:column;-webkit-flex-direction:column;height:100%}.nav:not(.nav-hidden).nav-stacked>.bslib-nav-spacer{margin-top:auto !important}}.bslib-card{overflow:auto}.bslib-card .card-body+.card-body{padding-top:0}.bslib-card .card-body{overflow:auto}.bslib-card .card-body p{margin-top:0}.bslib-card .card-body p:last-child{margin-bottom:0}.bslib-card .card-body{max-height:var(--bslib-card-body-max-height, none)}.bslib-card[data-full-screen=true]>.card-body{max-height:var(--bslib-card-body-max-height-full-screen, none)}.bslib-card 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1)}.bslib-full-screen-exit svg{margin-left:.5rem;font-size:1.5rem}#bslib-full-screen-overlay{position:fixed;inset:0;background-color:rgba(var(--bs-body-color-rgb), 0.6);backdrop-filter:blur(2px);-webkit-backdrop-filter:blur(2px);z-index:1069;animation:bslib-full-screen-overlay-enter 400ms cubic-bezier(0.6, 0.02, 0.65, 1) forwards}@keyframes bslib-full-screen-overlay-enter{0%{opacity:0}100%{opacity:1}}.bslib-grid{display:grid !important;gap:var(--bslib-spacer, 1rem);height:var(--bslib-grid-height)}.bslib-grid.grid{grid-template-columns:repeat(var(--bs-columns, 12), minmax(0, 1fr));grid-template-rows:unset;grid-auto-rows:var(--bslib-grid--row-heights);--bslib-grid--row-heights--xs: unset;--bslib-grid--row-heights--sm: unset;--bslib-grid--row-heights--md: unset;--bslib-grid--row-heights--lg: unset;--bslib-grid--row-heights--xl: unset;--bslib-grid--row-heights--xxl: unset}.bslib-grid.grid.bslib-grid--row-heights--xs{--bslib-grid--row-heights: var(--bslib-grid--row-heights--xs)}@media(min-width: 576px){.bslib-grid.grid.bslib-grid--row-heights--sm{--bslib-grid--row-heights: var(--bslib-grid--row-heights--sm)}}@media(min-width: 768px){.bslib-grid.grid.bslib-grid--row-heights--md{--bslib-grid--row-heights: var(--bslib-grid--row-heights--md)}}@media(min-width: 992px){.bslib-grid.grid.bslib-grid--row-heights--lg{--bslib-grid--row-heights: var(--bslib-grid--row-heights--lg)}}@media(min-width: 1200px){.bslib-grid.grid.bslib-grid--row-heights--xl{--bslib-grid--row-heights: var(--bslib-grid--row-heights--xl)}}@media(min-width: 1400px){.bslib-grid.grid.bslib-grid--row-heights--xxl{--bslib-grid--row-heights: var(--bslib-grid--row-heights--xxl)}}.bslib-grid>*>.shiny-input-container{width:100%}.bslib-grid-item{grid-column:auto/span 1}@media(max-width: 767.98px){.bslib-grid-item{grid-column:1/-1}}@media(max-width: 575.98px){.bslib-grid{grid-template-columns:1fr 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.accordion-button:not(.collapsed):focus{box-shadow:var(--bs-accordion-btn-focus-box-shadow)}.navbar+.container-fluid:has(>.tab-content>.tab-pane.active.html-fill-container),.navbar+.container-sm:has(>.tab-content>.tab-pane.active.html-fill-container),.navbar+.container-md:has(>.tab-content>.tab-pane.active.html-fill-container),.navbar+.container-lg:has(>.tab-content>.tab-pane.active.html-fill-container),.navbar+.container-xl:has(>.tab-content>.tab-pane.active.html-fill-container),.navbar+.container-xxl:has(>.tab-content>.tab-pane.active.html-fill-container){padding-left:0;padding-right:0}.navbar+.container-fluid>.tab-content>.tab-pane.active.html-fill-container,.navbar+.container-sm>.tab-content>.tab-pane.active.html-fill-container,.navbar+.container-md>.tab-content>.tab-pane.active.html-fill-container,.navbar+.container-lg>.tab-content>.tab-pane.active.html-fill-container,.navbar+.container-xl>.tab-content>.tab-pane.active.html-fill-container,.navbar+.container-xxl>.tab-content>.tab-pane.active.html-fill-container{padding:var(--bslib-spacer, 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1rem)}.navbar+.container-fluid>.tab-content>.tab-pane.active.html-fill-container:has(>.bslib-sidebar-layout:only-child),.navbar+.container-sm>.tab-content>.tab-pane.active.html-fill-container:has(>.bslib-sidebar-layout:only-child),.navbar+.container-md>.tab-content>.tab-pane.active.html-fill-container:has(>.bslib-sidebar-layout:only-child),.navbar+.container-lg>.tab-content>.tab-pane.active.html-fill-container:has(>.bslib-sidebar-layout:only-child),.navbar+.container-xl>.tab-content>.tab-pane.active.html-fill-container:has(>.bslib-sidebar-layout:only-child),.navbar+.container-xxl>.tab-content>.tab-pane.active.html-fill-container:has(>.bslib-sidebar-layout:only-child){padding:0}.navbar+.container-fluid>.tab-content>.tab-pane.active.html-fill-container>.bslib-sidebar-layout:only-child:not([data-bslib-sidebar-border=true]),.navbar+.container-sm>.tab-content>.tab-pane.active.html-fill-container>.bslib-sidebar-layout:only-child:not([data-bslib-sidebar-border=true]),.navbar+.container-md>.tab-content>.tab-pane.active.html-fill-container>.bslib-sidebar-layout:only-child:not([data-bslib-sidebar-border=true]),.navbar+.container-lg>.tab-content>.tab-pane.active.html-fill-container>.bslib-sidebar-layout:only-child:not([data-bslib-sidebar-border=true]),.navbar+.container-xl>.tab-content>.tab-pane.active.html-fill-container>.bslib-sidebar-layout:only-child:not([data-bslib-sidebar-border=true]),.navbar+.container-xxl>.tab-content>.tab-pane.active.html-fill-container>.bslib-sidebar-layout:only-child:not([data-bslib-sidebar-border=true]){border-left:none;border-right:none;border-bottom:none}.navbar+.container-fluid>.tab-content>.tab-pane.active.html-fill-container>.bslib-sidebar-layout:only-child:not([data-bslib-sidebar-border-radius=true]),.navbar+.container-sm>.tab-content>.tab-pane.active.html-fill-container>.bslib-sidebar-layout:only-child:not([data-bslib-sidebar-border-radius=true]),.navbar+.container-md>.tab-content>.tab-pane.active.html-fill-container>.bslib-sidebar-layout:only-child:not([data-bslib-sidebar-border-radius=true]),.navbar+.container-lg>.tab-content>.tab-pane.active.html-fill-container>.bslib-sidebar-layout:only-child:not([data-bslib-sidebar-border-radius=true]),.navbar+.container-xl>.tab-content>.tab-pane.active.html-fill-container>.bslib-sidebar-layout:only-child:not([data-bslib-sidebar-border-radius=true]),.navbar+.container-xxl>.tab-content>.tab-pane.active.html-fill-container>.bslib-sidebar-layout:only-child:not([data-bslib-sidebar-border-radius=true]){border-radius:0}.navbar+div>.bslib-sidebar-layout{border-top:var(--bslib-sidebar-border)}html{height:100%}.bslib-page-fill{width:100%;height:100%;margin:0;padding:var(--bslib-spacer, 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30'%3e%3cpath stroke='%23fdfefe' stroke-linecap='round' stroke-miterlimit='10' stroke-width='2' d='M4 7h22M4 15h22M4 23h22'/%3e%3c/svg%3e")}[data-bs-theme=dark] .navbar-toggler-icon{--bs-navbar-toggler-icon-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 30 30'%3e%3cpath stroke='%23fdfefe' stroke-linecap='round' stroke-miterlimit='10' stroke-width='2' d='M4 7h22M4 15h22M4 23h22'/%3e%3c/svg%3e")}.card{--bs-card-spacer-y: 1rem;--bs-card-spacer-x: 1rem;--bs-card-title-spacer-y: 0.5rem;--bs-card-title-color: ;--bs-card-subtitle-color: ;--bs-card-border-width: 1px;--bs-card-border-color: rgba(0, 0, 0, 0.175);--bs-card-border-radius: 0.25rem;--bs-card-box-shadow: ;--bs-card-inner-border-radius: calc(0.25rem - 1px);--bs-card-cap-padding-y: 0.5rem;--bs-card-cap-padding-x: 1rem;--bs-card-cap-bg: rgba(52, 58, 64, 0.25);--bs-card-cap-color: ;--bs-card-height: ;--bs-card-color: ;--bs-card-bg: #ffffff;--bs-card-img-overlay-padding: 1rem;--bs-card-group-margin: 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var(--bs-card-spacer-x);color:var(--bs-card-color)}.card-title{margin-bottom:var(--bs-card-title-spacer-y);color:var(--bs-card-title-color)}.card-subtitle{margin-top:calc(-0.5*var(--bs-card-title-spacer-y));margin-bottom:0;color:var(--bs-card-subtitle-color)}.card-text:last-child{margin-bottom:0}.card-link+.card-link{margin-left:var(--bs-card-spacer-x)}.card-header{padding:var(--bs-card-cap-padding-y) var(--bs-card-cap-padding-x);margin-bottom:0;color:var(--bs-card-cap-color);background-color:var(--bs-card-cap-bg);border-bottom:var(--bs-card-border-width) solid var(--bs-card-border-color)}.card-header:first-child{border-radius:var(--bs-card-inner-border-radius) var(--bs-card-inner-border-radius) 0 0}.card-footer{padding:var(--bs-card-cap-padding-y) var(--bs-card-cap-padding-x);color:var(--bs-card-cap-color);background-color:var(--bs-card-cap-bg);border-top:var(--bs-card-border-width) solid var(--bs-card-border-color)}.card-footer:last-child{border-radius:0 0 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.nav-link.active{background-color:var(--bs-card-bg);border-bottom-color:var(--bs-card-bg)}.card-header-pills{margin-right:calc(-0.5*var(--bs-card-cap-padding-x));margin-left:calc(-0.5*var(--bs-card-cap-padding-x))}.card-img-overlay{position:absolute;top:0;right:0;bottom:0;left:0;padding:var(--bs-card-img-overlay-padding);border-radius:var(--bs-card-inner-border-radius)}.card-img,.card-img-top,.card-img-bottom{width:100%}.card-img,.card-img-top{border-top-left-radius:var(--bs-card-inner-border-radius);border-top-right-radius:var(--bs-card-inner-border-radius)}.card-img,.card-img-bottom{border-bottom-right-radius:var(--bs-card-inner-border-radius);border-bottom-left-radius:var(--bs-card-inner-border-radius)}.card-group>.card{margin-bottom:var(--bs-card-group-margin)}@media(min-width: 576px){.card-group{display:flex;display:-webkit-flex;flex-flow:row wrap;-webkit-flex-flow:row wrap}.card-group>.card{flex:1 0 0%;-webkit-flex:1 0 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6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-focus-border-color: #86b7fe;--bs-accordion-btn-focus-box-shadow: 0 0 0 0.25rem rgba(13, 110, 253, 0.25);--bs-accordion-body-padding-x: 1.25rem;--bs-accordion-body-padding-y: 1rem;--bs-accordion-active-color: #052c65;--bs-accordion-active-bg: #cfe2ff}.accordion-button{position:relative;display:flex;display:-webkit-flex;align-items:center;-webkit-align-items:center;width:100%;padding:var(--bs-accordion-btn-padding-y) var(--bs-accordion-btn-padding-x);font-size:1rem;color:var(--bs-accordion-btn-color);text-align:left;background-color:var(--bs-accordion-btn-bg);border:0;border-radius:0;overflow-anchor:none;transition:var(--bs-accordion-transition)}@media(prefers-reduced-motion: reduce){.accordion-button{transition:none}}.accordion-button:not(.collapsed){color:var(--bs-accordion-active-color);background-color:var(--bs-accordion-active-bg);box-shadow:inset 0 calc(-1*var(--bs-accordion-border-width)) 0 var(--bs-accordion-border-color)}.accordion-button:not(.collapsed)::after{background-image:var(--bs-accordion-btn-active-icon);transform:var(--bs-accordion-btn-icon-transform)}.accordion-button::after{flex-shrink:0;-webkit-flex-shrink:0;width:var(--bs-accordion-btn-icon-width);height:var(--bs-accordion-btn-icon-width);margin-left:auto;content:"";background-image:var(--bs-accordion-btn-icon);background-repeat:no-repeat;background-size:var(--bs-accordion-btn-icon-width);transition:var(--bs-accordion-btn-icon-transition)}@media(prefers-reduced-motion: reduce){.accordion-button::after{transition:none}}.accordion-button:hover{z-index:2}.accordion-button:focus{z-index:3;border-color:var(--bs-accordion-btn-focus-border-color);outline:0;box-shadow:var(--bs-accordion-btn-focus-box-shadow)}.accordion-header{margin-bottom:0}.accordion-item{color:var(--bs-accordion-color);background-color:var(--bs-accordion-bg);border:var(--bs-accordion-border-width) solid var(--bs-accordion-border-color)}.accordion-item:first-of-type{border-top-left-radius:var(--bs-accordion-border-radius);border-top-right-radius:var(--bs-accordion-border-radius)}.accordion-item:first-of-type .accordion-button{border-top-left-radius:var(--bs-accordion-inner-border-radius);border-top-right-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:not(:first-of-type){border-top:0}.accordion-item:last-of-type{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-item:last-of-type .accordion-button.collapsed{border-bottom-right-radius:var(--bs-accordion-inner-border-radius);border-bottom-left-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:last-of-type .accordion-collapse{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-body{padding:var(--bs-accordion-body-padding-y) var(--bs-accordion-body-padding-x)}.accordion-flush .accordion-collapse{border-width:0}.accordion-flush .accordion-item{border-right:0;border-left:0;border-radius:0}.accordion-flush .accordion-item:first-child{border-top:0}.accordion-flush .accordion-item:last-child{border-bottom:0}.accordion-flush .accordion-item .accordion-button,.accordion-flush .accordion-item .accordion-button.collapsed{border-radius:0}[data-bs-theme=dark] .accordion-button::after{--bs-accordion-btn-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%236ea8fe'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-active-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%236ea8fe'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e")}.breadcrumb{--bs-breadcrumb-padding-x: 0;--bs-breadcrumb-padding-y: 0;--bs-breadcrumb-margin-bottom: 1rem;--bs-breadcrumb-bg: ;--bs-breadcrumb-border-radius: ;--bs-breadcrumb-divider-color: rgba(33, 37, 41, 0.75);--bs-breadcrumb-item-padding-x: 0.5rem;--bs-breadcrumb-item-active-color: rgba(33, 37, 41, 0.75);display:flex;display:-webkit-flex;flex-wrap:wrap;-webkit-flex-wrap:wrap;padding:var(--bs-breadcrumb-padding-y) var(--bs-breadcrumb-padding-x);margin-bottom:var(--bs-breadcrumb-margin-bottom);font-size:var(--bs-breadcrumb-font-size);list-style:none;background-color:var(--bs-breadcrumb-bg);border-radius:var(--bs-breadcrumb-border-radius)}.breadcrumb-item+.breadcrumb-item{padding-left:var(--bs-breadcrumb-item-padding-x)}.breadcrumb-item+.breadcrumb-item::before{float:left;padding-right:var(--bs-breadcrumb-item-padding-x);color:var(--bs-breadcrumb-divider-color);content:var(--bs-breadcrumb-divider, ">") /* rtl: var(--bs-breadcrumb-divider, ">") */}.breadcrumb-item.active{color:var(--bs-breadcrumb-item-active-color)}.pagination{--bs-pagination-padding-x: 0.75rem;--bs-pagination-padding-y: 0.375rem;--bs-pagination-font-size:1rem;--bs-pagination-color: #0d6efd;--bs-pagination-bg: #ffffff;--bs-pagination-border-width: 1px;--bs-pagination-border-color: #dee2e6;--bs-pagination-border-radius: 0.25rem;--bs-pagination-hover-color: #0a58ca;--bs-pagination-hover-bg: #f8f9fa;--bs-pagination-hover-border-color: #dee2e6;--bs-pagination-focus-color: #0a58ca;--bs-pagination-focus-bg: #e9ecef;--bs-pagination-focus-box-shadow: 0 0 0 0.25rem rgba(13, 110, 253, 0.25);--bs-pagination-active-color: #ffffff;--bs-pagination-active-bg: #0d6efd;--bs-pagination-active-border-color: #0d6efd;--bs-pagination-disabled-color: rgba(33, 37, 41, 0.75);--bs-pagination-disabled-bg: #e9ecef;--bs-pagination-disabled-border-color: #dee2e6;display:flex;display:-webkit-flex;padding-left:0;list-style:none}.page-link{position:relative;display:block;padding:var(--bs-pagination-padding-y) var(--bs-pagination-padding-x);font-size:var(--bs-pagination-font-size);color:var(--bs-pagination-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-pagination-bg);border:var(--bs-pagination-border-width) solid var(--bs-pagination-border-color);transition:color .15s ease-in-out,background-color .15s ease-in-out,border-color .15s ease-in-out,box-shadow .15s ease-in-out}@media(prefers-reduced-motion: reduce){.page-link{transition:none}}.page-link:hover{z-index:2;color:var(--bs-pagination-hover-color);background-color:var(--bs-pagination-hover-bg);border-color:var(--bs-pagination-hover-border-color)}.page-link:focus{z-index:3;color:var(--bs-pagination-focus-color);background-color:var(--bs-pagination-focus-bg);outline:0;box-shadow:var(--bs-pagination-focus-box-shadow)}.page-link.active,.active>.page-link{z-index:3;color:var(--bs-pagination-active-color);background-color:var(--bs-pagination-active-bg);border-color:var(--bs-pagination-active-border-color)}.page-link.disabled,.disabled>.page-link{color:var(--bs-pagination-disabled-color);pointer-events:none;background-color:var(--bs-pagination-disabled-bg);border-color:var(--bs-pagination-disabled-border-color)}.page-item:not(:first-child) .page-link{margin-left:calc(1px*-1)}.page-item:first-child .page-link{border-top-left-radius:var(--bs-pagination-border-radius);border-bottom-left-radius:var(--bs-pagination-border-radius)}.page-item:last-child .page-link{border-top-right-radius:var(--bs-pagination-border-radius);border-bottom-right-radius:var(--bs-pagination-border-radius)}.pagination-lg{--bs-pagination-padding-x: 1.5rem;--bs-pagination-padding-y: 0.75rem;--bs-pagination-font-size:1.25rem;--bs-pagination-border-radius: 0.5rem}.pagination-sm{--bs-pagination-padding-x: 0.5rem;--bs-pagination-padding-y: 0.25rem;--bs-pagination-font-size:0.875rem;--bs-pagination-border-radius: 0.2em}.badge{--bs-badge-padding-x: 0.65em;--bs-badge-padding-y: 0.35em;--bs-badge-font-size:0.75em;--bs-badge-font-weight: 700;--bs-badge-color: #ffffff;--bs-badge-border-radius: 0.25rem;display:inline-block;padding:var(--bs-badge-padding-y) var(--bs-badge-padding-x);font-size:var(--bs-badge-font-size);font-weight:var(--bs-badge-font-weight);line-height:1;color:var(--bs-badge-color);text-align:center;white-space:nowrap;vertical-align:baseline;border-radius:var(--bs-badge-border-radius)}.badge:empty{display:none}.btn .badge{position:relative;top:-1px}.alert{--bs-alert-bg: transparent;--bs-alert-padding-x: 1rem;--bs-alert-padding-y: 1rem;--bs-alert-margin-bottom: 1rem;--bs-alert-color: inherit;--bs-alert-border-color: transparent;--bs-alert-border: 1px solid var(--bs-alert-border-color);--bs-alert-border-radius: 0.25rem;--bs-alert-link-color: inherit;position:relative;padding:var(--bs-alert-padding-y) var(--bs-alert-padding-x);margin-bottom:var(--bs-alert-margin-bottom);color:var(--bs-alert-color);background-color:var(--bs-alert-bg);border:var(--bs-alert-border);border-radius:var(--bs-alert-border-radius)}.alert-heading{color:inherit}.alert-link{font-weight:700;color:var(--bs-alert-link-color)}.alert-dismissible{padding-right:3rem}.alert-dismissible .btn-close{position:absolute;top:0;right:0;z-index:2;padding:1.25rem 1rem}.alert-default{--bs-alert-color: var(--bs-default-text-emphasis);--bs-alert-bg: var(--bs-default-bg-subtle);--bs-alert-border-color: var(--bs-default-border-subtle);--bs-alert-link-color: var(--bs-default-text-emphasis)}.alert-primary{--bs-alert-color: var(--bs-primary-text-emphasis);--bs-alert-bg: var(--bs-primary-bg-subtle);--bs-alert-border-color: var(--bs-primary-border-subtle);--bs-alert-link-color: var(--bs-primary-text-emphasis)}.alert-secondary{--bs-alert-color: var(--bs-secondary-text-emphasis);--bs-alert-bg: var(--bs-secondary-bg-subtle);--bs-alert-border-color: var(--bs-secondary-border-subtle);--bs-alert-link-color: var(--bs-secondary-text-emphasis)}.alert-success{--bs-alert-color: var(--bs-success-text-emphasis);--bs-alert-bg: var(--bs-success-bg-subtle);--bs-alert-border-color: var(--bs-success-border-subtle);--bs-alert-link-color: var(--bs-success-text-emphasis)}.alert-info{--bs-alert-color: var(--bs-info-text-emphasis);--bs-alert-bg: var(--bs-info-bg-subtle);--bs-alert-border-color: var(--bs-info-border-subtle);--bs-alert-link-color: var(--bs-info-text-emphasis)}.alert-warning{--bs-alert-color: var(--bs-warning-text-emphasis);--bs-alert-bg: var(--bs-warning-bg-subtle);--bs-alert-border-color: var(--bs-warning-border-subtle);--bs-alert-link-color: var(--bs-warning-text-emphasis)}.alert-danger{--bs-alert-color: var(--bs-danger-text-emphasis);--bs-alert-bg: var(--bs-danger-bg-subtle);--bs-alert-border-color: var(--bs-danger-border-subtle);--bs-alert-link-color: var(--bs-danger-text-emphasis)}.alert-light{--bs-alert-color: var(--bs-light-text-emphasis);--bs-alert-bg: var(--bs-light-bg-subtle);--bs-alert-border-color: var(--bs-light-border-subtle);--bs-alert-link-color: var(--bs-light-text-emphasis)}.alert-dark{--bs-alert-color: var(--bs-dark-text-emphasis);--bs-alert-bg: var(--bs-dark-bg-subtle);--bs-alert-border-color: var(--bs-dark-border-subtle);--bs-alert-link-color: var(--bs-dark-text-emphasis)}@keyframes progress-bar-stripes{0%{background-position-x:1rem}}.progress,.progress-stacked{--bs-progress-height: 1rem;--bs-progress-font-size:0.75rem;--bs-progress-bg: #e9ecef;--bs-progress-border-radius: 0.25rem;--bs-progress-box-shadow: inset 0 1px 2px rgba(0, 0, 0, 0.075);--bs-progress-bar-color: #ffffff;--bs-progress-bar-bg: #0d6efd;--bs-progress-bar-transition: width 0.6s ease;display:flex;display:-webkit-flex;height:var(--bs-progress-height);overflow:hidden;font-size:var(--bs-progress-font-size);background-color:var(--bs-progress-bg);border-radius:var(--bs-progress-border-radius)}.progress-bar{display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;justify-content:center;-webkit-justify-content:center;overflow:hidden;color:var(--bs-progress-bar-color);text-align:center;white-space:nowrap;background-color:var(--bs-progress-bar-bg);transition:var(--bs-progress-bar-transition)}@media(prefers-reduced-motion: reduce){.progress-bar{transition:none}}.progress-bar-striped{background-image:linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);background-size:var(--bs-progress-height) var(--bs-progress-height)}.progress-stacked>.progress{overflow:visible}.progress-stacked>.progress>.progress-bar{width:100%}.progress-bar-animated{animation:1s linear infinite progress-bar-stripes}@media(prefers-reduced-motion: reduce){.progress-bar-animated{animation:none}}.list-group{--bs-list-group-color: #212529;--bs-list-group-bg: #ffffff;--bs-list-group-border-color: #dee2e6;--bs-list-group-border-width: 1px;--bs-list-group-border-radius: 0.25rem;--bs-list-group-item-padding-x: 1rem;--bs-list-group-item-padding-y: 0.5rem;--bs-list-group-action-color: rgba(33, 37, 41, 0.75);--bs-list-group-action-hover-color: #000;--bs-list-group-action-hover-bg: #f8f9fa;--bs-list-group-action-active-color: #212529;--bs-list-group-action-active-bg: #e9ecef;--bs-list-group-disabled-color: rgba(33, 37, 41, 0.75);--bs-list-group-disabled-bg: #ffffff;--bs-list-group-active-color: #ffffff;--bs-list-group-active-bg: #0d6efd;--bs-list-group-active-border-color: #0d6efd;display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;padding-left:0;margin-bottom:0;border-radius:var(--bs-list-group-border-radius)}.list-group-numbered{list-style-type:none;counter-reset:section}.list-group-numbered>.list-group-item::before{content:counters(section, ".") ". ";counter-increment:section}.list-group-item-action{width:100%;color:var(--bs-list-group-action-color);text-align:inherit}.list-group-item-action:hover,.list-group-item-action:focus{z-index:1;color:var(--bs-list-group-action-hover-color);text-decoration:none;background-color:var(--bs-list-group-action-hover-bg)}.list-group-item-action:active{color:var(--bs-list-group-action-active-color);background-color:var(--bs-list-group-action-active-bg)}.list-group-item{position:relative;display:block;padding:var(--bs-list-group-item-padding-y) var(--bs-list-group-item-padding-x);color:var(--bs-list-group-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-list-group-bg);border:var(--bs-list-group-border-width) solid var(--bs-list-group-border-color)}.list-group-item:first-child{border-top-left-radius:inherit;border-top-right-radius:inherit}.list-group-item:last-child{border-bottom-right-radius:inherit;border-bottom-left-radius:inherit}.list-group-item.disabled,.list-group-item:disabled{color:var(--bs-list-group-disabled-color);pointer-events:none;background-color:var(--bs-list-group-disabled-bg)}.list-group-item.active{z-index:2;color:var(--bs-list-group-active-color);background-color:var(--bs-list-group-active-bg);border-color:var(--bs-list-group-active-border-color)}.list-group-item+.list-group-item{border-top-width:0}.list-group-item+.list-group-item.active{margin-top:calc(-1*var(--bs-list-group-border-width));border-top-width:var(--bs-list-group-border-width)}.list-group-horizontal{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal>.list-group-item.active{margin-top:0}.list-group-horizontal>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}@media(min-width: 576px){.list-group-horizontal-sm{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-sm>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-sm>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-sm>.list-group-item.active{margin-top:0}.list-group-horizontal-sm>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-sm>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 768px){.list-group-horizontal-md{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-md>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-md>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-md>.list-group-item.active{margin-top:0}.list-group-horizontal-md>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-md>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 992px){.list-group-horizontal-lg{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-lg>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-lg>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-lg>.list-group-item.active{margin-top:0}.list-group-horizontal-lg>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-lg>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 1200px){.list-group-horizontal-xl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xl>.list-group-item.active{margin-top:0}.list-group-horizontal-xl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xl>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 1400px){.list-group-horizontal-xxl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xxl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xxl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xxl>.list-group-item.active{margin-top:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}.list-group-flush{border-radius:0}.list-group-flush>.list-group-item{border-width:0 0 var(--bs-list-group-border-width)}.list-group-flush>.list-group-item:last-child{border-bottom-width:0}.list-group-item-default{--bs-list-group-color: var(--bs-default-text-emphasis);--bs-list-group-bg: var(--bs-default-bg-subtle);--bs-list-group-border-color: var(--bs-default-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-default-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-default-border-subtle);--bs-list-group-active-color: var(--bs-default-bg-subtle);--bs-list-group-active-bg: var(--bs-default-text-emphasis);--bs-list-group-active-border-color: var(--bs-default-text-emphasis)}.list-group-item-primary{--bs-list-group-color: var(--bs-primary-text-emphasis);--bs-list-group-bg: var(--bs-primary-bg-subtle);--bs-list-group-border-color: var(--bs-primary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-primary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-primary-border-subtle);--bs-list-group-active-color: var(--bs-primary-bg-subtle);--bs-list-group-active-bg: var(--bs-primary-text-emphasis);--bs-list-group-active-border-color: var(--bs-primary-text-emphasis)}.list-group-item-secondary{--bs-list-group-color: var(--bs-secondary-text-emphasis);--bs-list-group-bg: var(--bs-secondary-bg-subtle);--bs-list-group-border-color: var(--bs-secondary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-secondary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-secondary-border-subtle);--bs-list-group-active-color: var(--bs-secondary-bg-subtle);--bs-list-group-active-bg: var(--bs-secondary-text-emphasis);--bs-list-group-active-border-color: var(--bs-secondary-text-emphasis)}.list-group-item-success{--bs-list-group-color: var(--bs-success-text-emphasis);--bs-list-group-bg: var(--bs-success-bg-subtle);--bs-list-group-border-color: var(--bs-success-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-success-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-success-border-subtle);--bs-list-group-active-color: var(--bs-success-bg-subtle);--bs-list-group-active-bg: var(--bs-success-text-emphasis);--bs-list-group-active-border-color: var(--bs-success-text-emphasis)}.list-group-item-info{--bs-list-group-color: var(--bs-info-text-emphasis);--bs-list-group-bg: var(--bs-info-bg-subtle);--bs-list-group-border-color: var(--bs-info-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-info-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-info-border-subtle);--bs-list-group-active-color: var(--bs-info-bg-subtle);--bs-list-group-active-bg: var(--bs-info-text-emphasis);--bs-list-group-active-border-color: var(--bs-info-text-emphasis)}.list-group-item-warning{--bs-list-group-color: var(--bs-warning-text-emphasis);--bs-list-group-bg: var(--bs-warning-bg-subtle);--bs-list-group-border-color: var(--bs-warning-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-warning-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-warning-border-subtle);--bs-list-group-active-color: var(--bs-warning-bg-subtle);--bs-list-group-active-bg: var(--bs-warning-text-emphasis);--bs-list-group-active-border-color: var(--bs-warning-text-emphasis)}.list-group-item-danger{--bs-list-group-color: var(--bs-danger-text-emphasis);--bs-list-group-bg: var(--bs-danger-bg-subtle);--bs-list-group-border-color: var(--bs-danger-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-danger-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-danger-border-subtle);--bs-list-group-active-color: var(--bs-danger-bg-subtle);--bs-list-group-active-bg: var(--bs-danger-text-emphasis);--bs-list-group-active-border-color: var(--bs-danger-text-emphasis)}.list-group-item-light{--bs-list-group-color: var(--bs-light-text-emphasis);--bs-list-group-bg: var(--bs-light-bg-subtle);--bs-list-group-border-color: var(--bs-light-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-light-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-light-border-subtle);--bs-list-group-active-color: var(--bs-light-bg-subtle);--bs-list-group-active-bg: var(--bs-light-text-emphasis);--bs-list-group-active-border-color: var(--bs-light-text-emphasis)}.list-group-item-dark{--bs-list-group-color: var(--bs-dark-text-emphasis);--bs-list-group-bg: var(--bs-dark-bg-subtle);--bs-list-group-border-color: var(--bs-dark-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-dark-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-dark-border-subtle);--bs-list-group-active-color: var(--bs-dark-bg-subtle);--bs-list-group-active-bg: var(--bs-dark-text-emphasis);--bs-list-group-active-border-color: var(--bs-dark-text-emphasis)}.btn-close{--bs-btn-close-color: #000;--bs-btn-close-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' 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0.25rem;--bs-toast-box-shadow: 0 0.5rem 1rem rgba(0, 0, 0, 0.15);--bs-toast-header-color: rgba(33, 37, 41, 0.75);--bs-toast-header-bg: rgba(255, 255, 255, 0.85);--bs-toast-header-border-color: rgba(0, 0, 0, 0.175);width:var(--bs-toast-max-width);max-width:100%;font-size:var(--bs-toast-font-size);color:var(--bs-toast-color);pointer-events:auto;background-color:var(--bs-toast-bg);background-clip:padding-box;border:var(--bs-toast-border-width) solid var(--bs-toast-border-color);box-shadow:var(--bs-toast-box-shadow);border-radius:var(--bs-toast-border-radius)}.toast.showing{opacity:0}.toast:not(.show){display:none}.toast-container{--bs-toast-zindex: 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.value-box-grid{grid-template-columns:var(---bslib-value-box-showcase-w-fs, 1fr) auto}.bslib-value-box.showcase-left-center:not([data-fill-screen=true]) .value-box-grid .value-box-showcase{grid-area:left}.bslib-value-box.showcase-left-center:not([data-fill-screen=true]) .value-box-grid .value-box-area{grid-area:right}.bslib-value-box.showcase-bottom .value-box-grid{grid-template-columns:1fr;grid-template-rows:1fr var(---bslib-value-box-showcase-h, auto);grid-template-areas:"top" "bottom";overflow:hidden}.bslib-value-box.showcase-bottom .value-box-grid .value-box-showcase{grid-area:bottom;padding:0;margin:0}.bslib-value-box.showcase-bottom .value-box-grid .value-box-area{grid-area:top}.bslib-value-box.showcase-bottom[data-full-screen=true] .value-box-grid{grid-template-rows:1fr var(---bslib-value-box-showcase-h-fs, 2fr)}.bslib-value-box.showcase-bottom[data-full-screen=true] .value-box-grid .value-box-showcase{padding:1rem}[data-bs-theme=dark] .bslib-value-box{--bslib-value-box-shadow: 0 0.5rem 1rem rgb(0 0 0 / 50%)}@media(min-width: 576px){.nav:not(.nav-hidden){display:flex !important;display:-webkit-flex !important}.nav:not(.nav-hidden):not(.nav-stacked):not(.flex-column){float:none !important}.nav:not(.nav-hidden):not(.nav-stacked):not(.flex-column)>.bslib-nav-spacer{margin-left:auto !important}.nav:not(.nav-hidden):not(.nav-stacked):not(.flex-column)>.form-inline{margin-top:auto;margin-bottom:auto}.nav:not(.nav-hidden).nav-stacked{flex-direction:column;-webkit-flex-direction:column;height:100%}.nav:not(.nav-hidden).nav-stacked>.bslib-nav-spacer{margin-top:auto !important}}.bslib-card{overflow:auto}.bslib-card .card-body+.card-body{padding-top:0}.bslib-card .card-body{overflow:auto}.bslib-card .card-body p{margin-top:0}.bslib-card .card-body p:last-child{margin-bottom:0}.bslib-card .card-body{max-height:var(--bslib-card-body-max-height, none)}.bslib-card[data-full-screen=true]>.card-body{max-height:var(--bslib-card-body-max-height-full-screen, none)}.bslib-card 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1)}.bslib-full-screen-exit svg{margin-left:.5rem;font-size:1.5rem}#bslib-full-screen-overlay{position:fixed;inset:0;background-color:rgba(var(--bs-body-color-rgb), 0.6);backdrop-filter:blur(2px);-webkit-backdrop-filter:blur(2px);z-index:1069;animation:bslib-full-screen-overlay-enter 400ms cubic-bezier(0.6, 0.02, 0.65, 1) forwards}@keyframes bslib-full-screen-overlay-enter{0%{opacity:0}100%{opacity:1}}.bslib-grid{display:grid !important;gap:var(--bslib-spacer, 1rem);height:var(--bslib-grid-height)}.bslib-grid.grid{grid-template-columns:repeat(var(--bs-columns, 12), minmax(0, 1fr));grid-template-rows:unset;grid-auto-rows:var(--bslib-grid--row-heights);--bslib-grid--row-heights--xs: unset;--bslib-grid--row-heights--sm: unset;--bslib-grid--row-heights--md: unset;--bslib-grid--row-heights--lg: unset;--bslib-grid--row-heights--xl: unset;--bslib-grid--row-heights--xxl: unset}.bslib-grid.grid.bslib-grid--row-heights--xs{--bslib-grid--row-heights: 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.block-title,#title-block-header.quarto-title-block.default .abstract .block-title{margin-top:1em;text-transform:uppercase;font-size:.8em;opacity:.8;font-weight:400}#title-block-header.quarto-title-block.default .quarto-title-meta-author{display:grid;grid-template-columns:minmax(max-content, 1fr) 1fr;grid-column-gap:1em}.quarto-title-tools-only{display:flex;justify-content:right} diff --git a/docs/site_libs/quarto-html/quarto-syntax-highlighting.css b/docs/site_libs/quarto-html/quarto-syntax-highlighting.css index 30b79c4..b30ce57 100644 --- a/docs/site_libs/quarto-html/quarto-syntax-highlighting.css +++ b/docs/site_libs/quarto-html/quarto-syntax-highlighting.css @@ -33,7 +33,7 @@ /* other quarto variables */ :root { - --quarto-font-monospace: "JuliaMono-Light"; + --quarto-font-monospace: SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", "Courier New", monospace; } pre > code.sourceCode > span { diff --git a/docs/sitemap.xml b/docs/sitemap.xml index ec52a3b..73754e1 100644 --- a/docs/sitemap.xml +++ b/docs/sitemap.xml @@ -62,7 +62,7 @@ https://www.taija.org/blog/posts/causal-recourse/index.html - 2024-09-17T11:51:51.700Z + 2024-09-17T12:22:00.192Z https://www.taija.org/blog/posts/conformal-prediction/index.html diff --git a/profile/_freeze/blog/posts/causal-recourse/index/execute-results/html.json b/profile/_freeze/blog/posts/causal-recourse/index/execute-results/html.json index d347bce..711889c 100644 --- a/profile/_freeze/blog/posts/causal-recourse/index/execute-results/html.json +++ b/profile/_freeze/blog/posts/causal-recourse/index/execute-results/html.json @@ -1,8 +1,8 @@ { - "hash": "cc0cc232d9ce1a91f7c42084f0162fdc", + "hash": "5dfbe079ad3f3a119c776079a28b73be", "result": { "engine": "julia", - "markdown": "---\ntitle: \"When Causality meets Recourse\"\nsubtitle: \"Counterfactual Explanations through Structural Causal Models\"\ndate: '2024-09-17'\ndescription: |\n This post introduces a new tool in CounterfactualExplanations.jl, enhancing the package with causal reasoning to generate counterfactual explanations.\nauthor: \n - name: Jorge Luiz Franco \n url: https://www.linkedin.com/in/jorgelwyz/\ncategories:\n - counterfactuals\n - explainable AI\n - causality\n - Julia\nimage: www/intro.png\nexecute:\n eval: true\n echo: true\nengine: julia\njulia: \n exeflags: [\"--project=./\"]\ncode-fold: show\n---\n\n\n\n# Introduction\n\nIn recent years, the need for interpretable and explainable AI has surged, particularly in high-stakes domains. Counterfactual explanations provide a means to understand how changes to input features could alter the outcomes of machine learning models. This blog post presents a new tool in the CounterfactualExplanations.jl package, developed during my JSoC (Julia Summer of Code) project, which incorporates causal reasoning into counterfactual generation.\n\n# Project Overview\n\nThis project aimed to enhance the CounterfactualExplanations.jl package by infusing it with a robust mathematical foundation for minimal algorithmic recourse, based on the principles of causal reasoning [@karimi2021algorithmic]. \n\n## Key Contributions\n\nDuring the project, I contributed to two key repositories:\n\n1. **CounterfactualExplanations.jl**: Developed a new tool for generating counterfactual explanations using causal information. This allows users to create smarter perturbations rather than random adjustments, ultimately providing more meaningful insights.\n\n2. **CausalInference.jl**: Implemented a Structural Causal Model (SCM) structure that extracts information from data, laying the groundwork for the causal reasoning capabilities in CounterfactualExplanations.jl.\n\nThis was an amazing experience, not just experience contribute to two repositories simultaneously, but also to work with the mantainers of these repos. I learned a lot about the Julia language and the Julia community. This was possible because of the mentorship of Patrick Altmeyer (CounterfactualExplanations) and Moritz Schauer (CausalInference), who guided me throughout the project and are amazing researchers.\n\n## The `MINTGenerator`\n\nIn this project, we developed the MINTGenerator, a counterfactual generator based on the Recourse through Minimal\nIntervention (MINT) method proposed by @karimi2021algorithmic.\n\n## Description\n\nThe MINTGenerator incorporates causal reeasoning in algorithm recourse to achieve minimal interventions when generating a counterfactual explanation. In this sense, the main ideia is that just perturbating a black box model without taking into account the causal relations in the data can guide to misleading recommendations. Here we now shift to a perspective where every action/pertubation is an intervetion in the causal graph of the problem, thus the change is not made just in the intervened upon variable, but also in its childs in the causal structure. The generator utilizes a Structural Causal Model(SCM) to encode the variables in a way that causal effects are propagated and uses a generic gradient-based generator to create the search path, that is, any gradient-base generator (ECCo, REVISE, Watcher, ...) can be used with the MINT SCM encoder to generate counterfactual samples in latent space for minimal intervetions algorithm recourse.\n\nThe MINT algorithm minimizes a loss function that combines the causal constraints of the SCM and the distance between the generated counterfactual and the original input. Since we want a gradient-based generator, we need to pass the constrained optimizaiton problem into an unconstrained one and we do this by using the Lagrangian. Initially, as defined in [@karimi2021algorithmic], we aim to aim to find the minimal cost set of actions $A$ (in the form of structural interventions) that results in a counterfactual instance yielding the favorable output from $h$,\n\n$$\n\\begin{aligned}\n\nA^* \\in \\arg\\min_A \\text{cost}(A; \\mathbf{x}_F)\\\\\n\\textrm{s.t.} \\quad h(\\mathbf{x}_{SCF}) \\neq h(\\mathbf{x}_F) \\; \\; \\text{,}\\\\\n\n\\end{aligned} \n$$\n\nwhere $\\mathbf{x}_F$ is the original input, $\\mathbf{x}_{SCF}$ is the counterfactual instance, and $h$ is the black-box model. We use the $\\mathbf{x}_{SCF}$ terminology because the counterfactual is derived from the SCM,\n\n$$\nx_{SCF_i} = \n\\begin{cases}\nx_{F_i} + \\delta_i, & \\text{if } i \\in I \\\\\nx_{F_i} + f_i(\\text{pa}_{SCF_i}) - f_i(\\text{pa}_{F_i}), & \\text{if } i \\notin I \\; \\; \\text{,}\n\\end{cases} \n$$\n\nwhere $I$ is the set of intervened upon variables, $f_i$ is the function that generates the value of the variable $i$ given its parents, and $\\text{pa}_{SCF_i}$ and $\\text{pa}_{F_i}$ are the parents of the variable $i$ in the counterfactual and original instance, respectively. This closed formula for the decision variable $\\mathbf{x}_{SCF}$ is what makes possible to use a gradient-based generator, since with it the lagrangian is differentiable,\n\n$$\n\\mathcal{L}(A ; \\lambda) = \\text{cost}(A; \\mathbf{x}_F) + \\lambda \\left(h(\\mathbf{x}_{SCF}) - h(\\mathbf{x}_F) \\right) \\; \\; \\text{,}\n$$\n\nor in simple terms and more standard, since $\\lambda$ is constant,\n\n$$\n\\mathcal{L_{\\texttt{MINT}}}(\\mathbf{x}_{SCF}) = \\lambda \\text{cost}(\\mathbf{x}_{SCF}; \\mathbf{x}_F) + \\text{yloss}(\\mathbf{x}_{SCF},y^*) \\; \\; \\text{,}\n$$\n\nwhere $y^*$ is clearly $h(x_F)$ and $\\text{yloss}$ is : \n\n$$\n\\text{yloss}(\\mathbf{x}_{SCF}, y^*) = h \\left(\\left\\{ x_{F_i} + \\delta_i [i \\in I] + \\left(f_i(\\text{pa}_{SCF_i}) - f_i(\\text{pa}_{F_i}) \\right) [i \\notin I] \\right\\}_{i=1}^n \\right) - y^* \\; \\; \\text{.} \n$$\n\n## Implementation\n\n### `CausalInference.jl`\n\nIn terms of implementation, we need to capture the causal relations from the data, that's where `CausalInference.jl` comes in. However, before the project, the package did not have a SCM structure, in the sense that the methods just captured the topological Directed Acyclic Graph (DAG) that showed the causality ruling the data, that is, no causal structural equations were provided,\n\n\n\n::: {#2 .cell execution_count=1}\n``` {.julia .cell-code}\nusing CausalInference\nusing Plots, GraphRecipes\nusing Random\nRandom.seed!(1)\n\nN = 2000 # number of data points\n\nx = randn(N)\nv = x + randn(N)*0.25\nw = x + randn(N)*0.25\nz = v + w + randn(N)*0.25\ns = z + randn(N)*0.25\n\ndf = (x=x, v=v, w=w, z=z, s=s)\n\nest_g, score = ges(df; penalty=1.0, parallel=true)\n\nplt = graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)], size=(500,500), nodesize=0.1, fontsize=2)\nsavefig(plt, \"www/intro.png\")\ndisplay(plt)\n```\n\n::: {.cell-output .cell-output-stdout}\n```\n┌ Warning: Only one thread available\n└ @ CausalInference ~/.julia/packages/CausalInference/ozcj8/src/ges.jl:52\n```\n:::\n\n::: {.cell-output .cell-output-display}\n```{=html}\n\n\n\n \n \n \n\n\n\n \n \n \n\n\n\n \n \n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n```\n:::\n:::\n\n\n\n\n\nSo, our goal was given the DAG provided by the `ges` method in the causal discovery [@chickering2003optimal], generate equations that rules each of these causal relations, represented in the DAG as directed edges. The SCM is the union of the DAG and these causal equations, that is, the SCM is a tuple $(G, \\mathbf{f})$, where $G$ is the DAG and $\\mathbf{f}$ is the set of functions that generates the value of each variable given its parents. \n\nOur solution for constructing the structural causal equations was to assume that the data was generated by a linear model, ie, the causal relations were linear. For the DAG provided in the code example we derive\n\n$$ v = \\mathcal{b}_v $$\n\n$$ x = \\mathcal{a}_{v \\to x} v + \\mathcal{b}_x $$\n\n$$ w = \\mathcal{a}_{x \\to w} x + \\mathcal{b}_w $$\n\n$$ z = \\mathcal{a}_{v \\to z} v+ \\mathcal{a}_{w \\to z} w + \\mathcal{b}_z $$\n\n$$ s = \\mathcal{a}_{z \\to s} z + \\mathcal{b}_s $$\n\nand that's the tricky thing, as we can see these causal equations are different than the ones that generated the data, but they are the ones that respect the causal system obtained from the obtained DAG. Here $\\mathcal{b}_i$ and $\\mathcal{a}_{i \\to j}$ are the intercept term and the coefficient obtained from the linear regression, respectively. To correctly solve the linear regression respecting the dependencies of the causal graph, we use `topological_sort_by_dfs` from `Graphs.jl`.\n\nNow, with the SCM structure in hand, we see that the representation could be a struct containing the DAG and the coefficients/intercepts of the causal equations, this maps exactly the tuple $(G, \\mathbf{f})$ that we defined. However, since we need these equations to be differentiable, we need to define a function that takes the SCM and returns the value of the variable given its parents and using just the coefficients and the DAG, lead to errors, because `AutoDiff` does not deal well with functions that are conditioned (`if` statements). So, we need to define a way to retrieve the system of causal equations in a smooth way and that's where the `causal_effects` matrix comes to the rescue.\n\nLet the factual vector of features be denoted as:\n\n$$\n\\mathbf{x}_F = \n\\begin{bmatrix}\nx_{F_1} \\\\\nx_{F_2} \\\\\nx_{F_3} \\\\\n\\vdots \\\\\nx_{F_n}\n\\end{bmatrix}\n$$\n\nLet the `causal_effects` matrix be:\n\n$$\n\\mathbf{C} =\n\\begin{bmatrix}\na_{11} & a_{12} & \\cdots & a_{1n} & b_1 \\\\\na_{21} & a_{22} & \\cdots & a_{2n} & b_2 \\\\\na_{31} & a_{32} & \\cdots & a_{3n} & b_3 \\\\\n\\vdots & \\vdots & \\ddots & \\vdots & \\vdots \\\\\na_{n1} & a_{n2} & \\cdots & a_{nn} & b_n \\\\\n\\end{bmatrix}\n$$\n\nHere, $a_{ij}$ represents the coefficient from the causal effect of $x_{F_j}$ on $x_{F_i}$, and $b_i$ represents the intercept term for the variable $x_{F_i}$.\n\nThe matrix multiplication of the `causal_effects` matrix with the factual vector (excluding the bias term) is given by:\n\n$$\n\\mathbf{C}_{:, 1:n} \\cdot \\mathbf{x}_F =\n\\begin{bmatrix}\na_{11} & a_{12} & \\cdots & a_{1n} \\\\\na_{21} & a_{22} & \\cdots & a_{2n} \\\\\na_{31} & a_{32} & \\cdots & a_{3n} \\\\\n\\vdots & \\vdots & \\ddots & \\vdots \\\\\na_{n1} & a_{n2} & \\cdots & a_{nn}\n\\end{bmatrix}\n\\begin{bmatrix}\nx_{F_1} \\\\\nx_{F_2} \\\\\nx_{F_3} \\\\\n\\vdots \\\\\nx_{F_n}\n\\end{bmatrix}\n$$\n\nFinally, we add the bias term:\n\n$$\n\\mathbf{x}_{SCF} = \\mathbf{C}_{:, 1:n} \\cdot \\mathbf{x}_F + \n\\begin{bmatrix}\nb_1 \\\\\nb_2 \\\\\nb_3 \\\\\n\\vdots \\\\\nb_n\n\\end{bmatrix}\n$$\n\nIn expanded form:\n\n$$\n\\mathbf{x}_{SCF_i} = a_{i1} x_{F_1} + a_{i2} x_{F_2} + \\cdots + a_{in} x_{F_n} + b_i, \\quad \\forall i = 1, 2, \\dots, n\n$$\n\nThis equation shows how each counterfactual variable $x_{SCF_i}$ is generated as a linear combination of the factual inputs $x_{F_j}$ based on the causal effects matrix, with an intercept term $b_i$ added for each variable.\n\nOne can note that the `orphan` nodes, that is, the nodes that do not have parents in the DAG, are going to be equal to the intercept term $\\mathcal{b}_\\hat{o}$. The intuition behind this is that when we do the linear regression, variables that have no causal parents are just equal to the unconditional mean of the variable, i.e, we get $x_{SCF_\\hat{o}} = \\mathbb{E}(x_\\hat{o})$. Because of this, in some cases a better understanding of the regression is needed, so the residuals are also part of the SCM structure,\n\n\n\n::: {#4 .cell execution_count=0}\n``` {.julia .cell-code}\nstruct SCM\n variables::Vector{String}\n coefficients::Vector{Vector{Float64}}\n residuals::Vector{Vector{Float64}}\n dag::DiGraph\n causal_effects::Matrix{Float64}\nend\n```\n:::\n\n\n\n\n\n### `CounterfactualExplanations.jl` \n\n\n# Conclusion\n\n\n\n# References\n\n", + "markdown": "---\ntitle: \"When Causality meets Recourse\"\nsubtitle: \"Counterfactual Explanations through Structural Causal Models\"\ndate: '2024-09-17'\ndescription: |\n This post introduces a new tool in CounterfactualExplanations.jl, enhancing the package with causal reasoning to generate counterfactual explanations.\nauthor: \n - name: Jorge Luiz Franco \n url: https://www.linkedin.com/in/jorgelwyz/\ncategories:\n - counterfactuals\n - explainable AI\n - causality\n - Julia\nimage: www/intro.png\nexecute:\n eval: true\n echo: true\nengine: julia\njulia: \n exeflags: [\"--project=./\"]\ncode-fold: show\n---\n\n\n\n# Introduction\n\nIn recent years, the need for interpretable and explainable AI has surged, particularly in high-stakes domains. Counterfactual explanations provide a means to understand how changes to input features could alter the outcomes of machine learning models. This blog post presents a new tool in the CounterfactualExplanations.jl package, developed during my JSoC (Julia Summer of Code) project, which incorporates causal reasoning into counterfactual generation.\n\n# Project Overview\n\nThis project aimed to enhance the CounterfactualExplanations.jl package by infusing it with a robust mathematical foundation for minimal algorithmic recourse, based on the principles of causal reasoning [@karimi2021algorithmic]. \n\n## Key Contributions\n\nDuring the project, I contributed to two key repositories:\n\n1. **CounterfactualExplanations.jl**: Developed a new tool for generating counterfactual explanations using causal information. This allows users to create smarter perturbations rather than random adjustments, ultimately providing more meaningful insights.\n\n2. **CausalInference.jl**: Implemented a Structural Causal Model (SCM) structure that extracts information from data, laying the groundwork for the causal reasoning capabilities in CounterfactualExplanations.jl.\n\nThis was an amazing experience, not just experience contribute to two repositories simultaneously, but also to work with the mantainers of these repos. I learned a lot about the Julia language and the Julia community. This was possible because of the mentorship of Patrick Altmeyer (CounterfactualExplanations) and Moritz Schauer (CausalInference), who guided me throughout the project and are amazing researchers.\n\n## The `MINTGenerator`\n\nIn this project, we developed the MINTGenerator, a counterfactual generator based on the Recourse through Minimal\nIntervention (MINT) method proposed by @karimi2021algorithmic.\n\n## Description\n\nThe MINTGenerator incorporates causal reeasoning in algorithm recourse to achieve minimal interventions when generating a counterfactual explanation. In this sense, the main ideia is that just perturbating a black box model without taking into account the causal relations in the data can guide to misleading recommendations. Here we now shift to a perspective where every action/pertubation is an intervetion in the causal graph of the problem, thus the change is not made just in the intervened upon variable, but also in its childs in the causal structure. The generator utilizes a Structural Causal Model(SCM) to encode the variables in a way that causal effects are propagated and uses a generic gradient-based generator to create the search path, that is, any gradient-base generator (ECCo, REVISE, Watcher, ...) can be used with the MINT SCM encoder to generate counterfactual samples in latent space for minimal intervetions algorithm recourse.\n\nThe MINT algorithm minimizes a loss function that combines the causal constraints of the SCM and the distance between the generated counterfactual and the original input. Since we want a gradient-based generator, we need to pass the constrained optimizaiton problem into an unconstrained one and we do this by using the Lagrangian. Initially, as defined in [@karimi2021algorithmic], we aim to aim to find the minimal cost set of actions $A$ (in the form of structural interventions) that results in a counterfactual instance yielding the favorable output from $h$,\n\n$$\n\\begin{aligned}\nA^* \\in \\arg\\min_A \\text{cost}(A; \\mathbf{x}_F)\\\\\n\\textrm{s.t.} \\quad h(\\mathbf{x}_{SCF}) \\neq h(\\mathbf{x}_F) \\; \\; \\text{,}\\\\\n\\end{aligned} \n$$\n\nwhere $\\mathbf{x}_F$ is the original input, $\\mathbf{x}_{SCF}$ is the counterfactual instance, and $h$ is the black-box model. We use the $\\mathbf{x}_{SCF}$ terminology because the counterfactual is derived from the SCM,\n\n$$\nx_{SCF_i} = \n\\begin{cases}\nx_{F_i} + \\delta_i, & \\text{if } i \\in I \\\\\nx_{F_i} + f_i(\\text{pa}_{SCF_i}) - f_i(\\text{pa}_{F_i}), & \\text{if } i \\notin I \\; \\; \\text{,}\n\\end{cases} \n$$\n\nwhere $I$ is the set of intervened upon variables, $f_i$ is the function that generates the value of the variable $i$ given its parents, and $\\text{pa}_{SCF_i}$ and $\\text{pa}_{F_i}$ are the parents of the variable $i$ in the counterfactual and original instance, respectively. This closed formula for the decision variable $\\mathbf{x}_{SCF}$ is what makes possible to use a gradient-based generator, since with it the lagrangian is differentiable,\n\n$$\n\\mathcal{L}(A ; \\lambda) = \\text{cost}(A; \\mathbf{x}_F) + \\lambda \\left(h(\\mathbf{x}_{SCF}) - h(\\mathbf{x}_F) \\right) \\; \\; \\text{,}\n$$\n\nor in simple terms and more standard, since $\\lambda$ is constant,\n\n$$\n\\mathcal{L_{\\texttt{MINT}}}(\\mathbf{x}_{SCF}) = \\lambda \\text{cost}(\\mathbf{x}_{SCF}; \\mathbf{x}_F) + \\text{yloss}(\\mathbf{x}_{SCF},y^*) \\; \\; \\text{,}\n$$\n\nwhere $y^*$ is clearly $h(x_F)$ and $\\text{yloss}$ is : \n\n$$\n\\text{yloss}(\\mathbf{x}_{SCF}, y^*) = h \\left(\\left\\{ x_{F_i} + \\delta_i [i \\in I] + \\left(f_i(\\text{pa}_{SCF_i}) - f_i(\\text{pa}_{F_i}) \\right) [i \\notin I] \\right\\}_{i=1}^n \\right) - y^* \\; \\; \\text{.} \n$$\n\n## Implementation\n\n### `CausalInference.jl`\n\nIn terms of implementation, we need to capture the causal relations from the data, that's where `CausalInference.jl` comes in. However, before the project, the package did not have a SCM structure, in the sense that the methods just captured the topological Directed Acyclic Graph (DAG) that showed the causality ruling the data, that is, no causal structural equations were provided,\n\n\n\n::: {#2 .cell execution_count=1}\n``` {.julia .cell-code}\nusing CausalInference\nusing CounterfactualExplanations\nusing CounterfactualExplanations.GenerativeModels\nusing Graphs\nusing GraphRecipes\nusing MultivariateStats\nusing Plots\nusing Random\nRandom.seed!(1)\nusing StatsBase\n\nN = 2000 # number of data points\n\nx = randn(N)\nv = x + randn(N)*0.25\nw = x + randn(N)*0.25\nz = v + w + randn(N)*0.25\ns = z + randn(N)*0.25\n\ndf = (x=x, v=v, w=w, z=z, s=s)\n\nest_g, score = ges(df; penalty=1.0, parallel=true)\n\nplt = graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)], size=(500,500), nodesize=0.1, fontsize=25)\nsavefig(plt, \"www/intro.png\")\ndisplay(plt)\n```\n\n::: {.cell-output .cell-output-stdout}\n```\n┌ Warning: Only one thread available\n└ @ CausalInference ~/.julia/packages/CausalInference/ozcj8/src/ges.jl:52\n```\n:::\n\n::: {.cell-output .cell-output-display}\n```{=html}\n\n\n\n \n \n \n\n\n\n \n \n \n\n\n\n \n \n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n```\n:::\n:::\n\n\n\n\n\nSo, our goal was given the DAG provided by the `ges` method in the causal discovery [@chickering2003optimal], generate equations that rules each of these causal relations, represented in the DAG as directed edges. The SCM is the union of the DAG and these causal equations, that is, the SCM is a tuple $(G, \\mathbf{f})$, where $G$ is the DAG and $\\mathbf{f}$ is the set of functions that generates the value of each variable given its parents. \n\nOur solution for constructing the structural causal equations was to assume that the data was generated by a linear model, ie, the causal relations were linear. For the DAG provided in the code example we derive\n\n$$ v = \\mathcal{b}_v $$\n\n$$ x = \\mathcal{a}_{v \\to x} v + \\mathcal{b}_x $$\n\n$$ w = \\mathcal{a}_{x \\to w} x + \\mathcal{b}_w $$\n\n$$ z = \\mathcal{a}_{v \\to z} v+ \\mathcal{a}_{w \\to z} w + \\mathcal{b}_z $$\n\n$$ s = \\mathcal{a}_{z \\to s} z + \\mathcal{b}_s $$\n\nand that's the tricky thing, as we can see these causal equations are different than the ones that generated the data, but they are the ones that respect the causal system obtained from the obtained DAG. Here $\\mathcal{b}_i$ and $\\mathcal{a}_{i \\to j}$ are the intercept term and the coefficient obtained from the linear regression, respectively. To correctly solve the linear regression respecting the dependencies of the causal graph, we use `topological_sort_by_dfs` from `Graphs.jl`.\n\nNow, with the SCM structure in hand, we see that the representation could be a struct containing the DAG and the coefficients/intercepts of the causal equations, this maps exactly the tuple $(G, \\mathbf{f})$ that we defined. However, since we need these equations to be differentiable, we need to define a function that takes the SCM and returns the value of the variable given its parents and using just the coefficients and the DAG, lead to errors, because `AutoDiff` does not deal well with functions that are conditioned (`if` statements). So, we need to define a way to retrieve the system of causal equations in a smooth way and that's where the `causal_effects` matrix comes to the rescue.\n\nLet the factual vector of features be denoted as:\n\n$$\n\\mathbf{x}_F = \n\\begin{bmatrix}\nx_{F_1} \\\\\nx_{F_2} \\\\\nx_{F_3} \\\\\n\\vdots \\\\\nx_{F_n}\n\\end{bmatrix}\n$$\n\nLet the `causal_effects` matrix be:\n\n$$\n\\mathbf{C} =\n\\begin{bmatrix}\na_{11} & a_{12} & \\cdots & a_{1n} & b_1 \\\\\na_{21} & a_{22} & \\cdots & a_{2n} & b_2 \\\\\na_{31} & a_{32} & \\cdots & a_{3n} & b_3 \\\\\n\\vdots & \\vdots & \\ddots & \\vdots & \\vdots \\\\\na_{n1} & a_{n2} & \\cdots & a_{nn} & b_n \\\\\n\\end{bmatrix}\n$$\n\nHere, $a_{ij}$ represents the coefficient from the causal effect of $x_{F_j}$ on $x_{F_i}$, and $b_i$ represents the intercept term for the variable $x_{F_i}$.\n\nThe matrix multiplication of the `causal_effects` matrix with the factual vector (excluding the bias term) is given by:\n\n$$\n\\mathbf{C}_{:, 1:n} \\cdot \\mathbf{x}_F =\n\\begin{bmatrix}\na_{11} & a_{12} & \\cdots & a_{1n} \\\\\na_{21} & a_{22} & \\cdots & a_{2n} \\\\\na_{31} & a_{32} & \\cdots & a_{3n} \\\\\n\\vdots & \\vdots & \\ddots & \\vdots \\\\\na_{n1} & a_{n2} & \\cdots & a_{nn}\n\\end{bmatrix}\n\\begin{bmatrix}\nx_{F_1} \\\\\nx_{F_2} \\\\\nx_{F_3} \\\\\n\\vdots \\\\\nx_{F_n}\n\\end{bmatrix}\n$$\n\nFinally, we add the bias term:\n\n$$\n\\mathbf{x}_{SCF} = \\mathbf{C}_{:, 1:n} \\cdot \\mathbf{x}_F + \n\\begin{bmatrix}\nb_1 \\\\\nb_2 \\\\\nb_3 \\\\\n\\vdots \\\\\nb_n\n\\end{bmatrix}\n$$\n\nIn expanded form:\n\n$$\n\\mathbf{x}_{SCF_i} = a_{i1} x_{F_1} + a_{i2} x_{F_2} + \\cdots + a_{in} x_{F_n} + b_i, \\quad \\forall i = 1, 2, \\dots, n\n$$\n\nThis equation shows how each counterfactual variable $x_{SCF_i}$ is generated as a linear combination of the factual inputs $x_{F_j}$ based on the causal effects matrix, with an intercept term $b_i$ added for each variable.\n\nOne can note that the `orphan` nodes, that is, the nodes that do not have parents in the DAG, are going to be equal to the intercept term $\\mathcal{b}_\\hat{o}$. The intuition behind this is that when we do the linear regression, variables that have no causal parents are just equal to the unconditional mean of the variable, i.e, we get $x_{SCF_\\hat{o}} = \\mathbb{E}(x_\\hat{o})$. Because of this, in some cases a better understanding of the regression is needed, so the residuals are also part of the SCM structure,\n\n\n\n::: {#4 .cell execution_count=0}\n``` {.julia .cell-code}\nstruct SCM\n variables::Vector{String}\n coefficients::Vector{Vector{Float64}}\n residuals::Vector{Vector{Float64}}\n dag::DiGraph\n causal_effects::Matrix{Float64}\nend\n```\n:::\n\n\n\n\n\n### `CounterfactualExplanations.jl` \n\nNow, we need to go into the optimization problem previously described. We seek to minimize the lagrangian function we defined where now we have a differentiable function. The standard way to implement generators in `CounterfactualExplanations.jl` is to use `AutoDiff` exactly using composable functions in the lagrangian. The definition of $\\mathcal{L_{\\texttt{MINT}}}$ is in the same shape of the the others gradient-based generators in the package, so the optimization is straightforward. However, we needed some way to pass the $x_F$ into the $x_{SCF}$ and that's where `transformer.jl` comes in. This is where `InputTransformer`s are defined in the package and in some way this is what we are doing, we are passing our factual to the \"latent\" causal space of the counterfactual. Our first step is to create a new kind of `InputTransformer` that is the SCM itself,\n\n\n\n::: {#6 .cell execution_count=1}\n``` {.julia .cell-code}\nconst TypedInputTransformer = Union{\n Type{<:StatsBase.AbstractDataTransform},\n Type{<:MultivariateStats.AbstractDimensionalityReduction},\n Type{<:GenerativeModels.AbstractGenerativeModel},\n Type{<:CausalInference.SCM} # The SCM transfromer\n}\n```\n:::\n\n\n\n\n\nand then we need a way to create this transformer, that's where we \"overload\" `fit_transformer` using `CausalInferece.jl`, \n\n\n\n::: {#8 .cell execution_count=1}\n``` {.julia .cell-code}\nfunction fit_transformer(\n data::CounterfactualData, input_encoder::Type{<:CausalInference.SCM}; kwargs...\n)\n t = Tables.table(transpose(data.X))\n est_g, score = CausalInference.ges(t; penalty=1.0, parallel=true)\n est_dag = CausalInference.pdag2dag!(est_g)\n scm = CausalInference.estimate_equations(t, est_dag)\n return scm\nend\n```\n:::\n\n\n\n\n... We are getting there! However, now comes the hardest part, where this is placed?\n\n\n\n\n\n# Conclusion\n\n\n\n# References\n\n", "supporting": [ "index_files/figure-html" ], diff --git a/profile/blog/posts/_metadata.yml b/profile/blog/posts/_metadata.yml index a1d1b66..5e761a9 100755 --- a/profile/blog/posts/_metadata.yml +++ b/profile/blog/posts/_metadata.yml @@ -16,7 +16,7 @@ author: comments: utterances: - repo: pat-alt/pat-alt.github.io + repo: JuliaTrustworthyAI/.github citation: true diff --git a/profile/blog/posts/causal-recourse/Manifest.toml b/profile/blog/posts/causal-recourse/Manifest.toml index cc05f85..3c3a243 100644 --- a/profile/blog/posts/causal-recourse/Manifest.toml +++ b/profile/blog/posts/causal-recourse/Manifest.toml @@ -2,7 +2,18 @@ julia_version = "1.10.5" manifest_format = "2.0" -project_hash = "25611679d220fb8d8ed8d4ecc80ba962141010d1" +project_hash = "41bd819777c272263800d4520c39fc5fadc9a79b" + +[[deps.AbstractFFTs]] +deps = ["LinearAlgebra"] +git-tree-sha1 = "d92ad398961a3ed262d8bf04a1a2b8340f915fef" +uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c" +version = "1.5.0" +weakdeps = ["ChainRulesCore", "Test"] + + [deps.AbstractFFTs.extensions] + AbstractFFTsChainRulesCoreExt = "ChainRulesCore" + AbstractFFTsTestExt = "Test" [[deps.AbstractTrees]] git-tree-sha1 = "2d9c9a55f9c93e8887ad391fbae72f8ef55e1177" @@ -65,9 +76,27 @@ git-tree-sha1 = "d57bd3762d308bded22c3b82d033bff85f6195c6" uuid = "ec485272-7323-5ecc-a04f-4719b315124d" version = "0.4.0" +[[deps.Arpack]] +deps = ["Arpack_jll", "Libdl", "LinearAlgebra", "Logging"] +git-tree-sha1 = "9b9b347613394885fd1c8c7729bfc60528faa436" +uuid = "7d9fca2a-8960-54d3-9f78-7d1dccf2cb97" +version = "0.5.4" + +[[deps.Arpack_jll]] +deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "OpenBLAS_jll", "Pkg"] +git-tree-sha1 = "5ba6c757e8feccf03a1554dfaf3e26b3cfc7fd5e" +uuid = "68821587-b530-5797-8361-c406ea357684" +version = "3.5.1+1" + [[deps.Artifacts]] uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33" +[[deps.Atomix]] +deps = ["UnsafeAtomics"] +git-tree-sha1 = "c06a868224ecba914baa6942988e2f2aade419be" +uuid = "a9b6321e-bd34-4604-b9c9-b65b8de01458" +version = "0.1.0" + [[deps.AxisAlgorithms]] deps = ["LinearAlgebra", "Random", "SparseArrays", "WoodburyMatrices"] git-tree-sha1 = "01b8ccb13d68535d73d2b0c23e39bd23155fb712" @@ -115,12 +144,47 @@ git-tree-sha1 = "9e2a6b69137e6969bab0152632dcb3bc108c8bdd" uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0" version = "1.0.8+1" +[[deps.CEnum]] +git-tree-sha1 = "389ad5c84de1ae7cf0e28e381131c98ea87d54fc" +uuid = "fa961155-64e5-5f13-b03f-caf6b980ea82" +version = "0.5.0" + [[deps.Cairo_jll]] deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"] git-tree-sha1 = "a2f1c8c668c8e3cb4cca4e57a8efdb09067bb3fd" uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a" version = "1.18.0+2" +[[deps.CategoricalArrays]] +deps = ["DataAPI", "Future", "Missings", "Printf", "Requires", "Statistics", "Unicode"] +git-tree-sha1 = "1568b28f91293458345dabba6a5ea3f183250a61" +uuid = "324d7699-5711-5eae-9e2f-1d82baa6b597" +version = "0.10.8" + + [deps.CategoricalArrays.extensions] + CategoricalArraysJSONExt = "JSON" + CategoricalArraysRecipesBaseExt = "RecipesBase" + CategoricalArraysSentinelArraysExt = "SentinelArrays" + CategoricalArraysStructTypesExt = "StructTypes" + + [deps.CategoricalArrays.weakdeps] + JSON = "682c06a0-de6a-54ab-a142-c8b1cf79cde6" + RecipesBase = "3cdcf5f2-1ef4-517c-9805-6587b60abb01" + SentinelArrays = "91c51154-3ec4-41a3-a24f-3f23e20d615c" + StructTypes = "856f2bd8-1eba-4b0a-8007-ebc267875bd4" + +[[deps.CategoricalDistributions]] +deps = ["CategoricalArrays", "Distributions", "Missings", "OrderedCollections", "Random", "ScientificTypes"] +git-tree-sha1 = "926862f549a82d6c3a7145bc7f1adff2a91a39f0" +uuid = "af321ab8-2d2e-40a6-b165-3d674595d28e" +version = "0.1.15" + + [deps.CategoricalDistributions.extensions] + UnivariateFiniteDisplayExt = "UnicodePlots" + + [deps.CategoricalDistributions.weakdeps] + UnicodePlots = "b8865327-cd53-5732-bb35-84acbb429228" + [[deps.CausalInference]] deps = ["Combinatorics", "Distances", "Distributions", "Graphs", "LRUCache", "LinearAlgebra", "LinkedLists", "LogarithmicNumbers", "Memoization", "MetaGraphs", "NearestNeighbors", "OffsetArrays", "PrecompileTools", "ProgressMeter", "Random", "Requires", "SpecialFunctions", "Statistics", "Tables", "TabularDisplay", "ThreadsX"] git-tree-sha1 = "8e5ff009a8eedb719bb0d450c9f65ef1e110c693" @@ -138,6 +202,12 @@ version = "0.17.0" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" TikzGraphs = "b4f28e30-c73f-5eaf-a395-8a9db949a742" +[[deps.ChainRules]] +deps = ["Adapt", "ChainRulesCore", "Compat", "Distributed", "GPUArraysCore", "IrrationalConstants", "LinearAlgebra", "Random", "RealDot", "SparseArrays", "SparseInverseSubset", "Statistics", "StructArrays", "SuiteSparse"] +git-tree-sha1 = "83806b5196e1e9827db0429a7579824c8b0e03ce" +uuid = "082447d4-558c-5d27-93f4-14fc19e9eca2" +version = "1.70.0" + [[deps.ChainRulesCore]] deps = ["Compat", "LinearAlgebra"] git-tree-sha1 = "71acdbf594aab5bbb2cec89b208c41b4c411e49f" @@ -187,6 +257,12 @@ git-tree-sha1 = "08c8b6831dc00bfea825826be0bc8336fc369860" uuid = "861a8166-3701-5b0c-9a16-15d98fcdc6aa" version = "1.0.2" +[[deps.CommonSubexpressions]] +deps = ["MacroTools"] +git-tree-sha1 = "cda2cfaebb4be89c9084adaca7dd7333369715c5" +uuid = "bbf7d656-a473-5ed7-a52c-81e309532950" +version = "0.3.1" + [[deps.Compat]] deps = ["TOML", "UUIDs"] git-tree-sha1 = "8ae8d32e09f0dcf42a36b90d4e17f5dd2e4c4215" @@ -211,6 +287,11 @@ weakdeps = ["InverseFunctions"] [deps.CompositionsBase.extensions] CompositionsBaseInverseFunctionsExt = "InverseFunctions" +[[deps.ComputationalResources]] +git-tree-sha1 = "52cb3ec90e8a8bea0e62e275ba577ad0f74821f7" +uuid = "ed09eef8-17a6-5b46-8889-db040fac31e3" +version = "0.3.2" + [[deps.ConcurrentUtilities]] deps = ["Serialization", "Sockets"] git-tree-sha1 = "ea32b83ca4fefa1768dc84e504cc0a94fb1ab8d1" @@ -232,16 +313,51 @@ version = "1.5.8" LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" StaticArrays = "90137ffa-7385-5640-81b9-e52037218182" +[[deps.ContextVariablesX]] +deps = ["Compat", "Logging", "UUIDs"] +git-tree-sha1 = "25cc3803f1030ab855e383129dcd3dc294e322cc" +uuid = "6add18c4-b38d-439d-96f6-d6bc489c04c5" +version = "0.1.3" + [[deps.Contour]] git-tree-sha1 = "439e35b0b36e2e5881738abc8857bd92ad6ff9a8" uuid = "d38c429a-6771-53c6-b99e-75d170b6e991" version = "0.6.3" +[[deps.CounterfactualExplanations]] +deps = ["CategoricalArrays", "CausalInference", "ChainRulesCore", "DataFrames", "Distributions", "EnergySamplers", "Flux", "Graphs", "LazyArtifacts", "LinearAlgebra", "Logging", "MLJBase", "MLJDecisionTreeInterface", "MLUtils", "MultivariateStats", "PackageExtensionCompat", "ProgressMeter", "Random", "Serialization", "Statistics", "StatsBase", "Tables", "TaijaBase", "UUIDs"] +git-tree-sha1 = "780286593014415bd22e552182decf9a82045bfd" +uuid = "2f13d31b-18db-44c1-bc43-ebaf2cff0be0" +version = "1.2.0" + + [deps.CounterfactualExplanations.extensions] + DecisionTreeExt = "DecisionTree" + JEMExt = "JointEnergyModels" + LaplaceReduxExt = "LaplaceRedux" + NeuroTreeExt = "NeuroTreeModels" + + [deps.CounterfactualExplanations.weakdeps] + DecisionTree = "7806a523-6efd-50cb-b5f6-3fa6f1930dbb" + JointEnergyModels = "48c56d24-211d-4463-bbc0-7a701b291131" + LaplaceRedux = "c52c1a26-f7c5-402b-80be-ba1e638ad478" + NeuroTreeModels = "1db4e0a5-a364-4b0c-897c-2bd5a4a3a1f2" + +[[deps.Crayons]] +git-tree-sha1 = "249fe38abf76d48563e2f4556bebd215aa317e15" +uuid = "a8cc5b0e-0ffa-5ad4-8c14-923d3ee1735f" +version = "4.1.1" + [[deps.DataAPI]] git-tree-sha1 = "abe83f3a2f1b857aac70ef8b269080af17764bbe" uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a" version = "1.16.0" +[[deps.DataFrames]] +deps = ["Compat", "DataAPI", "DataStructures", "Future", "InlineStrings", "InvertedIndices", "IteratorInterfaceExtensions", "LinearAlgebra", "Markdown", "Missings", "PooledArrays", "PrecompileTools", "PrettyTables", "Printf", "REPL", "Random", "Reexport", "SentinelArrays", "SortingAlgorithms", "Statistics", "TableTraits", "Tables", "Unicode"] +git-tree-sha1 = "04c738083f29f86e62c8afc341f0967d8717bdb8" +uuid = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0" +version = "1.6.1" + [[deps.DataStructures]] deps = ["Compat", "InteractiveUtils", "OrderedCollections"] git-tree-sha1 = "1d0a14036acb104d9e89698bd408f63ab58cdc82" @@ -263,6 +379,12 @@ git-tree-sha1 = "fc173b380865f70627d7dd1190dc2fce6cc105af" uuid = "ee1fde0b-3d02-5ea6-8484-8dfef6360eab" version = "1.14.10+0" +[[deps.DecisionTree]] +deps = ["AbstractTrees", "DelimitedFiles", "LinearAlgebra", "Random", "ScikitLearnBase", "Statistics"] +git-tree-sha1 = "526ca14aaaf2d5a0e242f3a8a7966eb9065d7d78" +uuid = "7806a523-6efd-50cb-b5f6-3fa6f1930dbb" +version = "0.12.4" + [[deps.DefineSingletons]] git-tree-sha1 = "0fba8b706d0178b4dc7fd44a96a92382c9065c2c" uuid = "244e2a9f-e319-4986-a169-4d1fe445cd52" @@ -274,6 +396,18 @@ git-tree-sha1 = "9e2f36d3c96a820c678f2f1f1782582fcf685bae" uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab" version = "1.9.1" +[[deps.DiffResults]] +deps = ["StaticArraysCore"] +git-tree-sha1 = "782dd5f4561f5d267313f23853baaaa4c52ea621" +uuid = "163ba53b-c6d8-5494-b064-1a9d43ac40c5" +version = "1.1.0" + +[[deps.DiffRules]] +deps = ["IrrationalConstants", "LogExpFunctions", "NaNMath", "Random", "SpecialFunctions"] +git-tree-sha1 = "23163d55f885173722d1e4cf0f6110cdbaf7e272" +uuid = "b552c78f-8df3-52c6-915a-8e097449b14b" +version = "1.15.1" + [[deps.Distances]] deps = ["LinearAlgebra", "Statistics", "StatsAPI"] git-tree-sha1 = "66c4c81f259586e8f002eacebc177e1fb06363b0" @@ -322,6 +456,12 @@ git-tree-sha1 = "e3290f2d49e661fbd94046d7e3726ffcb2d41053" uuid = "5ae413db-bbd1-5e63-b57d-d24a61df00f5" version = "2.2.4+0" +[[deps.EnergySamplers]] +deps = ["CategoricalArrays", "Distributions", "Flux", "MLUtils", "Optimisers", "StatsBase", "Tables"] +git-tree-sha1 = "6072d358f2208c7cf56c18d4112d94f8660fa4b0" +uuid = "f446124b-5d5e-4171-a6dd-a1d99768d3ce" +version = "1.0.0" + [[deps.EpollShim_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "8e9441ee83492030ace98f9789a654a6d0b1f643" @@ -357,6 +497,18 @@ git-tree-sha1 = "466d45dc38e15794ec7d5d63ec03d776a9aff36e" uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5" version = "4.4.4+1" +[[deps.FLoops]] +deps = ["BangBang", "Compat", "FLoopsBase", "InitialValues", "JuliaVariables", "MLStyle", "Serialization", "Setfield", "Transducers"] +git-tree-sha1 = "0a2e5873e9a5f54abb06418d57a8df689336a660" +uuid = "cc61a311-1640-44b5-9fba-1b764f453329" +version = "0.2.2" + +[[deps.FLoopsBase]] +deps = ["ContextVariablesX"] +git-tree-sha1 = "656f7a6859be8673bf1f35da5670246b923964f7" +uuid = "b9860ae5-e623-471e-878b-f6a53c775ea6" +version = "0.1.1" + [[deps.FileIO]] deps = ["Pkg", "Requires", "UUIDs"] git-tree-sha1 = "82d8afa92ecf4b52d78d869f038ebfb881267322" @@ -384,6 +536,26 @@ git-tree-sha1 = "05882d6995ae5c12bb5f36dd2ed3f61c98cbb172" uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93" version = "0.8.5" +[[deps.Flux]] +deps = ["Adapt", "ChainRulesCore", "Compat", "Functors", "LinearAlgebra", "MLUtils", "MacroTools", "NNlib", "OneHotArrays", "Optimisers", "Preferences", "ProgressLogging", "Random", "Reexport", "SparseArrays", "SpecialFunctions", "Statistics", "Zygote"] +git-tree-sha1 = "fbf100b4bed74c9b6fac0ebd1031e04977d35b3b" +uuid = "587475ba-b771-5e3f-ad9e-33799f191a9c" +version = "0.14.19" + + [deps.Flux.extensions] + FluxAMDGPUExt = "AMDGPU" + FluxCUDAExt = "CUDA" + FluxCUDAcuDNNExt = ["CUDA", "cuDNN"] + FluxEnzymeExt = "Enzyme" + FluxMetalExt = "Metal" + + [deps.Flux.weakdeps] + AMDGPU = "21141c5a-9bdb-4563-92ae-f87d6854732e" + CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba" + Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9" + Metal = "dde4c033-4e86-420c-a63e-0dd931031962" + cuDNN = "02a925ec-e4fe-4b08-9a7e-0d78e3d38ccd" + [[deps.Fontconfig_jll]] deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Zlib_jll"] git-tree-sha1 = "db16beca600632c95fc8aca29890d83788dd8b23" @@ -401,6 +573,16 @@ git-tree-sha1 = "fb409abab2caf118986fc597ba84b50cbaf00b87" uuid = "59287772-0a20-5a39-b81b-1366585eb4c0" version = "0.4.3" +[[deps.ForwardDiff]] +deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "LogExpFunctions", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions"] +git-tree-sha1 = "cf0fe81336da9fb90944683b8c41984b08793dad" +uuid = "f6369f11-7733-5829-9624-2563aa707210" +version = "0.10.36" +weakdeps = ["StaticArrays"] + + [deps.ForwardDiff.extensions] + ForwardDiffStaticArraysExt = "StaticArrays" + [[deps.FreeType2_jll]] deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Zlib_jll"] git-tree-sha1 = "5c1d8ae0efc6c2e7b1fc502cbe25def8f661b7bc" @@ -413,6 +595,12 @@ git-tree-sha1 = "1ed150b39aebcc805c26b93a8d0122c940f64ce2" uuid = "559328eb-81f9-559d-9380-de523a88c83c" version = "1.0.14+0" +[[deps.Functors]] +deps = ["LinearAlgebra"] +git-tree-sha1 = "64d8e93700c7a3f28f717d265382d52fac9fa1c1" +uuid = "d9f16b24-f501-4c13-a1f2-28368ffc5196" +version = "0.4.12" + [[deps.Future]] deps = ["Random"] uuid = "9fa8497b-333b-5362-9e8d-4d0656e87820" @@ -423,6 +611,18 @@ git-tree-sha1 = "532f9126ad901533af1d4f5c198867227a7bb077" uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89" version = "3.4.0+1" +[[deps.GPUArrays]] +deps = ["Adapt", "GPUArraysCore", "LLVM", "LinearAlgebra", "Printf", "Random", "Reexport", "Serialization", "Statistics"] +git-tree-sha1 = "62ee71528cca49be797076a76bdc654a170a523e" +uuid = "0c68f7d7-f131-5f86-a1c3-88cf8149b2d7" +version = "10.3.1" + +[[deps.GPUArraysCore]] +deps = ["Adapt"] +git-tree-sha1 = "ec632f177c0d990e64d955ccc1b8c04c485a0950" +uuid = "46192b85-c4d5-4398-a991-12ede77f4527" +version = "0.1.6" + [[deps.GR]] deps = ["Artifacts", "Base64", "DelimitedFiles", "Downloads", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Preferences", "Printf", "Qt6Wayland_jll", "Random", "Serialization", "Sockets", "TOML", "Tar", "Test", "p7zip_jll"] git-tree-sha1 = "629693584cef594c3f6f99e76e7a7ad17e60e8d5" @@ -511,6 +711,12 @@ git-tree-sha1 = "7c4195be1649ae622304031ed46a2f4df989f1eb" uuid = "34004b35-14d8-5ef3-9330-4cdb6864b03a" version = "0.3.24" +[[deps.IRTools]] +deps = ["InteractiveUtils", "MacroTools"] +git-tree-sha1 = "950c3717af761bc3ff906c2e8e52bd83390b6ec2" +uuid = "7869d1d1-7146-5819-86e3-90919afe41df" +version = "0.4.14" + [[deps.Inflate]] git-tree-sha1 = "d1b1b796e47d94588b3757fe84fbf65a5ec4a80d" uuid = "d25df0c9-e2be-5dd7-82c8-3ad0b3e990b9" @@ -521,6 +727,19 @@ git-tree-sha1 = "4da0f88e9a39111c2fa3add390ab15f3a44f3ca3" uuid = "22cec73e-a1b8-11e9-2c92-598750a2cf9c" version = "0.3.1" +[[deps.InlineStrings]] +git-tree-sha1 = "45521d31238e87ee9f9732561bfee12d4eebd52d" +uuid = "842dd82b-1e85-43dc-bf29-5d0ee9dffc48" +version = "1.4.2" + + [deps.InlineStrings.extensions] + ArrowTypesExt = "ArrowTypes" + ParsersExt = "Parsers" + + [deps.InlineStrings.weakdeps] + ArrowTypes = "31f734f8-188a-4ce0-8406-c8a06bd891cd" + Parsers = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0" + [[deps.InteractiveUtils]] deps = ["Markdown"] uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240" @@ -545,6 +764,11 @@ weakdeps = ["Dates", "Test"] InverseFunctionsDatesExt = "Dates" InverseFunctionsTestExt = "Test" +[[deps.InvertedIndices]] +git-tree-sha1 = "0dc7b50b8d436461be01300fd8cd45aa0274b038" +uuid = "41ab1584-1d38-5bbf-9106-f11c6c58b48f" +version = "1.3.0" + [[deps.IrrationalConstants]] git-tree-sha1 = "630b497eafcc20001bba38a4651b327dcfc491d2" uuid = "92d709cd-6900-40b7-9082-c6be49f344b6" @@ -590,6 +814,28 @@ git-tree-sha1 = "c84a835e1a09b289ffcd2271bf2a337bbdda6637" uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8" version = "3.0.3+0" +[[deps.JuliaVariables]] +deps = ["MLStyle", "NameResolution"] +git-tree-sha1 = "49fb3cb53362ddadb4415e9b73926d6b40709e70" +uuid = "b14d175d-62b4-44ba-8fb7-3064adc8c3ec" +version = "0.2.4" + +[[deps.KernelAbstractions]] +deps = ["Adapt", "Atomix", "InteractiveUtils", "MacroTools", "PrecompileTools", "Requires", "StaticArrays", "UUIDs", "UnsafeAtomics", "UnsafeAtomicsLLVM"] +git-tree-sha1 = "cb1cff88ef2f3a157cbad75bbe6b229e1975e498" +uuid = "63c18a36-062a-441e-b654-da1e3ab1ce7c" +version = "0.9.25" + + [deps.KernelAbstractions.extensions] + EnzymeExt = "EnzymeCore" + LinearAlgebraExt = "LinearAlgebra" + SparseArraysExt = "SparseArrays" + + [deps.KernelAbstractions.weakdeps] + EnzymeCore = "f151be2c-9106-41f4-ab19-57ee4f262869" + LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" + SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" + [[deps.LAME_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "170b660facf5df5de098d866564877e119141cbd" @@ -602,6 +848,24 @@ git-tree-sha1 = "bf36f528eec6634efc60d7ec062008f171071434" uuid = "88015f11-f218-50d7-93a8-a6af411a945d" version = "3.0.0+1" +[[deps.LLVM]] +deps = ["CEnum", "LLVMExtra_jll", "Libdl", "Preferences", "Printf", "Requires", "Unicode"] +git-tree-sha1 = "4ad43cb0a4bb5e5b1506e1d1f48646d7e0c80363" +uuid = "929cbde3-209d-540e-8aea-75f648917ca0" +version = "9.1.2" + + [deps.LLVM.extensions] + BFloat16sExt = "BFloat16s" + + [deps.LLVM.weakdeps] + BFloat16s = "ab4f0b2a-ad5b-11e8-123f-65d77653426b" + +[[deps.LLVMExtra_jll]] +deps = ["Artifacts", "JLLWrappers", "LazyArtifacts", "Libdl", "TOML"] +git-tree-sha1 = "05a8bd5a42309a9ec82f700876903abce1017dd3" +uuid = "dad2f222-ce93-54a1-a47d-0025e8a3acab" +version = "0.0.34+0" + [[deps.LLVMOpenMP_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "78211fb6cbc872f77cad3fc0b6cf647d923f4929" @@ -644,6 +908,16 @@ version = "0.16.5" SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" SymEngine = "123dc426-2d89-5057-bbad-38513e3affd8" +[[deps.LazyArtifacts]] +deps = ["Artifacts", "Pkg"] +uuid = "4af54fe1-eca0-43a8-85a7-787d91b784e3" + +[[deps.LearnAPI]] +deps = ["InteractiveUtils", "Statistics"] +git-tree-sha1 = "ec695822c1faaaa64cee32d0b21505e1977b4809" +uuid = "92ad9a40-7767-427a-9ee6-6e577f1266cb" +version = "0.1.0" + [[deps.LibCURL]] deps = ["LibCURL_jll", "MozillaCACerts_jll"] uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21" @@ -749,13 +1023,11 @@ deps = ["Random"] git-tree-sha1 = "427421c277f82c5749002c1b23cb1aac91beb0a8" uuid = "aa2f6b4e-9042-5d33-9679-40d3a6b85899" version = "1.4.0" +weakdeps = ["ForwardDiff"] [deps.LogarithmicNumbers.extensions] LogarithmicNumbersForwardDiffExt = "ForwardDiff" - [deps.LogarithmicNumbers.weakdeps] - ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210" - [[deps.Logging]] uuid = "56ddb016-857b-54e1-b83d-db4d58db5568" @@ -765,6 +1037,41 @@ git-tree-sha1 = "c1dd6d7978c12545b4179fb6153b9250c96b0075" uuid = "e6f89c97-d47a-5376-807f-9c37f3926c36" version = "1.0.3" +[[deps.MLJBase]] +deps = ["CategoricalArrays", "CategoricalDistributions", "ComputationalResources", "Dates", "DelimitedFiles", "Distributed", "Distributions", "InteractiveUtils", "InvertedIndices", "LearnAPI", "LinearAlgebra", "MLJModelInterface", "Missings", "OrderedCollections", "Parameters", "PrettyTables", "ProgressMeter", "Random", "RecipesBase", "Reexport", "ScientificTypes", "Serialization", "StatisticalMeasuresBase", "StatisticalTraits", "Statistics", "StatsBase", "Tables"] +git-tree-sha1 = "6f45e12073bc2f2e73ed0473391db38c31e879c9" +uuid = "a7f614a8-145f-11e9-1d2a-a57a1082229d" +version = "1.7.0" + + [deps.MLJBase.extensions] + DefaultMeasuresExt = "StatisticalMeasures" + + [deps.MLJBase.weakdeps] + StatisticalMeasures = "a19d573c-0a75-4610-95b3-7071388c7541" + +[[deps.MLJDecisionTreeInterface]] +deps = ["CategoricalArrays", "DecisionTree", "MLJModelInterface", "Random", "Tables"] +git-tree-sha1 = "90ef4d3b6cacec631c57cc034e1e61b4aa0ce511" +uuid = "c6f25543-311c-4c74-83dc-3ea6d1015661" +version = "0.4.2" + +[[deps.MLJModelInterface]] +deps = ["Random", "ScientificTypesBase", "StatisticalTraits"] +git-tree-sha1 = "ceaff6618408d0e412619321ae43b33b40c1a733" +uuid = "e80e1ace-859a-464e-9ed9-23947d8ae3ea" +version = "1.11.0" + +[[deps.MLStyle]] +git-tree-sha1 = "bc38dff0548128765760c79eb7388a4b37fae2c8" +uuid = "d8e11817-5142-5d16-987a-aa16d5891078" +version = "0.4.17" + +[[deps.MLUtils]] +deps = ["ChainRulesCore", "Compat", "DataAPI", "DelimitedFiles", "FLoops", "NNlib", "Random", "ShowCases", "SimpleTraits", "Statistics", "StatsBase", "Tables", "Transducers"] +git-tree-sha1 = "b45738c2e3d0d402dffa32b2c1654759a2ac35a4" +uuid = "f1d291b0-491e-4a28-83b9-f70985020b54" +version = "0.4.4" + [[deps.MacroTools]] deps = ["Markdown", "Random"] git-tree-sha1 = "2fa9ee3e63fd3a4f7a9a4f4744a52f4856de82df" @@ -822,12 +1129,46 @@ uuid = "a63ad114-7e13-5084-954f-fe012c677804" uuid = "14a3606d-f60d-562e-9121-12d972cd8159" version = "2023.1.10" +[[deps.MultivariateStats]] +deps = ["Arpack", "Distributions", "LinearAlgebra", "SparseArrays", "Statistics", "StatsAPI", "StatsBase"] +git-tree-sha1 = "816620e3aac93e5b5359e4fdaf23ca4525b00ddf" +uuid = "6f286f6a-111f-5878-ab1e-185364afe411" +version = "0.10.3" + +[[deps.NNlib]] +deps = ["Adapt", "Atomix", "ChainRulesCore", "GPUArraysCore", "KernelAbstractions", "LinearAlgebra", "Random", "Statistics"] +git-tree-sha1 = "4a83c2e01027a0bfcea28589222f2df60b2e20cb" +uuid = "872c559c-99b0-510c-b3b7-b6c96a88d5cd" +version = "0.9.23" + + [deps.NNlib.extensions] + NNlibAMDGPUExt = "AMDGPU" + NNlibCUDACUDNNExt = ["CUDA", "cuDNN"] + NNlibCUDAExt = "CUDA" + NNlibEnzymeCoreExt = "EnzymeCore" + NNlibFFTWExt = "FFTW" + NNlibForwardDiffExt = "ForwardDiff" + + [deps.NNlib.weakdeps] + AMDGPU = "21141c5a-9bdb-4563-92ae-f87d6854732e" + CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba" + EnzymeCore = "f151be2c-9106-41f4-ab19-57ee4f262869" + FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341" + ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210" + cuDNN = "02a925ec-e4fe-4b08-9a7e-0d78e3d38ccd" + [[deps.NaNMath]] deps = ["OpenLibm_jll"] git-tree-sha1 = "0877504529a3e5c3343c6f8b4c0381e57e4387e4" uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3" version = "1.0.2" +[[deps.NameResolution]] +deps = ["PrettyPrint"] +git-tree-sha1 = "1a0fa0e9613f46c9b8c11eee38ebb4f590013c5e" +uuid = "71a1bf82-56d0-4bbc-8a3c-48b961074391" +version = "0.1.5" + [[deps.NearestNeighbors]] deps = ["Distances", "StaticArrays"] git-tree-sha1 = "91a67b4d73842da90b526011fa85c5c4c9343fe0" @@ -863,6 +1204,12 @@ git-tree-sha1 = "887579a3eb005446d514ab7aeac5d1d027658b8f" uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051" version = "1.3.5+1" +[[deps.OneHotArrays]] +deps = ["Adapt", "ChainRulesCore", "Compat", "GPUArraysCore", "LinearAlgebra", "NNlib"] +git-tree-sha1 = "963a3f28a2e65bb87a68033ea4a616002406037d" +uuid = "0b1bfda6-eb8a-41d2-88d8-f5af5cad476f" +version = "0.2.5" + [[deps.OpenBLAS_jll]] deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"] uuid = "4536629a-c528-5b80-bd46-f80d51c5b363" @@ -891,6 +1238,12 @@ git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1" uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e" version = "0.5.5+0" +[[deps.Optimisers]] +deps = ["ChainRulesCore", "Functors", "LinearAlgebra", "Random", "Statistics"] +git-tree-sha1 = "6572fe0c5b74431aaeb0b18a4aa5ef03c84678be" +uuid = "3bd65402-5787-11e9-1adc-39752487f4e2" +version = "0.3.3" + [[deps.Opus_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "6703a85cb3781bd5909d48730a67205f3f31a575" @@ -913,12 +1266,24 @@ git-tree-sha1 = "949347156c25054de2db3b166c52ac4728cbad65" uuid = "90014a1f-27ba-587c-ab20-58faa44d9150" version = "0.11.31" +[[deps.PackageExtensionCompat]] +git-tree-sha1 = "fb28e33b8a95c4cee25ce296c817d89cc2e53518" +uuid = "65ce6f38-6b18-4e1d-a461-8949797d7930" +version = "1.0.2" +weakdeps = ["Requires", "TOML"] + [[deps.Pango_jll]] deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "FriBidi_jll", "Glib_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl"] git-tree-sha1 = "e127b609fb9ecba6f201ba7ab753d5a605d53801" uuid = "36c8627f-9965-5494-a995-c6b170f724f3" version = "1.54.1+0" +[[deps.Parameters]] +deps = ["OrderedCollections", "UnPack"] +git-tree-sha1 = "34c0e9ad262e5f7fc75b10a9952ca7692cfc5fbe" +uuid = "d96e819e-fc66-5662-9728-84c9c7592b0a" +version = "0.12.3" + [[deps.Parsers]] deps = ["Dates", "PrecompileTools", "UUIDs"] git-tree-sha1 = "8489905bcdbcfac64d1daa51ca07c0d8f0283821" @@ -973,6 +1338,12 @@ version = "1.40.8" ImageInTerminal = "d8c32880-2388-543b-8c61-d9f865259254" Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d" +[[deps.PooledArrays]] +deps = ["DataAPI", "Future"] +git-tree-sha1 = "36d8b4b899628fb92c2749eb488d884a926614d3" +uuid = "2dfb63ee-cc39-5dd5-95bd-886bf059d720" +version = "1.4.3" + [[deps.PrecompileTools]] deps = ["Preferences"] git-tree-sha1 = "5aa36f7049a63a1528fe8f7c3f2113413ffd4e1f" @@ -985,10 +1356,27 @@ git-tree-sha1 = "9306f6085165d270f7e3db02af26a400d580f5c6" uuid = "21216c6a-2e73-6563-6e65-726566657250" version = "1.4.3" +[[deps.PrettyPrint]] +git-tree-sha1 = "632eb4abab3449ab30c5e1afaa874f0b98b586e4" +uuid = "8162dcfd-2161-5ef2-ae6c-7681170c5f98" +version = "0.2.0" + +[[deps.PrettyTables]] +deps = ["Crayons", "LaTeXStrings", "Markdown", "PrecompileTools", "Printf", "Reexport", "StringManipulation", "Tables"] +git-tree-sha1 = "66b20dd35966a748321d3b2537c4584cf40387c7" +uuid = "08abe8d2-0d0c-5749-adfa-8a2ac140af0d" +version = "2.3.2" + [[deps.Printf]] deps = ["Unicode"] uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7" +[[deps.ProgressLogging]] +deps = ["Logging", "SHA", "UUIDs"] +git-tree-sha1 = "80d919dee55b9c50e8d9e2da5eeafff3fe58b539" +uuid = "33c8b6b6-d38a-422a-b730-caa89a2f386c" +version = "0.1.4" + [[deps.ProgressMeter]] deps = ["Distributed", "Printf"] git-tree-sha1 = "8f6bc219586aef8baf0ff9a5fe16ee9c70cb65e4" @@ -1054,6 +1442,12 @@ weakdeps = ["FixedPointNumbers"] [deps.Ratios.extensions] RatiosFixedPointNumbersExt = "FixedPointNumbers" +[[deps.RealDot]] +deps = ["LinearAlgebra"] +git-tree-sha1 = "9f0a1b71baaf7650f4fa8a1d168c7fb6ee41f0c9" +uuid = "c1ae055f-0cd5-4b69-90a6-9a35b1a98df9" +version = "0.1.0" + [[deps.RecipesBase]] deps = ["PrecompileTools"] git-tree-sha1 = "5c3d09cc4f31f5fc6af001c250bf1278733100ff" @@ -1105,12 +1499,35 @@ version = "0.5.1+0" uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce" version = "0.7.0" +[[deps.ScientificTypes]] +deps = ["CategoricalArrays", "ColorTypes", "Dates", "Distributions", "PrettyTables", "Reexport", "ScientificTypesBase", "StatisticalTraits", "Tables"] +git-tree-sha1 = "75ccd10ca65b939dab03b812994e571bf1e3e1da" +uuid = "321657f4-b219-11e9-178b-2701a2544e81" +version = "3.0.2" + +[[deps.ScientificTypesBase]] +git-tree-sha1 = "a8e18eb383b5ecf1b5e6fc237eb39255044fd92b" +uuid = "30f210dd-8aff-4c5f-94ba-8e64358c1161" +version = "3.0.0" + +[[deps.ScikitLearnBase]] +deps = ["LinearAlgebra", "Random", "Statistics"] +git-tree-sha1 = "7877e55c1523a4b336b433da39c8e8c08d2f221f" +uuid = "6e75b9c4-186b-50bd-896f-2d2496a4843e" +version = "0.5.0" + [[deps.Scratch]] deps = ["Dates"] git-tree-sha1 = "3bac05bc7e74a75fd9cba4295cde4045d9fe2386" uuid = "6c6a2e73-6563-6170-7368-637461726353" version = "1.2.1" +[[deps.SentinelArrays]] +deps = ["Dates", "Random"] +git-tree-sha1 = "ff11acffdb082493657550959d4feb4b6149e73a" +uuid = "91c51154-3ec4-41a3-a24f-3f23e20d615c" +version = "1.4.5" + [[deps.Serialization]] uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b" @@ -1124,6 +1541,11 @@ version = "1.1.1" deps = ["Distributed", "Mmap", "Random", "Serialization"] uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383" +[[deps.ShowCases]] +git-tree-sha1 = "7f534ad62ab2bd48591bdeac81994ea8c445e4a5" +uuid = "605ecd9f-84a6-4c9e-81e2-4798472b76a3" +version = "0.1.0" + [[deps.Showoff]] deps = ["Dates", "Grisu"] git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de" @@ -1155,6 +1577,12 @@ deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"] uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" version = "1.10.0" +[[deps.SparseInverseSubset]] +deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse"] +git-tree-sha1 = "52962839426b75b3021296f7df242e40ecfc0852" +uuid = "dc90abb0-5640-4711-901d-7e5b23a2fada" +version = "0.1.2" + [[deps.SpecialFunctions]] deps = ["IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"] git-tree-sha1 = "2f5d4697f21388cbe1ff299430dd169ef97d7e14" @@ -1187,6 +1615,18 @@ git-tree-sha1 = "192954ef1208c7019899fbf8049e717f92959682" uuid = "1e83bf80-4336-4d27-bf5d-d5a4f845583c" version = "1.4.3" +[[deps.StatisticalMeasuresBase]] +deps = ["CategoricalArrays", "InteractiveUtils", "MLUtils", "MacroTools", "OrderedCollections", "PrecompileTools", "ScientificTypesBase", "Statistics"] +git-tree-sha1 = "17dfb22e2e4ccc9cd59b487dce52883e0151b4d3" +uuid = "c062fc1d-0d66-479b-b6ac-8b44719de4cc" +version = "0.1.1" + +[[deps.StatisticalTraits]] +deps = ["ScientificTypesBase"] +git-tree-sha1 = "542d979f6e756f13f862aa00b224f04f9e445f11" +uuid = "64bff920-2084-43da-a3e6-9bb72801c0c9" +version = "3.4.0" + [[deps.Statistics]] deps = ["LinearAlgebra", "SparseArrays"] uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" @@ -1215,11 +1655,18 @@ weakdeps = ["ChainRulesCore", "InverseFunctions"] StatsFunsChainRulesCoreExt = "ChainRulesCore" StatsFunsInverseFunctionsExt = "InverseFunctions" +[[deps.StringManipulation]] +deps = ["PrecompileTools"] +git-tree-sha1 = "a04cabe79c5f01f4d723cc6704070ada0b9d46d5" +uuid = "892a3eda-7b42-436c-8928-eab12a02cf0e" +version = "0.3.4" + [[deps.StructArrays]] deps = ["ConstructionBase", "DataAPI", "Tables"] git-tree-sha1 = "f4dc295e983502292c4c3f951dbb4e985e35b3be" uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a" version = "0.6.18" +weakdeps = ["Adapt", "GPUArraysCore", "SparseArrays", "StaticArrays"] [deps.StructArrays.extensions] StructArraysAdaptExt = "Adapt" @@ -1227,12 +1674,6 @@ version = "0.6.18" StructArraysSparseArraysExt = "SparseArrays" StructArraysStaticArraysExt = "StaticArrays" - [deps.StructArrays.weakdeps] - Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e" - GPUArraysCore = "46192b85-c4d5-4398-a991-12ede77f4527" - SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" - StaticArrays = "90137ffa-7385-5640-81b9-e52037218182" - [[deps.SuiteSparse]] deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"] uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9" @@ -1265,6 +1706,11 @@ git-tree-sha1 = "ab1c4fe069f16cbb62bf4b39a0b9dab9c1699752" uuid = "3eeacb1d-13c2-54cc-9b18-30c86af3cadb" version = "1.2.0" +[[deps.TaijaBase]] +git-tree-sha1 = "4076f60078b12095ca71a2c26e2e4515e3a6a5e5" +uuid = "10284c91-9f28-4c9a-abbf-ee43576dfff6" +version = "1.2.3" + [[deps.Tar]] deps = ["ArgTools", "SHA"] uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e" @@ -1320,6 +1766,11 @@ version = "1.5.1" deps = ["Random", "SHA"] uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4" +[[deps.UnPack]] +git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b" +uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed" +version = "1.0.2" + [[deps.Unicode]] uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5" @@ -1346,6 +1797,17 @@ git-tree-sha1 = "975c354fcd5f7e1ddcc1f1a23e6e091d99e99bc8" uuid = "45397f5d-5981-4c77-b2b3-fc36d6e9b728" version = "1.6.4" +[[deps.UnsafeAtomics]] +git-tree-sha1 = "6331ac3440856ea1988316b46045303bef658278" +uuid = "013be700-e6cd-48c3-b4a1-df204f14c38f" +version = "0.2.1" + +[[deps.UnsafeAtomicsLLVM]] +deps = ["LLVM", "UnsafeAtomics"] +git-tree-sha1 = "2d17fabcd17e67d7625ce9c531fb9f40b7c42ce4" +uuid = "d80eeb9a-aca5-4d75-85e5-170c8b632249" +version = "0.2.1" + [[deps.Unzip]] git-tree-sha1 = "ca0969166a028236229f63514992fc073799bb78" uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d" @@ -1548,6 +2010,28 @@ git-tree-sha1 = "e678132f07ddb5bfa46857f0d7620fb9be675d3b" uuid = "3161d3a3-bdf6-5164-811a-617609db77b4" version = "1.5.6+0" +[[deps.Zygote]] +deps = ["AbstractFFTs", "ChainRules", "ChainRulesCore", "DiffRules", "Distributed", "FillArrays", "ForwardDiff", "GPUArrays", "GPUArraysCore", "IRTools", "InteractiveUtils", "LinearAlgebra", "LogExpFunctions", "MacroTools", "NaNMath", "PrecompileTools", "Random", "Requires", "SparseArrays", "SpecialFunctions", "Statistics", "ZygoteRules"] +git-tree-sha1 = "19c586905e78a26f7e4e97f81716057bd6b1bc54" +uuid = "e88e6eb3-aa80-5325-afca-941959d7151f" +version = "0.6.70" + + [deps.Zygote.extensions] + ZygoteColorsExt = "Colors" + ZygoteDistancesExt = "Distances" + ZygoteTrackerExt = "Tracker" + + [deps.Zygote.weakdeps] + Colors = "5ae59095-9a9b-59fe-a467-6f913c188581" + Distances = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7" + Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c" + +[[deps.ZygoteRules]] +deps = ["ChainRulesCore", "MacroTools"] +git-tree-sha1 = "27798139afc0a2afa7b1824c206d5e87ea587a00" +uuid = "700de1a5-db45-46bc-99cf-38207098b444" +version = "0.2.5" + [[deps.eudev_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "gperf_jll"] git-tree-sha1 = "431b678a28ebb559d224c0b6b6d01afce87c51ba" diff --git a/profile/blog/posts/causal-recourse/Project.toml b/profile/blog/posts/causal-recourse/Project.toml index cfc4483..32df96d 100644 --- a/profile/blog/posts/causal-recourse/Project.toml +++ b/profile/blog/posts/causal-recourse/Project.toml @@ -1,5 +1,9 @@ [deps] CausalInference = "8e462317-f959-576b-b3c1-403f26cec956" +CounterfactualExplanations = "2f13d31b-18db-44c1-bc43-ebaf2cff0be0" GraphRecipes = "bd48cda9-67a9-57be-86fa-5b3c104eda73" +Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6" +MultivariateStats = "6f286f6a-111f-5878-ab1e-185364afe411" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" +StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91" diff --git a/profile/blog/posts/causal-recourse/index.html b/profile/blog/posts/causal-recourse/index.html deleted file mode 100644 index 6a09123..0000000 --- a/profile/blog/posts/causal-recourse/index.html +++ /dev/null @@ -1,800 +0,0 @@ - - - - - - - - - - - - -When Causal meets Recourse - - - - - - - - - - - - - - - - - - - - - - - -
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When Causal meets Recourse

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Counterfactual Explanations through Structural Causal Models

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explainable AI
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This post introduces a new tool in CounterfactualExplanations.jl, enhancing the package with causal reasoning to generate counterfactual explanations. The functionality can be used to explain machine learning algorithms developed in Julia and other popular programming languages like Python and R. Unlike traditional counterfactual generators, this approach utilizes causal information to perturb features intelligently.

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Jorge Luiz Franco

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September 3, 2024

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Introduction

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In recent years, the need for interpretable and explainable AI has surged, particularly in high-stakes domains. Counterfactual explanations provide a means to understand how changes to input features could alter the outcomes of machine learning models. This blog post presents a new tool in the CounterfactualExplanations.jl package, developed during my JSoC (Julia Summer of Code) project, which incorporates causal reasoning into counterfactual generation.

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Project Overview

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This project aimed to enhance the CounterfactualExplanations.jl package by infusing it with a robust mathematical foundation for minimal algorithmic recourse, based on the principles of causal reasoning (Karimi, Schölkopf, and Valera 2021).

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Key Contributions

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During the project, I contributed to two key repositories:

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  1. CounterfactualExplanations.jl: Developed a new tool for generating counterfactual explanations using causal information. This allows users to create smarter perturbations rather than random adjustments, ultimately providing more meaningful insights.

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  2. CausalInference.jl: Implemented a Structural Causal Model (SCM) structure that extracts information from data, laying the groundwork for the causal reasoning capabilities in CounterfactualExplanations.jl.

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This was an amazing experience, not just experience contribute to two repositories simultaneously, but also to work with the mantainers of these repos. I learned a lot about the Julia language and the Julia community. This was possible because of the mentorship of Patrick Altmeyer(CounterfactualExplanations) and Moritz Schauer (CausalInference), who guided me throughout the project and are amazing researchers.

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The MINTGenerator

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In this project, we developed the MINTGenerator, a counterfactual generator based on the Recourse through Minimal Intervention (MINT) method proposed by Karimi, Schölkopf, and Valera (2021).

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Description

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The MINTGenerator incorporates causal reeasoning in algorithm recourse to achieve minimal interventions when generating a counterfactual explanation. In this sense, the main ideia is that just perturbating a black box model without taking into account the causal relations in the data can guide to misleading recommendations. Here we now shift to a perspective where every action/pertubation is an intervetion in the causal graph of the problem, thus the change is not made just in the intervened upon variable, but also in its childs in the causal structure. The generator utilizes a Structural Causal Model(SCM) to encode the variables in a way that causal effects are propagated and uses a generic gradient-based generator to create the search path, that is, any gradient-base generator (ECCo, REVISE, Watcher, …) can be used with the MINT SCM encoder to generate counterfactual samples in latent space for minimal intervetions algorithm recourse.

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The MINT algorithm minimizes a loss function that combines the causal constraints of the SCM and the distance between the generated counterfactual and the original input. Since we want a gradient-based generator, we need to pass the constrained optimizaiton problem into an unconstrained one and we do this by using the Lagrangian. Initially, as defined in (Karimi, Schölkopf, and Valera 2021), we aim to aim to find the minimal cost set of actions \(A\) (in the form of structural interventions) that results in a counterfactual instance yielding the favorable output from \(h\),

-\[\begin{aligned} - -A^* \in \arg\min_A \text{cost}(A; \mathbf{x}_F)\\ -\textrm{s.t.} \quad h(\mathbf{x}_{SCF}) \neq h(\mathbf{x}_F) \; \; \text{,}\\ - -\end{aligned}\] -

where \(\mathbf{x}_F\) is the original input, \(\mathbf{x}_{SCF}\) is the counterfactual instance, and \(h\) is the black-box model. We use the \(\mathbf{x}_{SCF}\) terminology because the counterfactual is derived from the SCM,

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\[\begin{equation} - -x_{SCF_i} = -\begin{cases} -x_{F_i} + \delta_i, & \text{if } i \in I \\ -x_{F_i} + f_i(\text{pa}_{SCF_i}) - f_i(\text{pa}_{F_i}), & \text{if } i \notin I \; \; \text{,} -\end{cases} - -\end{equation}\]

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where \(I\) is the set of intervened upon variables, \(f_i\) is the function that generates the value of the variable \(i\) given its parents, and \(\text{pa}_{SCF_i}\) and \(\text{pa}_{F_i}\) are the parents of the variable \(i\) in the counterfactual and original instance, respectively. This closed formula for the decision variable \(\mathbf{x}_{SCF}\) is what makes possible to use a gradient-based generator, since with it the lagrangian is differentiable,

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\[\begin{equation} -\mathcal{L}(A ; \lambda) = \text{cost}(A; \mathbf{x}_F) + \lambda \left(h(\mathbf{x}_{SCF}) - h(\mathbf{x}_F) \right) \; \; \text{,} -\end{equation}\]

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or in simple terms and more standard, since \(\lambda\) is constant,

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\[\begin{equation} -\mathcal{L_{\texttt{MINT}}}(\mathbf{x}_{SCF}) = \lambda \text{cost}(\mathbf{x}_{SCF}; \mathbf{x}_F) + \text{yloss}(\mathbf{x}_{SCF},y^*) \; \; \text{,} -\end{equation}\]

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where \(y^*\) is clearly \(h(x_F)\) and \(\text{yloss}\) is :

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\[\begin{equation} -\text{yloss}(\mathbf{x}_{SCF}, y^*) = h \left(\left\{ x_{F_i} + \delta_i [i \in I] + \left(f_i(\text{pa}_{SCF_i}) - f_i(\text{pa}_{F_i}) \right) [i \notin I] \right\}_{i=1}^n \right) - y^* \; \; \text{.} -\end{equation}\]

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Implementation

-
-

CausalInference.jl

-

In terms of implementation, we need to capture the causal relations from the data, that’s where CausalInference.jl comes in. However, before the project, the package did not have a SCM structure, in the sense that the methods just captured the topological Directed Acyclic Graph (DAG) that showed the causality ruling the data, that is, no causal structural equations were provided,

-
-
using CausalInference
-using Plots, GraphRecipes
-using Random
-Random.seed!(1)
-
-N = 2000 # number of data points
-
-x = randn(N)
-v = x + randn(N)*0.25
-w = x + randn(N)*0.25
-z = v + w + randn(N)*0.25
-s = z + randn(N)*0.25
-
-df = (x=x, v=v, w=w, z=z, s=s)
-
-est_g, score = ges(df; penalty=1.0, parallel=true)
-
-graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)])
-
-

So, our goal was given the DAG provided by the ges method in the causal discovery (Chickering 2003), generate equations that rules each of these causal relations, represented in the DAG as directed edges. The SCM is the union of the DAG and these causal equations, that is, the SCM is a tuple \((G, \mathbf{f})\), where \(G\) is the DAG and \(\mathbf{f}\) is the set of functions that generates the value of each variable given its parents.

-

Our solution for constructing the structural causal equations was to assume that the data was generated by a linear model, ie, the causal relations were linear. For the DAG provided in the code example we derive

-

\[ v = \mathcal{b}_v \]

-

\[ x = \mathcal{a}_{v \to x} v + \mathcal{b}_x \]

-

\[ w = \mathcal{a}_{x \to w} x + \mathcal{b}_w \]

-

\[ z = \mathcal{a}_{v \to z} v+ \mathcal{a}_{w \to z} w + \mathcal{b}_z \]

-

\[ s = \mathcal{a}_{z \to s} z + \mathcal{b}_s \]

-

and that’s the tricky thing, as we can see these causal equations are different than the ones that generated the data, but they are the ones that respect the causal system obtained from the obtained DAG. Here \(\mathcal{b}_i\) and \(\mathcal{a}_{i \to j}\) are the intercept term and the coefficient obtained from the linear regression, respectively. To correctly solve the linear regression respecting the dependencies of the causal graph, we use topological_sort_by_dfs from Graphs.jl.

-

Now, with the SCM structure in hand, we see that the representation could be a struct containing the DAG and the coefficients/intercepts of the causal equations, this maps exactly the tuple \((G, \mathbf{f})\) that we defined. However, since we need these equations to be differentiable, we need to define a function that takes the SCM and returns the value of the variable given its parents and using just the coefficients and the DAG, lead to errors, because AutoDiff does not deal well with functions that are conditioned (if statements). So, we need to define a way to retrieve the system of causal equations in a smooth way and that’s where the causal_effects matrix comes to the rescue.

-

Let the factual vector of features be denoted as:

-

\[ -\mathbf{x}_F = -\begin{bmatrix} -x_{F_1} \\ -x_{F_2} \\ -x_{F_3} \\ -\vdots \\ -x_{F_n} -\end{bmatrix} -\]

-

Let the causal_effects matrix be:

-

\[ -\mathbf{C} = -\begin{bmatrix} -a_{11} & a_{12} & \cdots & a_{1n} & b_1 \\ -a_{21} & a_{22} & \cdots & a_{2n} & b_2 \\ -a_{31} & a_{32} & \cdots & a_{3n} & b_3 \\ -\vdots & \vdots & \ddots & \vdots & \vdots \\ -a_{n1} & a_{n2} & \cdots & a_{nn} & b_n \\ -\end{bmatrix} -\]

-

Here, \(a_{ij}\) represents the coefficient from the causal effect of \(x_{F_j}\) on \(x_{F_i}\), and \(b_i\) represents the intercept term for the variable \(x_{F_i}\).

-

The matrix multiplication of the causal_effects matrix with the factual vector (excluding the bias term) is given by:

-

\[ -\mathbf{C}_{:, 1:n} \cdot \mathbf{x}_F = -\begin{bmatrix} -a_{11} & a_{12} & \cdots & a_{1n} \\ -a_{21} & a_{22} & \cdots & a_{2n} \\ -a_{31} & a_{32} & \cdots & a_{3n} \\ -\vdots & \vdots & \ddots & \vdots \\ -a_{n1} & a_{n2} & \cdots & a_{nn} -\end{bmatrix} -\begin{bmatrix} -x_{F_1} \\ -x_{F_2} \\ -x_{F_3} \\ -\vdots \\ -x_{F_n} -\end{bmatrix} -\]

-

Finally, we add the bias term:

-

\[ -\mathbf{x}_{SCF} = \mathbf{C}_{:, 1:n} \cdot \mathbf{x}_F + -\begin{bmatrix} -b_1 \\ -b_2 \\ -b_3 \\ -\vdots \\ -b_n -\end{bmatrix} -\]

-

In expanded form:

-

\[ -\mathbf{x}_{SCF_i} = a_{i1} x_{F_1} + a_{i2} x_{F_2} + \cdots + a_{in} x_{F_n} + b_i, \quad \forall i = 1, 2, \dots, n -\]

-

This equation shows how each counterfactual variable \(x_{SCF_i}\) is generated as a linear combination of the factual inputs \(x_{F_j}\) based on the causal effects matrix, with an intercept term \(b_i\) added for each variable.

-

One can note that the orphan nodes, that is, the nodes that do not have parents in the DAG, are going to be equal to the intercept term \(\mathcal{b}_\hat{o}\). The intuition behind this is that when we do the linear regression, variables that have no causal parents are just equal to the unconditional mean of the variable, i.e, we get \(x_{SCF_\hat{o}} = \mathbb{E}(x_\hat{o})\). Because of this, in some cases a better understanding of the regression is needed, so the residuals are also part of the SCM structure,

-
-
struct SCM
-    variables::Vector{String}
-    coefficients::Vector{Vector{Float64}}
-    residuals::Vector{Vector{Float64}}
-    dag::DiGraph
-    causal_effects::Matrix{Float64}
-end
-
-
-
-

CounterfactualExplanations.jl

-

Now, we need to go into the optimization problem previously described. We seek to minimize the lagrangian function we defined where now we have a differentiable function. The standard way to implement generators in CounterfactualExplanations.jl is to use AutoDiff exactly using composable functions in the lagrangian. The definition of \(\mathcal{L_{\texttt{MINT}}}\) is in the same shape of the the others gradient-based generators in the package, so the optimization is straightforward. However, we needed some way to pass the \(x_F\) into the \(x_{SCF}\) and that’s where transformer.jl comes in. This is where InputTransformers are defined in the package and in some way this is what we are doing, we are passing our factual to the “latent” causal space of the counterfactual. Our first step is to create a new kind of InputTransformer that is the SCM itself,

-
-
const TypedInputTransformer = Union{
-    Type{<:StatsBase.AbstractDataTransform},
-    Type{<:MultivariateStats.AbstractDimensionalityReduction},
-    Type{<:GenerativeModels.AbstractGenerativeModel},
-    Type{<:CausalInference.SCM} # The SCM transfromer
-}
-
-

and then we need a way to create this transformer, that’s where we “overload” fit_transformer using CausalInferece.jl,

-
-
function fit_transformer(
-    data::CounterfactualData, input_encoder::Type{<:CausalInference.SCM}; kwargs...
-)
-    t = Tables.table(transpose(data.X))
-    est_g, score = CausalInference.ges(t; penalty=1.0, parallel=true)
-    est_dag = CausalInference.pdag2dag!(est_g)
-    scm = CausalInference.estimate_equations(t, est_dag)
-    return scm
-end
-
-

.

-
-
-
-
-

Conclusion

- -
-
- - -
- -

References

-
-Chickering, David Maxwell. 2003. “Optimal Structure Identification with Greedy Search.” J. Mach. Learn. Res. 3 (null): 507–54. https://doi.org/10.1162/153244303321897717. -
-
-Karimi, Amir-Hossein, Bernhard Schölkopf, and Isabel Valera. 2021. “Algorithmic Recourse: From Counterfactual Explanations to Interventions.” In Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency, 353–62. FAccT ’21. New York, NY, USA: Association for Computing Machinery. https://doi.org/10.1145/3442188.3445899. -
-
- - -
- - - - - \ No newline at end of file diff --git a/profile/blog/posts/causal-recourse/index.qmd b/profile/blog/posts/causal-recourse/index.qmd index 35fe405..7bb0ccd 100644 --- a/profile/blog/posts/causal-recourse/index.qmd +++ b/profile/blog/posts/causal-recourse/index.qmd @@ -53,10 +53,8 @@ The MINT algorithm minimizes a loss function that combines the causal constraint $$ \begin{aligned} - A^* \in \arg\min_A \text{cost}(A; \mathbf{x}_F)\\ \textrm{s.t.} \quad h(\mathbf{x}_{SCF}) \neq h(\mathbf{x}_F) \; \; \text{,}\\ - \end{aligned} $$ @@ -98,9 +96,15 @@ In terms of implementation, we need to capture the causal relations from the dat #| output: true using CausalInference -using Plots, GraphRecipes +using CounterfactualExplanations +using CounterfactualExplanations.GenerativeModels +using Graphs +using GraphRecipes +using MultivariateStats +using Plots using Random Random.seed!(1) +using StatsBase N = 2000 # number of data points @@ -114,7 +118,7 @@ df = (x=x, v=v, w=w, z=z, s=s) est_g, score = ges(df; penalty=1.0, parallel=true) -plt = graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)], size=(500,500), nodesize=0.1, fontsize=2) +plt = graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)], size=(500,500), nodesize=0.1, fontsize=25) savefig(plt, "www/intro.png") display(plt) ``` diff --git a/profile/blog/posts/causal-recourse/www/intro.png b/profile/blog/posts/causal-recourse/www/intro.png index 226a52830d533edd1e3d0ac2b7acdf36cf244d1c..2dee71fe8a3ce80133fbedc74cd63c295dd425a8 100644 GIT binary patch literal 19542 zcmdSBg4yyBn8PsBS=UI(g@Ni-CYXO-5t_Mcf*}L z@ArQ9{tNd!zo$I=tiAS%ImZ}ttnH^DCyt3ugpNQUFeN2K-XIV+X5sIdJ2&A^&|+e% z;9s}jNsEghuCD(|tj!2RASe)$B0`D|u^Uqcs)`e2x3>l2Jl|1LCQ?48q)5I=z>qlV z=Xfyc?>Fi_r6tbi)LqE;&OQJgol-a04ue60>bZ@8d*Dr0=fm+|XU>~GIEOh0{6`JW z51kLErG+R%?jsO)zEQ5hje`a7*%0o6Nr^WQx6n~B5fln^#t6jcS3)R=JNW2C2*E^! zUIgN%x5sV7eY*cYU)r97B4}cDcDRA@ka?RmDlF{nd~@JQG=|_Od}`dgYxfj()6&z4 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z1aZVTY%TP(@jRmzQyu(pOH^7KGS#f|;s~Q&fN=2Al`HQtls2^;C>^Lzs6@80eVWL$ zFfvF8Zoy2#Ig={?pN+^w9GzPji-r+ni6uq`FGMFt7uq@1Mh9Pna{xS` zxRj)Ka3|{!!jxeKhW`DLj3nhDh4EW%p` z?qPGzg4kmx>f-e{V+p8q)xxU(WE zJ~?@Mdb)*9r`=g^g0=B+1l2xzv>yr!0{O>}A6k?A!<^RQ>+-q(j5e%nTFO~no6EIR z7*k8dNwe|aCEZEM$@Y8p6onqJv5`|!nyz^4&_5HtlkgKm5ECS)_dUD;9njz2xm=U0=^-20_RhYXo6 zJCLa4lR*=mv);RMnyaSS?G%nuruVvz1SySPW^oqP|GuHArFE-aU|k7QWL+NbA6p}a zPsa+yr}f7=Ovmk%+6$@_#=? jDE|M4|JMOo5;6~r=sW#kas>a)0Aa^gYqN)24u=0f<=|l9 From 0d31976b21b458d22a99a9e8201fc1102948a729 Mon Sep 17 00:00:00 2001 From: JorgeLuizFranco Date: Thu, 19 Sep 2024 09:19:52 -0300 Subject: [PATCH 10/13] finalized Conclusion --- .../blog/posts/causal-recourse/Manifest.toml | 2 +- .../blog/posts/causal-recourse/Project.toml | 1 + profile/blog/posts/causal-recourse/index.html | 946 ++++++++++++++++++ profile/blog/posts/causal-recourse/index.qmd | 107 +- 4 files changed, 1052 insertions(+), 4 deletions(-) create mode 100644 profile/blog/posts/causal-recourse/index.html diff --git a/profile/blog/posts/causal-recourse/Manifest.toml b/profile/blog/posts/causal-recourse/Manifest.toml index 3c3a243..e62dbb0 100644 --- a/profile/blog/posts/causal-recourse/Manifest.toml +++ b/profile/blog/posts/causal-recourse/Manifest.toml @@ -2,7 +2,7 @@ julia_version = "1.10.5" manifest_format = "2.0" -project_hash = "41bd819777c272263800d4520c39fc5fadc9a79b" +project_hash = "424afa5cc696387221e452ef51b1267b3f24adc9" [[deps.AbstractFFTs]] deps = ["LinearAlgebra"] diff --git a/profile/blog/posts/causal-recourse/Project.toml b/profile/blog/posts/causal-recourse/Project.toml index 32df96d..cfe120d 100644 --- a/profile/blog/posts/causal-recourse/Project.toml +++ b/profile/blog/posts/causal-recourse/Project.toml @@ -7,3 +7,4 @@ MultivariateStats = "6f286f6a-111f-5878-ab1e-185364afe411" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91" +Tables = "bd369af6-aec1-5ad0-b16a-f7cc5008161c" diff --git a/profile/blog/posts/causal-recourse/index.html b/profile/blog/posts/causal-recourse/index.html new file mode 100644 index 0000000..f57dc49 --- /dev/null +++ b/profile/blog/posts/causal-recourse/index.html @@ -0,0 +1,946 @@ + + + + + + + + + + + + +When Causality meets Recourse + + + + + + + + + + + + + + + + + + + + + + + + + + +
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When Causality meets Recourse

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Counterfactual Explanations through Structural Causal Models

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counterfactuals
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explainable AI
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causality
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Julia
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This post introduces a new tool in CounterfactualExplanations.jl, enhancing the package with causal reasoning to generate counterfactual explanations.

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Author
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Jorge Luiz Franco

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Published
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September 17, 2024

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Introduction

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In recent years, the need for interpretable and explainable AI has surged, particularly in high-stakes domains. Counterfactual explanations provide a means to understand how changes to input features could alter the outcomes of machine learning models. This blog post presents a new tool in the CounterfactualExplanations.jl package, developed during my JSoC (Julia Summer of Code) project, which incorporates causal reasoning into counterfactual generation.

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Project Overview

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This project aimed to enhance the CounterfactualExplanations.jl package by infusing it with a robust mathematical foundation for minimal algorithmic recourse, based on the principles of causal reasoning [@karimi2021algorithmic].

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Key Contributions

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During the project, I contributed to two key repositories:

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  1. CounterfactualExplanations.jl: Developed a new tool for generating counterfactual explanations using causal information. This allows users to create smarter perturbations rather than random adjustments, ultimately providing more meaningful insights.

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  2. CausalInference.jl: Implemented a Structural Causal Model (SCM) structure that extracts information from data, laying the groundwork for the causal reasoning capabilities in CounterfactualExplanations.jl.

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This was an amazing experience, not just experience contribute to two repositories simultaneously, but also to work with the mantainers of these repos. I learned a lot about the Julia language and the Julia community. This was possible because of the mentorship of Patrick Altmeyer (CounterfactualExplanations) and Moritz Schauer (CausalInference), who guided me throughout the project and are amazing researchers.

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The MINTGenerator

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In this project, we developed the MINTGenerator, a counterfactual generator based on the Recourse through Minimal Intervention (MINT) method proposed by @karimi2021algorithmic.

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Description

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The MINTGenerator incorporates causal reasoning in algorithm recourse to achieve minimal interventions when generating a counterfactual explanation. In this sense, the main ideia is that just perturbating a black box model without taking into account the causal relations in the data can guide to misleading recommendations. Here we now shift to a perspective where every action/pertubation is an intervetion in the causal graph of the problem, thus the change is not made just in the intervened upon variable, but also in its childs in the causal structure. The generator utilizes a Structural Causal Model(SCM) to encode the variables in a way that causal effects are propagated and uses a generic gradient-based generator to create the search path, that is, any gradient-base generator (ECCo [@altmeyer2024faithful], REVISE, Watcher, …) can be used with the MINT SCM encoder to generate counterfactual samples in latent space for minimal intervetions algorithm recourse.

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The MINT algorithm minimizes a loss function that combines the causal constraints of the SCM and the distance between the generated counterfactual and the original input. Since we want a gradient-based generator, we need to pass the constrained optimizaiton problem into an unconstrained one and we do this by using the Lagrangian. Initially, as defined in [@karimi2021algorithmic], we aim to aim to find the minimal cost set of actions \(A\) (in the form of structural interventions) that results in a counterfactual instance yielding the favorable output from \(h\),

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\[ +\begin{aligned} +A^* \in \arg\min_A \text{cost}(A; \mathbf{x}_F)\\ +\textrm{s.t.} \quad h(\mathbf{x}_{SCF}) \neq h(\mathbf{x}_F) \; \; \text{,}\\ +\end{aligned} +\]

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where \(\mathbf{x}_F\) is the original input, \(\mathbf{x}_{SCF}\) is the counterfactual instance, and \(h\) is the black-box model. We use the \(\mathbf{x}_{SCF}\) terminology because the counterfactual is derived from the SCM,

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\[ +x_{SCF_i} = +\begin{cases} +x_{F_i} + \delta_i, & \text{if } i \in I \\ +x_{F_i} + f_i(\text{pa}_{SCF_i}) - f_i(\text{pa}_{F_i}), & \text{if } i \notin I \; \; \text{,} +\end{cases} +\]

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where \(I\) is the set of intervened upon variables, \(f_i\) is the function that generates the value of the variable \(i\) given its parents, and \(\text{pa}_{SCF_i}\) and \(\text{pa}_{F_i}\) are the parents of the variable \(i\) in the counterfactual and original instance, respectively. This closed formula for the decision variable \(\mathbf{x}_{SCF}\) is what makes possible to use a gradient-based generator, since with it the lagrangian is differentiable,

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\[ +\mathcal{L}(A ; \lambda) = \text{cost}(A; \mathbf{x}_F) + \lambda \left(h(\mathbf{x}_{SCF}) - h(\mathbf{x}_F) \right) \; \; \text{,} +\]

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or in simple terms and more standard, since \(\lambda\) is constant,

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\[ +\mathcal{L_{\texttt{MINT}}}(\mathbf{x}_{SCF}) = \lambda \text{cost}(\mathbf{x}_{SCF}; \mathbf{x}_F) + \text{yloss}(\mathbf{x}_{SCF},y^*) \; \; \text{,} +\]

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where \(y^*\) is clearly \(h(x_F)\) and \(\text{yloss}\) is :

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\[ +\text{yloss}(\mathbf{x}_{SCF}, y^*) = h \left(\left\{ x_{F_i} + \delta_i [i \in I] + \left(f_i(\text{pa}_{SCF_i}) - f_i(\text{pa}_{F_i}) \right) [i \notin I] \right\}_{i=1}^n \right) - y^* \; \; \text{.} +\]

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Implementation

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CausalInference.jl

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In terms of implementation, we need to capture the causal relations from the data, that’s where CausalInference.jl comes in. However, before the project, the package did not have a SCM structure, in the sense that the methods just captured the topological Directed Acyclic Graph (DAG) that showed the causality ruling the data, that is, no causal structural equations were provided,

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+Code +
using CausalInference
+using CounterfactualExplanations
+using CounterfactualExplanations.GenerativeModels
+using Graphs
+using GraphRecipes
+using MultivariateStats
+using Plots
+using Random
+Random.seed!(1)
+using StatsBase
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+N = 2000 # number of data points
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+x = randn(N)
+v = x + randn(N)*0.25
+w = x + randn(N)*0.25
+z = v + w + randn(N)*0.25
+s = z + randn(N)*0.25
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+df = (x=x, v=v, w=w, z=z, s=s)
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+est_g, score = ges(df; penalty=1.0, parallel=true)
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+plt = graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)], size=(500,500), nodesize=0.1, fontsize=25)
+savefig(plt, "www/intro.png")
+display(plt)
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┌ Warning: Only one thread available
+└ @ CausalInference ~/.julia/packages/CausalInference/ozcj8/src/ges.jl:52
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So, our goal was given the DAG provided by the ges method in the causal discovery [@chickering2003optimal], generate equations that rules each of these causal relations, represented in the DAG as directed edges. The SCM is the union of the DAG and these causal equations, that is, the SCM is a tuple \((G, \mathbf{f})\), where \(G\) is the DAG and \(\mathbf{f}\) is the set of functions that generates the value of each variable given its parents.

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Our solution for constructing the structural causal equations was to assume that the data was generated by a linear model, ie, the causal relations were linear. For the DAG provided in the code example we derive

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\[ v = \mathcal{b}_v \]

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\[ x = \mathcal{a}_{v \to x} v + \mathcal{b}_x \]

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\[ w = \mathcal{a}_{x \to w} x + \mathcal{b}_w \]

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\[ z = \mathcal{a}_{v \to z} v+ \mathcal{a}_{w \to z} w + \mathcal{b}_z \]

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\[ s = \mathcal{a}_{z \to s} z + \mathcal{b}_s \]

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and that’s the tricky thing, as we can see these causal equations are different than the ones that generated the data, but they are the ones that respect the causal system obtained from the obtained DAG. Here \(\mathcal{b}_i\) and \(\mathcal{a}_{i \to j}\) are the intercept term and the coefficient obtained from the linear regression, respectively. To correctly solve the linear regression respecting the dependencies of the causal graph, we use topological_sort_by_dfs from Graphs.jl.

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Now, with the SCM structure in hand, we see that the representation could be a struct containing the DAG and the coefficients/intercepts of the causal equations, this maps exactly the tuple \((G, \mathbf{f})\) that we defined. However, since we need these equations to be differentiable, we need to define a function that takes the SCM and returns the value of the variable given its parents and using just the coefficients and the DAG, lead to errors, because AutoDiff does not deal well with functions that are conditioned (if statements). So, we need to define a way to retrieve the system of causal equations in a smooth way and that’s where the causal_effects matrix comes to the rescue.

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Let the factual vector of features be denoted as:

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\[ +\mathbf{x}_F = +\begin{bmatrix} +x_{F_1} \\ +x_{F_2} \\ +x_{F_3} \\ +\vdots \\ +x_{F_n} +\end{bmatrix} +\]

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Let the causal_effects matrix be:

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\[ +\mathbf{C} = +\begin{bmatrix} +a_{11} & a_{12} & \cdots & a_{1n} & b_1 \\ +a_{21} & a_{22} & \cdots & a_{2n} & b_2 \\ +a_{31} & a_{32} & \cdots & a_{3n} & b_3 \\ +\vdots & \vdots & \ddots & \vdots & \vdots \\ +a_{n1} & a_{n2} & \cdots & a_{nn} & b_n \\ +\end{bmatrix} +\]

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Here, \(a_{ij}\) represents the coefficient from the causal effect of \(x_{F_j}\) on \(x_{F_i}\), and \(b_i\) represents the intercept term for the variable \(x_{F_i}\).

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The matrix multiplication of the causal_effects matrix with the factual vector (excluding the bias term) is given by:

+

\[ +\mathbf{C}_{:, 1:n} \cdot \mathbf{x}_F = +\begin{bmatrix} +a_{11} & a_{12} & \cdots & a_{1n} \\ +a_{21} & a_{22} & \cdots & a_{2n} \\ +a_{31} & a_{32} & \cdots & a_{3n} \\ +\vdots & \vdots & \ddots & \vdots \\ +a_{n1} & a_{n2} & \cdots & a_{nn} +\end{bmatrix} +\begin{bmatrix} +x_{F_1} \\ +x_{F_2} \\ +x_{F_3} \\ +\vdots \\ +x_{F_n} +\end{bmatrix} +\]

+

Finally, we add the bias term:

+

\[ +\mathbf{x}_{SCF} = \mathbf{C}_{:, 1:n} \cdot \mathbf{x}_F + +\begin{bmatrix} +b_1 \\ +b_2 \\ +b_3 \\ +\vdots \\ +b_n +\end{bmatrix} +\]

+

In expanded form:

+

\[ +\mathbf{x}_{SCF_i} = a_{i1} x_{F_1} + a_{i2} x_{F_2} + \cdots + a_{in} x_{F_n} + b_i, \quad \forall i = 1, 2, \dots, n +\]

+

This equation shows how each counterfactual variable \(x_{SCF_i}\) is generated as a linear combination of the factual inputs \(x_{F_j}\) based on the causal effects matrix, with an intercept term \(b_i\) added for each variable.

+

One can note that the orphan nodes, that is, the nodes that do not have parents in the DAG, are going to be equal to the intercept term \(\mathcal{b}_\hat{o}\). The intuition behind this is that when we do the linear regression, variables that have no causal parents are just equal to the unconditional mean of the variable, i.e, we get \(x_{SCF_\hat{o}} = \mathbb{E}(x_\hat{o})\). Because of this, in some cases a better understanding of the regression is needed, so the residuals are also part of the SCM structure,

+
+
+Code +
struct SCM
+    variables::Vector{String}
+    coefficients::Vector{Vector{Float64}}
+    residuals::Vector{Vector{Float64}}
+    dag::DiGraph
+    causal_effects::Matrix{Float64}
+end
+
+
+
+
+

CounterfactualExplanations.jl

+

Now, we need to go into the optimization problem previously described. We seek to minimize the lagrangian function we defined where now we have a differentiable function. The standard way to implement generators in CounterfactualExplanations.jl is to use AutoDiff exactly using composable functions in the lagrangian. The definition of \(\mathcal{L_{\texttt{MINT}}}\) is in the same shape of the the others gradient-based generators in the package, so the optimization is straightforward. However, we needed some way to pass the \(x_F\) into the \(x_{SCF}\) and that’s where transformer.jl comes in. This is where InputTransformers are defined in the package and in some way this is what we are doing, we are passing our factual to the “latent” causal space of the counterfactual. Our first step is to create a new kind of InputTransformer that is the SCM itself,

+
+
+Code +
const TypedInputTransformer = Union{
+    Type{<:StatsBase.AbstractDataTransform},
+    Type{<:MultivariateStats.AbstractDimensionalityReduction},
+    Type{<:GenerativeModels.AbstractGenerativeModel},
+    Type{<:CausalInference.SCM} # The SCM transfromer
+}
+
+
+
Union{Type{<:AbstractDataTransform}, Type{<:MultivariateStats.AbstractDimensionalityReduction}, Type{<:CounterfactualExplanations.GenerativeModels.AbstractGenerativeModel}, Type{<:CausalInference.SCM}}
+
+
+

and then we need a way to create this transformer, that’s where we “overload” fit_transformer using CausalInferece.jl,

+
+
+Code +
function fit_transformer(
+    data::CounterfactualData, input_encoder::Type{<:CausalInference.SCM}; kwargs...
+)
+    t = Tables.table(transpose(data.X))
+    est_g, score = CausalInference.ges(t; penalty=1.0, parallel=true)
+    est_dag = CausalInference.pdag2dag!(est_g)
+    scm = CausalInference.estimate_equations(t, est_dag)
+    return scm
+end
+
+
+
fit_transformer (generic function with 1 method)
+
+
+

… We are getting there! However, now comes the hardest part, where this is placed in the package? Our idea were to place in encondings.jl where we “overloaded” the decode_array function to be composed with the causal effects operation,

+
+
+Code +
function decode_array(data::CounterfactualData, dt::CausalInference.SCM, x::AbstractArray)
+    return run_causal_effects(dt, x)
+end
+
+function run_causal_effects(scm::CausalInference.SCM, x::AbstractArray)
+
+    return scm.causal_effects[:, 1:(end - 1)] * x + scm.causal_effects[:, end] # bias
+
+end
+
+
+

Here we are! We have a way to pass the causal effects through the AutoDiff steps in the package. That way we didn’t change the workflow of gradient-based generator, but still could achieve the new minimization problem, where now the causal effects equations are part of the differentiable lagrangian automatically computed.

+
+
+
+

Limitations and Future Work

+

Altough the range of lines of code was not tremendous, the hard work was. The merged code does not show every research and development I was guided during this time by the mentors. For example, initially we were trying a different approach to work with differentiation inside the CounterfactualExplanations.jl package, where the code always broke 😅. But, without this obstacle, we couldn’t have in mind a possible future work where the run_causal_effects function could be more flexible. For example, as we said, the variables without causal parents are been assigned just to the unconditional mean, but in terms of counterfactuals theory, maybe using just the factual feature would be more realistic. But to do this we would need to work in the causal_effects_matrix and this was part of my work creating transformable_features for the SCM where we would probably need to use ignore_derivatives() from Zygote.jl.

+
+
+Code +
function transformable_features(
+    counterfactual_data::CounterfactualData, input_encoder::Type{CausalInference.SCM}
+)
+    g = counterfactual_data.input_encoder.dag
+    child_causal_nodes = [v for v in vertices(g) if indegree(g, v) >= 1]
+    return child_causal_nodes
+end
+
+
+

Another direction of future work is that the current implementation of the MINTGenerator is limited to linear causal relations. One could extend this to non-linear causal relations, such as those found in neural networks. Additionally, the we could shift the paradigm to use Bayesian Inference to generate the causal equations. This work would be a new extension in CausalInference.jl.

+
+
+

Github PRs and Issues

+

In the following links, you can find the PRs and issues that were opened and closed during the project. They show some kind of history of the work developed:

+

Causal Inference:

+ +

CounterfactualExplanations:

+ +

And one that still open:

+ +
+
+
+

Usage

+

The MINT algorithm can be implemented using the GenericGenerator and the SCM encoder, that we implement using CausalInference.jl package. The following code snippet shows how to use the MINT algorithm to generate counterfactuals using any gradient-based generator:

+
+
+Code +
using CausalInference
+using CounterfactualExplanations
+using CounterfactualExplanations.DataPreprocessing: fit_transformer
+using Tables
+
+N = 2000
+df = (
+    x = randn(N), 
+    v = randn(N) .^ 2 + randn(N) * 0.25, 
+    w = cos.(randn(N)) + randn(N) * 0.25, 
+    z = randn(N) .^ 2 + cos.(randn(N)) + randn(N) * 0.25 + randn(N) * 0.25, 
+    s = sin.(randn(N) .^ 2 + cos.(randn(N)) + randn(N) * 0.25 + randn(N) * 0.25) + randn(N) * 0.25
+)
+y_lab = rand(0:2, N)
+counterfactual_data_scm = CounterfactualData(Tables.matrix(df; transpose=true), y_lab)
+
+M = fit_model(counterfactual_data_scm, :Linear)
+chosen = rand(findall(predict_label(M, counterfactual_data_scm) .== 1))
+x = select_factual(counterfactual_data_scm, chosen)
+
+data_scm = deepcopy(counterfactual_data_scm)
+data_scm.input_encoder = fit_transformer(data_scm, CausalInference.SCM)
+
+ce = generate_counterfactual(x, 2, data_scm, M, GenericGenerator(); initialization=:identity)
+
+
+

For further usage reference access the MINT official documentation.

+
+
+

Conclusion

+

During this project, I had the opportunity to contribute to both the XAI and Julia communities, where I developed a SOTA method that used causal information to generate counterfactuals explanations [@karimi2021algorithmic]. It was an amazing experience to work with incredible mentors and the community. I would like to once again thank Patrick and Moritz for all their guidance, as well as Jacob Zelko and JuliaHUB for all their support. I learned a lot about the Julia language and the Julia community, and I witnessed firsthand the benefits of Open Source. In fact, it was Open Source that made it possible to contribute to two repositories simultaneously. This experience of working locally on CounterfactualExplanations.jl and CausalInference.jl was invaluable, as it allowed me to truly understand how things work under the hood.

+

I hope that the MINTGenerator can be useful to the community and that the package continues to be improved in the future. Contributing to a more trustworthy Artificial Intelligence has always been a goal of mine, and even though my contribution may be small, I feel proud to have achieved something meaningful. My wish is to continue contributing to the responsible use of AI. I am very grateful for this opportunity, and I look forward to continuing to contribute to the community. 🚀🚀🚀

+
+
+

References

+
+ +
+ + +
+ + + + + \ No newline at end of file diff --git a/profile/blog/posts/causal-recourse/index.qmd b/profile/blog/posts/causal-recourse/index.qmd index 7bb0ccd..1c005c2 100644 --- a/profile/blog/posts/causal-recourse/index.qmd +++ b/profile/blog/posts/causal-recourse/index.qmd @@ -47,7 +47,7 @@ Intervention (MINT) method proposed by @karimi2021algorithmic. ## Description -The MINTGenerator incorporates causal reeasoning in algorithm recourse to achieve minimal interventions when generating a counterfactual explanation. In this sense, the main ideia is that just perturbating a black box model without taking into account the causal relations in the data can guide to misleading recommendations. Here we now shift to a perspective where every action/pertubation is an intervetion in the causal graph of the problem, thus the change is not made just in the intervened upon variable, but also in its childs in the causal structure. The generator utilizes a Structural Causal Model(SCM) to encode the variables in a way that causal effects are propagated and uses a generic gradient-based generator to create the search path, that is, any gradient-base generator (ECCo, REVISE, Watcher, ...) can be used with the MINT SCM encoder to generate counterfactual samples in latent space for minimal intervetions algorithm recourse. +The MINTGenerator incorporates causal reasoning in algorithm recourse to achieve minimal interventions when generating a counterfactual explanation. In this sense, the main ideia is that just perturbating a black box model without taking into account the causal relations in the data can guide to misleading recommendations. Here we now shift to a perspective where every action/pertubation is an intervetion in the causal graph of the problem, thus the change is not made just in the intervened upon variable, but also in its childs in the causal structure. The generator utilizes a Structural Causal Model(SCM) to encode the variables in a way that causal effects are propagated and uses a generic gradient-based generator to create the search path, that is, any gradient-base generator (ECCo [@altmeyer2024faithful], REVISE, Watcher, ...) can be used with the MINT SCM encoder to generate counterfactual samples in latent space for minimal intervetions algorithm recourse. The MINT algorithm minimizes a loss function that combines the causal constraints of the SCM and the distance between the generated counterfactual and the original input. Since we want a gradient-based generator, we need to pass the constrained optimizaiton problem into an unconstrained one and we do this by using the Lagrangian. Initially, as defined in [@karimi2021algorithmic], we aim to aim to find the minimal cost set of actions $A$ (in the form of structural interventions) that results in a counterfactual instance yielding the favorable output from $h$, @@ -250,14 +250,115 @@ function fit_transformer( return scm end ``` -... We are getting there! However, now comes the hardest part, where this is placed? +... We are getting there! However, now comes the hardest part, where this is placed in the package? Our idea were to place in `encondings.jl` where we "overloaded" the `decode_array` function to be composed with the causal effects operation, +```{julia} +#| output: false + +function decode_array(data::CounterfactualData, dt::CausalInference.SCM, x::AbstractArray) + return run_causal_effects(dt, x) +end + +function run_causal_effects(scm::CausalInference.SCM, x::AbstractArray) + + return scm.causal_effects[:, 1:(end - 1)] * x + scm.causal_effects[:, end] # bias + +end +``` + +Here we are! We have a way to pass the causal effects through the `AutoDiff` steps in the package. That way we didn't change the workflow of gradient-based generator, but still could achieve the new minimization problem, where now the causal effects equations are part of the differentiable lagrangian automatically computed. + + +## Limitations and Future Work + +Altough the range of lines of code was not tremendous, the hard work was. The merged code does not show every research and development I was guided during this time by the mentors. For example, initially we were trying a different approach to work with differentiation inside the `CounterfactualExplanations.jl` package, where the code always broke 😅. But, without this obstacle, we couldn't have in mind a possible future work where the `run_causal_effects` function could be more flexible. For example, as we said, the variables without causal parents are been assigned just to the unconditional mean, but in terms of counterfactuals theory, maybe using just the factual feature would be more realistic. But to do this we would need to work in the `causal_effects_matrix` and this was part of my work creating `transformable_features` for the SCM where we would probably need to use `ignore_derivatives()` from `Zygote.jl`. +```{julia} +#| output: false +function transformable_features( + counterfactual_data::CounterfactualData, input_encoder::Type{CausalInference.SCM} +) + g = counterfactual_data.input_encoder.dag + child_causal_nodes = [v for v in vertices(g) if indegree(g, v) >= 1] + return child_causal_nodes +end +``` + + + Another direction of future work is that the current implementation of the MINTGenerator is limited to linear causal relations. One could extend this to non-linear causal relations, such as those found in neural networks. Additionally, the we could shift the paradigm to use Bayesian Inference to generate the causal equations. This work would be a new extension in `CausalInference.jl`. + + + +## Github PRs and Issues + +In the following links, you can find the PRs and issues that were opened and closed during the project. They show some kind of history of the work developed: + +*Causal Inference*: + +- [PR1 - SCM](https://github.com/mschauer/CausalInference.jl/pull/155) +- [PR2 - causal effects matrix](https://github.com/mschauer/CausalInference.jl/pull/157) +- [PR3 - version Julia register](https://github.com/mschauer/CausalInference.jl/pull/158) +- [Issue1 - Retrieve equations CausalGraph](https://github.com/mschauer/CausalInference.jl/issues/154) +*CounterfactualExplanations*: + +- [PR1 - encondings.jl](https://github.com/JuliaTrustworthyAI/CounterfactualExplanations.jl/pull/461) +- [PR2 - Constrained Optimization](https://github.com/JuliaTrustworthyAI/CounterfactualExplanations.jl/pull/464) +- [PR3 - add MINT docs](https://github.com/JuliaTrustworthyAI/CounterfactualExplanations.jl/pull/468) +- [Issue1 - support for SCM](https://github.com/JuliaTrustworthyAI/CounterfactualExplanations.jl/issues/456) +- [Issue2 - Constrained Optimization](https://github.com/JuliaTrustworthyAI/CounterfactualExplanations.jl/issues/457) +- [Issue3 - Document MINT](https://github.com/JuliaTrustworthyAI/CounterfactualExplanations.jl/issues/467) + +And one that still open: + +- [Issue4 - MINTGenerator Interface](https://github.com/JuliaTrustworthyAI/CounterfactualExplanations.jl/issues/466) + + + +# Usage + +The MINT algorithm can be implemented using the `GenericGenerator` and the SCM encoder, that we implement using `CausalInference.jl` package. The following code snippet shows how to use the MINT algorithm to generate counterfactuals using any gradient-based generator: + +```{julia} +#| eval: false +#| output: true + +using CausalInference +using CounterfactualExplanations +using CounterfactualExplanations.DataPreprocessing: fit_transformer +using Tables + +N = 2000 +df = ( + x = randn(N), + v = randn(N) .^ 2 + randn(N) * 0.25, + w = cos.(randn(N)) + randn(N) * 0.25, + z = randn(N) .^ 2 + cos.(randn(N)) + randn(N) * 0.25 + randn(N) * 0.25, + s = sin.(randn(N) .^ 2 + cos.(randn(N)) + randn(N) * 0.25 + randn(N) * 0.25) + randn(N) * 0.25 +) +y_lab = rand(0:2, N) +counterfactual_data_scm = CounterfactualData(Tables.matrix(df; transpose=true), y_lab) + +M = fit_model(counterfactual_data_scm, :Linear) +chosen = rand(findall(predict_label(M, counterfactual_data_scm) .== 1)) +x = select_factual(counterfactual_data_scm, chosen) + +data_scm = deepcopy(counterfactual_data_scm) +data_scm.input_encoder = fit_transformer(data_scm, CausalInference.SCM) + +ce = generate_counterfactual(x, 2, data_scm, M, GenericGenerator(); initialization=:identity) +``` + + +For further usage reference access the [MINT official documentation](https://juliatrustworthyai.github.io/CounterfactualExplanations.jl/dev/explanation/generators/mint/). # Conclusion - +During this project, I had the opportunity to contribute to both the XAI and Julia communities, where I developed a SOTA method that used causal information to generate counterfactuals explanations [@karimi2021algorithmic]. It was an amazing experience to work with incredible mentors and the community. I would like to once again thank Patrick and Moritz for all their guidance, as well as Jacob Zelko and JuliaHUB for all their support. I learned a lot about the Julia language and the Julia community, and I witnessed firsthand the benefits of Open Source. In fact, it was Open Source that made it possible to contribute to two repositories simultaneously. This experience of working locally on `CounterfactualExplanations.jl` and `CausalInference.jl` was invaluable, as it allowed me to truly understand how things work under the hood. + +I hope that the MINTGenerator can be useful to the community and that the package continues to be improved in the future. Contributing to a more trustworthy Artificial Intelligence has always been a goal of mine, and even though my contribution may be small, I feel proud to have achieved something meaningful. My wish is to continue contributing to the responsible use of AI. I am very grateful for this opportunity, and I look forward to continuing to contribute to the community. 🚀🚀🚀 + + # References From bf7f14fb6a5842930007524ac5c5a18f321f8599 Mon Sep 17 00:00:00 2001 From: pat-alt Date: Fri, 20 Sep 2024 17:37:19 +0200 Subject: [PATCH 11/13] minor edits --- docs/blog/index.html | 39 +- docs/blog/index.xml | 14228 ++++++++-------- .../a-new-tool-for-explainable-ai/index.html | 744 +- docs/blog/posts/causal-recourse/index.html | 997 +- docs/blog/posts/causal-recourse/www/intro.png | Bin 19542 -> 19351 bytes .../conformal-image-classifier/index.html | 2447 +-- .../conformal-image-classifier/www/intro.gif | Bin 156116 -> 165244 bytes .../conformal-image-classifier/www/medium.gif | Bin 469884 -> 492183 bytes docs/blog/posts/conformal-llm/index.html | 450 +- .../posts/conformal-prediction/index.html | 698 +- .../posts/conformal-regression/index.html | 6596 +++---- .../posts/effortsless-bayesian-dl/index.html | 410 +- .../posts/guest-students-laplace/index.html | 18 +- .../new-package-energysamplers/index.html | 5247 +++--- docs/search.json | 43 +- docs/site_libs/bootstrap/bootstrap.min.css | 6 +- .../quarto-syntax-highlighting.css | 2 +- docs/sitemap.xml | 16 +- .../index/execute-results/html.json | 4 +- .../index/execute-results/html.json | 4 +- .../index/execute-results/html.json | 6 +- .../index/execute-results/html.json | 4 +- .../index/execute-results/html.json | 4 +- .../index/execute-results/html.json | 4 +- .../index/execute-results/html.json | 4 +- .../index/execute-results/html.json | 4 +- profile/bib.bib | 10 + profile/blog/posts/_metadata.yml | 18 +- .../a-new-tool-for-explainable-ai/index.qmd | 7 + profile/blog/posts/causal-recourse/index.html | 946 - profile/blog/posts/causal-recourse/index.qmd | 97 +- .../blog/posts/causal-recourse/www/intro.png | Bin 19542 -> 19351 bytes .../conformal-image-classifier/index.qmd | 7 + .../conformal-image-classifier/www/intro.gif | Bin 156116 -> 165244 bytes .../conformal-image-classifier/www/medium.gif | Bin 469884 -> 492183 bytes profile/blog/posts/conformal-llm/index.qmd | 7 + .../blog/posts/conformal-prediction/index.qmd | 7 + .../blog/posts/conformal-regression/index.qmd | 7 + .../posts/effortsless-bayesian-dl/index.qmd | 7 + .../new-package-energysamplers/index.qmd | 7 + 40 files changed, 16482 insertions(+), 16613 deletions(-) delete mode 100644 profile/blog/posts/causal-recourse/index.html diff --git a/docs/blog/index.html b/docs/blog/index.html index a962a1b..19108d6 100644 --- a/docs/blog/index.html +++ b/docs/blog/index.html @@ -129,6 +129,7 @@ }; + @@ -226,7 +227,7 @@

Taija’s Blog

-
+

@@ -249,18 +250,18 @@

Sep 17, 2024

-Patrick Altmeyer, Jorge Luiz Franco +Jorge Luiz Franco
-9 min +14 min
-9/17/24, 2:22:00 PM +9/20/24, 5:35:41 PM
-
+

@@ -289,12 +290,12 @@

7 min

-9/17/24, 7:52:15 AM +9/20/24, 4:26:55 PM
-
+

@@ -323,7 +324,7 @@

7 min

-8/28/24, 5:16:41 PM +9/20/24, 4:20:41 PM
@@ -351,7 +352,7 @@

Jul 4, 2023

-Patrick Altmeyer, Severin Bratus, Mark Ardman, Adelina Cazacu, Andrei Ionescu, Ivan Makarov +Severin Bratus, Mark Ardman, Adelina Cazacu, Andrei Ionescu, Ivan Makarov, Patrick Altmeyer
11 min @@ -362,7 +363,7 @@

-
+

@@ -391,12 +392,12 @@

11 min

-8/28/24, 4:44:08 PM +9/20/24, 4:15:32 PM
-
+

@@ -425,12 +426,12 @@

9 min

-9/17/24, 8:26:22 AM +9/20/24, 4:13:56 PM
-
+

@@ -459,12 +460,12 @@

15 min

-8/28/24, 4:44:08 PM +9/20/24, 4:05:30 PM
-
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12 min

-9/17/24, 8:24:40 AM +9/20/24, 4:05:12 PM
-
+

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12 min

-8/28/24, 4:44:08 PM +9/20/24, 4:04:17 PM
diff --git a/docs/blog/index.xml b/docs/blog/index.xml index c45f089..ec56355 100644 --- a/docs/blog/index.xml +++ b/docs/blog/index.xml @@ -13,7 +13,6 @@ Mon, 16 Sep 2024 22:00:00 GMT When Causality meets Recourse - Patrick Altmeyer Jorge Luiz Franco https://www.taija.org/blog/posts/causal-recourse/

Introduction

-

In recent years, the need for interpretable and explainable AI has surged, particularly in high-stakes domains. Counterfactual explanations provide a means to understand how changes to input features could alter the outcomes of machine learning models. This blog post presents a new tool in the CounterfactualExplanations.jl package, developed during my JSoC (Julia Summer of Code) project, which incorporates causal reasoning into counterfactual generation.

+

In recent years, the need for interpretable and explainable AI has surged, particularly in high-stakes domains. Counterfactual explanations provide a means to understand how changes to input features could alter the outcomes of machine learning models. This blog post presents a new tool in the CounterfactualExplanations.jl package, developed during my JSoC (Julia Summer of Code) project, which incorporates causal reasoning into counterfactual generation.

+
+

Testimonial

+
+

This was an amazing experience, not just experience to contribute to two repositories simultaneously, but also to work with the mantainers of these repos. I learned a lot about the Julia language and the Julia community. This was possible because of the mentorship of Patrick Altmeyer (CounterfactualExplanations) and Moritz Schauer (CausalInference), who guided me throughout the project and are amazing researchers.

+
+

Project Overview

@@ -32,18 +37,14 @@

Key Contributions

During the project, I contributed to two key repositories:

    -

  1. CounterfactualExplanations.jl: Developed a new tool for generating counterfactual explanations using causal information. This allows users to create smarter perturbations rather than random adjustments, ultimately providing more meaningful insights.

    2. -

  2. CausalInference.jl: Implemented a Structural Causal Model (SCM) structure that extracts information from data, laying the groundwork for the causal reasoning capabilities in CounterfactualExplanations.jl.

    3. +

  3. CounterfactualExplanations.jl: Developed a new tool for generating counterfactual explanations using causal information. This allows users to generate counterfactuals through causal interventions rather than minimal perturbations, ultimately providing more meaningful insights.

    4. +

  4. CausalInference.jl: Implemented a Structural Causal Model (SCM) structure that extracts information from data, laying the groundwork for the causal reasoning capabilities in CounterfactualExplanations.jl.

-

This was an amazing experience, not just experience contribute to two repositories simultaneously, but also to work with the mantainers of these repos. I learned a lot about the Julia language and the Julia community. This was possible because of the mentorship of Patrick Altmeyer (CounterfactualExplanations) and Moritz Schauer (CausalInference), who guided me throughout the project and are amazing researchers.

-
-

The MINTGenerator

-

In this project, we developed the MINTGenerator, a counterfactual generator based on the Recourse through Minimal Intervention (MINT) method proposed by Karimi, Schölkopf, and Valera (2021).

-
-
-

Description

-

The MINTGenerator incorporates causal reeasoning in algorithm recourse to achieve minimal interventions when generating a counterfactual explanation. In this sense, the main ideia is that just perturbating a black box model without taking into account the causal relations in the data can guide to misleading recommendations. Here we now shift to a perspective where every action/pertubation is an intervetion in the causal graph of the problem, thus the change is not made just in the intervened upon variable, but also in its childs in the causal structure. The generator utilizes a Structural Causal Model(SCM) to encode the variables in a way that causal effects are propagated and uses a generic gradient-based generator to create the search path, that is, any gradient-base generator (ECCo, REVISE, Watcher, …) can be used with the MINT SCM encoder to generate counterfactual samples in latent space for minimal intervetions algorithm recourse.

+
+

Theoretical Background

+

In this project, we developed a framework for the MINT Generator: a counterfactual generator based on the Recourse through Minimal Intervention (MINT) method proposed by Karimi, Schölkopf, and Valera (2021).

+

The MINT Generator incorporates causal reasoning to achieve algorithmic recourse through minimal interventions. In this sense, the main idea is that just perturbating a black-box model without taking into account the causal relations in the data can lead to misleading recommendations. Here we now shift to a perspective where every feature pertubation is an intervetion in the causal graph of the problem. Leveraging causal relationships, interventions on causal parents automatially lead to potentially useful changes in their causal children. The generator utilizes a Structural Causal Model(SCM) to encode the variables in a way that causal effects are propagated and uses a generic gradient-based generator to create the search path. This has the benefit that any existing gradient-based generator, such as ECCo (Altmeyer et al. 2024), Watcher (Wachter, Mittelstadt, and Russell 2017), DiCE (Mothilal, Sharma, and Tan 2020), and more, can be used with the MINT SCM encoder to generate counterfactual through causal interventions.

The MINT algorithm minimizes a loss function that combines the causal constraints of the SCM and the distance between the generated counterfactual and the original input. Since we want a gradient-based generator, we need to pass the constrained optimizaiton problem into an unconstrained one and we do this by using the Lagrangian. Initially, as defined in (Karimi, Schölkopf, and Valera 2021), we aim to aim to find the minimal cost set of actions (in the form of structural interventions) that results in a counterfactual instance yielding the favorable output from ,

where is the original input, is the counterfactual instance, and is the black-box model. We use the terminology because the counterfactual is derived from the SCM,

@@ -57,9 +58,7 @@

Implementation

-
-

CausalInference.jl

-

In terms of implementation, we need to capture the causal relations from the data, that’s where CausalInference.jl comes in. However, before the project, the package did not have a SCM structure, in the sense that the methods just captured the topological Directed Acyclic Graph (DAG) that showed the causality ruling the data, that is, no causal structural equations were provided,

+

As mentioned above, this project involved contributions to both CausalInference.jl and CounterfactualExplanations.jl. In this section, we will cover both of these. Before we begin, we load all necessary dependencies below:

Code @@ -114,22 +113,30 @@ font-style: inherit;">1) background-color: null; font-style: inherit;">using StatsBase - -N StatsBase
+ +
+
+

Causal Inference

+

In terms of implementation, we need to capture the causal relations from the data, which is where CausalInference.jl comes in. However, before the project, the package did not have a SCM structure, in the sense that the methods just captured the topological Directed Acyclic Graph (DAG) that showed the causality governing the data. There was previously no way to transform graphs into structural causal models.

+

Consider the following synthetic data:

+
+
+Code +
N = 2000 # number of data points
-
-x 
+x = randn(N)
-v v = x *0.25
-w w = x *0.25
-z z = v *0.25
-s s = z *0.25
-
-df df = (x=w, z=z, s=s)
-
-est_g, score =s)
+
+
+

Using CausalInference.jl, we can use the ges method for the causal discovery (Chickering 2003) and plot the resulting DAG Figure 1:

+
+
+Code +
est_g, score = =true)
-
-plt 
+plt = =25)
-savefig(plt, "www/intro.png")
-display(plt)
@@ -247,68 +258,75 @@ font-style: inherit;">display(plt)
┌ Warning: Only one thread available
 └ @ CausalInference ~/.julia/packages/CausalInference/ozcj8/src/ges.jl:52
-
+
+
+
- + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
-
-

So, our goal was given the DAG provided by the ges method in the causal discovery (Chickering 2003), generate equations that rules each of these causal relations, represented in the DAG as directed edges. The SCM is the union of the DAG and these causal equations, that is, the SCM is a tuple , where is the DAG and is the set of functions that generates the value of each variable given its parents.

-

Our solution for constructing the structural causal equations was to assume that the data was generated by a linear model, ie, the causal relations were linear. For the DAG provided in the code example we derive

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+Figure 1: A simple example of a causal graph. +
+ + + +

Given the DAG in Figure 1, our goal is to recover the equations that define the underlying causal relations. The SCM is the union of the DAG and these causal equations: formally, it can be represented as a tuple , where is the DAG and is the set of functions that generates the value of each variable given its parents.

+

Our solution for constructing the structural causal equations was to assume that the data was generated by a linear model, which in this simple synthetic example actually corresponds to the ground truth. For the DAG provided in the code example we derive

and that’s the tricky thing, as we can see these causal equations are different than the ones that generated the data, but they are the ones that respect the causal system obtained from the obtained DAG. Here and are the intercept term and the coefficient obtained from the linear regression, respectively. To correctly solve the linear regression respecting the dependencies of the causal graph, we use topological_sort_by_dfs from Graphs.jl.

-

Now, with the SCM structure in hand, we see that the representation could be a struct containing the DAG and the coefficients/intercepts of the causal equations, this maps exactly the tuple that we defined. However, since we need these equations to be differentiable, we need to define a function that takes the SCM and returns the value of the variable given its parents and using just the coefficients and the DAG, lead to errors, because AutoDiff does not deal well with functions that are conditioned (if statements). So, we need to define a way to retrieve the system of causal equations in a smooth way and that’s where the causal_effects matrix comes to the rescue.

+

Now, with the SCM structure at hand, we see that the representation could be a struct containing the DAG and the coefficients/intercepts of the causal equations, which corresponds exactly the tuple that we defined. A technical difficulty is that since we aim for gradient-based counterfactual generation, we need to define a differentiable function that takes the SCM and applies the encoded causal relationships to all variables. That is where the causal_effects matrix comes to the rescue.

Let the factual vector of features be denoted as:

Let the causal_effects matrix be:

@@ -322,39 +340,39 @@ font-style: inherit;">display(plt)

This equation shows how each counterfactual variable is generated as a linear combination of the factual inputs based on the causal effects matrix, with an intercept term added for each variable.

One can note that the orphan nodes, that is, the nodes that do not have parents in the DAG, are going to be equal to the intercept term . The intuition behind this is that when we do the linear regression, variables that have no causal parents are just equal to the unconditional mean of the variable, i.e, we get . Because of this, in some cases a better understanding of the regression is needed, so the residuals are also part of the SCM structure,

-
+
Code -
struct SCM
-    variables    variables::Vector{String}
-    coefficients    coefficients::Vector{Vector{Float64}}
-    residuals    residuals::Vector{Vector{Float64}}
-    dag    dag::DiGraph
-    causal_effects    causal_effects::Matrix{Float64}
-end
@@ -363,11 +381,13 @@ font-style: inherit;">end

CounterfactualExplanations.jl

-

Now, we need to go into the optimization problem previously described. We seek to minimize the lagrangian function we defined where now we have a differentiable function. The standard way to implement generators in CounterfactualExplanations.jl is to use AutoDiff exactly using composable functions in the lagrangian. The definition of is in the same shape of the the others gradient-based generators in the package, so the optimization is straightforward. However, we needed some way to pass the into the and that’s where transformer.jl comes in. This is where InputTransformers are defined in the package and in some way this is what we are doing, we are passing our factual to the “latent” causal space of the counterfactual. Our first step is to create a new kind of InputTransformer that is the SCM itself,

-
+

Next, we will dive to go into the optimization problem previously described in Section 2.2. Recall that we seek to minimize the Lagrangian function we defined where we now have a differentiable function. The standard way to implement generators in CounterfactualExplanations.jl is to use autodifferentiation to solve this Lagrangian. The definition of above is just an unconstrained objective function, much like with any other gradient-based generator in the package, so the optimization is straightforward (see docs for more details on gradient-based generators).

+

A challenge was to find a way to pass the into the . For the time being, we have decided to extend an existing feature of the package, namely InputTransformers: they can be used to transform features, for example, through standardization. All existing InputTransformers work under the premise of encoding features into some latent representation, searching counterfactuals in that latent space, and finally decoding latent features back into the original feature space. In some way, this is also what we are doing here: we are passing our factual to the “latent” causal space of the counterfactual.

+

Our first step is to create a new kind of InputTransformer for the SCM:

+
Code -
const TypedInputTransformer = Union{
-        Type{<:StatsBase.AbstractDataTransform},
-        Type{<:MultivariateStats.AbstractDimensionalityReduction},
-        Type{<:GenerativeModels.AbstractGenerativeModel},
-        Type{CausalInference.SCM} # The SCM transfromer
-}
+}
-

and then we need a way to create this transformer, that’s where we “overload” fit_transformer using CausalInferece.jl,

-
+

Next, we need a way to actually apply train this transformer. This is done by “overloading” the fit_transformer method,

+
Code -
function fit_transformer(
-    data    data::Type{<:CausalInference.SCM}; kwargs...
-)
-    t )
+    t = Tables.table(transpose(data.X))
-    est_g, score     est_g, score = CausalInference.=true)
-    est_dag     est_dag = CausalInference.pdag2dag!(est_g)
-    scm     scm = CausalInference.estimate_equations(t, est_dag)
-        return scm
-end
-

… We are getting there! However, now comes the hardest part, where this is placed?

-
- - -
-

Conclusion

- -
-
- - - - - - -
- -

References

-
-Chickering, David Maxwell. 2003. “Optimal Structure Identification with Greedy Search.” J. Mach. Learn. Res. 3 (null): 507–54. https://doi.org/10.1162/153244303321897717. -
-
-Karimi, Amir-Hossein, Bernhard Schölkopf, and Isabel Valera. 2021. “Algorithmic Recourse: From Counterfactual Explanations to Interventions.” In Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency, 353–62. FAccT ’21. New York, NY, USA: Association for Computing Machinery. https://doi.org/10.1145/3442188.3445899. -
-

Citation

BibTeX citation:
@online{altmeyer2024,
-  author = {Altmeyer, Patrick and Luiz Franco, Jorge},
-  title = {When {Causality} Meets {Recourse}},
-  date = {2024-09-17},
-  url = {https://www.taija.org/blog/posts/causal-recourse/},
-  langid = {en}
-}
-
For attribution, please cite this work as:
-Altmeyer, Patrick, and Jorge Luiz Franco. 2024. “When Causality -Meets Recourse.” September 17, 2024. https://www.taija.org/blog/posts/causal-recourse/. -
]]> - counterfactuals - explainable AI - causality - Julia - https://www.taija.org/blog/posts/causal-recourse/ - Mon, 16 Sep 2024 22:00:00 GMT - - - - New Package for Energy-Based Sampling - Patrick Altmeyer - https://www.taija.org/blog/posts/new-package-energysamplers/ - -

EnergySamplers

-

Stable Dev Build Status Coverage Code Style: Blue Aqua QA

-

EnergySamplers.jl is a small and lightweight package for sampling from probability distributions using methods from energy-based modelling (EBM). Its functionality is used in other Taija packages, including JointEnergyModels.jl and CounterfactualExplanations.jl.

- -
-

Extensions to Optimisers.jl

-

The package adds two new optimisers that are compatible with the Optimisers.jl interface:

-
    -
  1. Stochastic Gradient Langevin Dynamics (SGLD) (Welling and Teh 2011) — SGLD.
    2. -
  2. Improper SGLD (see, for example, Grathwohl et al. (2020)) — ImproperSGLD.
    3. -
-

SGLD is an efficient gradient-based Markov Chain Monte Carlo (MCMC) method that can be used in the context of EBM to draw samples from the model posterior (Murphy 2023). Formally, we can draw from as follows

-

-

where is a stochastic term and the step-size is typically polynomially decayed (Welling and Teh 2011). To allow for faster sampling, it is common practice to choose the step-size and the standard deviation of separately. While is only guaranteed to distribute as if and , the bias introduced for a small finite is negligible in practice (Murphy 2023). We denote this form of sampling as Improper SGLD.

-
-

Example: Bayesian Inferecne with SGLD

-

To illustrate how the custom optimisers can be used, we will go through an example adapted from this (great!) blog post by Sebastian Callh. First, let’s load some dependencies:

-
+

which takes an input dataset and then relies on CausalInference.jl for causal discovery.

+

We are getting there … but one implementation challenge is still left: how can we use the learned SCM during the counterfactual search?

+

Our idea was simple: during each gradient-step, just apply the SCM to all features of the counterfactual. Implementation-wise, this boiled down to overloading the decode_array function, which handles the actual decoding step for all InputTransformers:

+
Code -
# External dependencies:
-function using decode_array(dataFlux
-::using CounterfactualData, dtFlux: gpu
-::using CausalInference.SCM, xMLDataUtils: shuffleobs, stratifiedobs, rescale!
-::using AbstractArray)
+    Plots
-return using run_causal_effects(dt, x)
+Random
-end
+
+using function RDatasets 
-run_causal_effects(scmusing ::Statistics
-CausalInference.SCM, x# Custom optimisers:
-::using AbstractArray)
+    EnergySamplers: ImproperSGLD, SGLD
-
-
-

Next, we load some data and prepare it for training a logistic regression model in Flux.jl:

-
-
-Code -
return scm.causal_effects[Random.:, seed!(12024)
-
-data :(= end dataset(- "ISLR", 1)] "Default")
-* x todigit(x) + scm.causal_effects[= x :, == end] "Yes" ? # bias
+1.0 end
+
+
+

Here we are! Using this approach, gradient computations explicitly take the causal graph into account. We can now rely on standard workflows for gradient-based generators to solve a different minimization problem that incorporate causal effects.

+
+
+
+ +
+
+Concrete Generator Type +
+
+
+

One piece that is still missing here is to implement a concrete generator type of the MINT Generator (#466). That will make it easier for users to use the MINT Generator in the same way as all of our other counterfactual generators. This step has been postponed, because it hinges on an a larger development task (#435).

+
+
+
+
+
+

Limitations and Future Work

+

Altough the range of lines of code was not tremendous, the hard work was. The merged code does not show every research and development I was guided during this time by the mentors. For example, initially we were trying a different approach to work with differentiation inside the CounterfactualExplanations.jl package, where the code always broke 😅. But, without this obstacle, we could not have in mind a possible future work where the run_causal_effects function could be more flexible. For example, as we said, the variables without causal parents are been assigned just to the unconditional mean, but in terms of counterfactuals theory, maybe using just the factual feature would be more realistic. But to do this we would need to work in the causal_effects_matrix and this was part of my work creating transformable_features for the SCM where we would probably need to use ignore_derivatives() from Zygote.jl.

+
+
+Code +
: function 0.0
-data[!, transformable_features(
+    counterfactual_data:Default] ::= CounterfactualData, input_encodermap(todigit, data[:::, Type{CausalInference.SCM}
+)
+    g :Default])
-data[!, = counterfactual_data.input_encoder.dag
+    child_causal_nodes :Student] = [v for v = in map(todigit, data[vertices(g) if :, indegree(g, v) :Student])
-
-target >= = 1]
+    :Default
-numerics return child_causal_nodes
+= [end
+
+
+

Another direction of future work is that the current implementation of the MINT Generator is limited to linear causal relations. One could extend this to non-linear causal relations, such as those found in neural networks. Additionally, the we could shift the paradigm to use Bayesian Inference to generate the causal equations. This work would be a new extension in CausalInference.jl.

+
+
+

Github PRs and Issues

+

In the following links, you can find the PRs and issues that were opened and closed during the project. They show some kind of history of the work developed:

+

Causal Inference:

+ +

CounterfactualExplanations:

+ +

And one that still open:

+ +
+ +
+

Usage

+

The MINT algorithm can be implemented using the GenericGenerator and the SCM encoder, that we implement using CausalInference.jl package. The following code snippet shows how to use the MINT algorithm to generate counterfactuals using any gradient-based generator:

+
+
+Code +
:Balance, using :Income]
-features CausalInference
+= [using :Student, CounterfactualExplanations
+:Balance, using :Income]
-train, test CounterfactualExplanations.DataPreprocessing: fit_transformer
+= (d using -> Tables
+
+N stratifiedobs(first, d; p= =2000
+df 0.7))(= (
+    x shuffleobs(data))
-
-for feature = in numerics
-    μ, σ randn(N), 
+    v = rescale!(train[!, feature]; obsdim=randn(N) 1)
-    .^ rescale!(test[!, feature], μ, σ; obsdim2 =+ 1)
-randn(N) end
-
-* prep_X(x) 0.25, 
+    w = gpu(Matrix(x)')
-prep_y(y) cos.(= randn(N)) gpu(+ reshape(y, randn(N) 1, * :))
-train_X, test_X 0.25, 
+    z = prep_X.((train[:, features], test[randn(N) :, features]))
-train_y, test_y .^ = 2 prep_y.((train[+ :, target], test[cos.(:, target]))
-train_set randn(N)) = Flux.+ DataLoader((train_X, train_y); batchsizerandn(N) =* 100, shuffle0.25 =+ false)
-
-
-

Finally, we create a small helper function that runs the training loop for a given optimiser opt and number of steps:

-
-
-Code -
randn(N) function * train_logreg(; steps0.25, 
+    s ::= Int=sin.(1000, optrandn(N) =Flux..^ Descent(2 2))
-    + Random.cos.(seed!(randn(N)) 1)
-
-    + paramvec(θ) randn(N) = * reduce(hcat, 0.25 cpu(θ))
-    model + = randn(N) gpu(* Dense(0.25) length(features), + 1, sigmoid))
-    θ randn(N) = Flux.* params(model)
-    θ₀ 0.25
+)
+y_lab = paramvec(θ)
-
-    rand(predict(x; thres0=:0.5) 2, N)
+counterfactual_data_scm = model(x) CounterfactualData(Tables..> thres
-    matrix(df; transposeaccuracy(x, y) == true), y_lab)
+
+M mean(= cpu(fit_model(counterfactual_data_scm, predict(x)) :Linear)
+chosen .== = cpu(y))
-
-    rand(loss(yhat, y) findall(= Flux.predict_label(M, counterfactual_data_scm) binarycrossentropy(yhat, y)
-    .== avg_loss(yhat, y) 1))
+x = mean(loss(yhat, y))
-    trainloss() select_factual(counterfactual_data_scm, chosen)
+
+data_scm = avg_loss(deepcopy(counterfactual_data_scm)
+data_scm.input_encoder model(train_X), train_y)
-    = testloss() fit_transformer(data_scm, CausalInference.SCM)
+
+ce = avg_loss(generate_counterfactual(x, model(test_X), test_y)
-
-    trainlosses 2, data_scm, M, = [GenericGenerator(); initializationcpu(=:identity)
+
+
+

For further usage reference access the MINT official documentation.

+
+
+

Conclusion

+

During this project, I had the opportunity to contribute to both the XAI and Julia communities, where I implemented a SOTA method that used causal information to generate counterfactual explanations (Karimi, Schölkopf, and Valera 2021). It was an amazing experience to work with incredible mentors and the community. I would like to once again thank Patrick and Moritz for all their guidance, as well as Jacob Zelko and JuliaHUB for all their support. I learned a lot about the Julia language and the Julia community, and I witnessed firsthand the benefits of Open Source. In fact, it was Open Source that made it possible to contribute to two repositories simultaneously. This experience of working locally on CounterfactualExplanations.jl and CausalInference.jl was invaluable, as it allowed me to truly understand how things work under the hood.

+

I hope that the MINT Generator can be useful to the community and that the package continues to be improved in the future. Contributing to a more trustworthy Artificial Intelligence has always been a goal of mine, and even though my contribution may be small, I feel proud to have achieved something meaningful. My wish is to continue contributing to the responsible use of AI. I am very grateful for this opportunity, and I look forward to continuing to contribute to the community. 🚀🚀🚀

+
+
+ + + + + + +
+ +

References

+
+Altmeyer, Patrick, Mojtaba Farmanbar, Arie van Deursen, and Cynthia CS Liem. 2024. “Faithful Model Explanations Through Energy-Constrained Conformal Counterfactuals.” In Proceedings of the AAAI Conference on Artificial Intelligence, 38:10829–37. 10. +
+
+Chickering, David Maxwell. 2003. “Optimal Structure Identification with Greedy Search.” J. Mach. Learn. Res. 3 (null): 507–54. https://doi.org/10.1162/153244303321897717. +
+
+Karimi, Amir-Hossein, Bernhard Schölkopf, and Isabel Valera. 2021. “Algorithmic Recourse: From Counterfactual Explanations to Interventions.” In Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency, 353–62. FAccT ’21. New York, NY, USA: Association for Computing Machinery. https://doi.org/10.1145/3442188.3445899. +
+
+Mothilal, Ramaravind K, Amit Sharma, and Chenhao Tan. 2020. “Explaining Machine Learning Classifiers Through Diverse Counterfactual Explanations.” In Proceedings of the 2020 Conference on Fairness, Accountability, and Transparency, 607–17. https://doi.org/10.1145/3351095.3372850. +
+
+Wachter, Sandra, Brent Mittelstadt, and Chris Russell. 2017. “Counterfactual Explanations Without Opening the Black Box: Automated Decisions and the GDPR.” Harv. JL & Tech. 31: 841. https://doi.org/10.2139/ssrn.3063289. +
+

Citation

BibTeX citation:
@online{luiz_franco2024,
+  author = {Luiz Franco, Jorge},
+  title = {When {Causality} Meets {Recourse}},
+  date = {2024-09-17},
+  url = {https://www.taija.org/blog/posts/causal-recourse/},
+  langid = {en}
+}
+
For attribution, please cite this work as:
+Luiz Franco, Jorge. 2024. “When Causality Meets Recourse.” +September 17, 2024. https://www.taija.org/blog/posts/causal-recourse/. +
]]> + counterfactuals + explainable AI + causality + Julia + https://www.taija.org/blog/posts/causal-recourse/ + Mon, 16 Sep 2024 22:00:00 GMT + + + + New Package for Energy-Based Sampling + Patrick Altmeyer + https://www.taija.org/blog/posts/new-package-energysamplers/ + +

EnergySamplers

+

Stable Dev Build Status Coverage Code Style: Blue Aqua QA

+

EnergySamplers.jl is a small and lightweight package for sampling from probability distributions using methods from energy-based modelling (EBM). Its functionality is used in other Taija packages, including JointEnergyModels.jl and CounterfactualExplanations.jl.

+ +
+

Extensions to Optimisers.jl

+

The package adds two new optimisers that are compatible with the Optimisers.jl interface:

+
    +
  1. Stochastic Gradient Langevin Dynamics (SGLD) (Welling and Teh 2011) — SGLD.
    2. +
  2. Improper SGLD (see, for example, Grathwohl et al. (2020)) — ImproperSGLD.
    3. +
+

SGLD is an efficient gradient-based Markov Chain Monte Carlo (MCMC) method that can be used in the context of EBM to draw samples from the model posterior (Murphy 2023). Formally, we can draw from as follows

+

+

where is a stochastic term and the step-size is typically polynomially decayed (Welling and Teh 2011). To allow for faster sampling, it is common practice to choose the step-size and the standard deviation of separately. While is only guaranteed to distribute as if and , the bias introduced for a small finite is negligible in practice (Murphy 2023). We denote this form of sampling as Improper SGLD.

+
+

Example: Bayesian Inferecne with SGLD

+

To illustrate how the custom optimisers can be used, we will go through an example adapted from this (great!) blog post by Sebastian Callh. First, let’s load some dependencies:

+
+
+Code +
trainloss()); # External dependencies:
+zeros(steps)]
-    testlosses using = [Flux
+cpu(using testloss()); Flux: gpu
+zeros(steps)]
-    weights using = [MLDataUtils: shuffleobs, stratifiedobs, rescale!
+cpu(θ₀); using zeros(steps, Plots
+length(θ₀))]
-
-    opt_state = Flux.setup(opt, model)
-
-    for t using in Random
+1using :steps
-        RDatasets 
+for data using in train_set
-            input, label Statistics
+= data
-
-            # Custom optimisers:
+# Calculate the gradient of the objective
-            using # with respect to the parameters within the model:
-            grads EnergySamplers: ImproperSGLD, SGLD
+
+
+

Next, we load some data and prepare it for training a logistic regression model in Flux.jl:

+
+
+Code +
= Flux.Random.gradient(model) seed!(do m
-                result 2024)
+
+data = m(input)
-                dataset(loss(result, label)
-            "ISLR", end
-
-            Flux."Default")
+update!(opt_state, model, grads[todigit(x) 1])
-        = x end
-
-        == # Bookkeeping
-        weights[t "Yes" ? + 1.0 1, : :] 0.0
+data[!, :Default] = cpu(map(todigit, data[paramvec(θ))
-        trainlosses[t :, + :Default])
+data[!, 1] :Student] = cpu(map(todigit, data[trainloss())
-        testlosses[t :, + :Student])
+
+target 1] = = :Default
+numerics cpu(= [testloss())
-    :Balance, end
-
-    :Income]
+features println(= ["Final parameters are :Student, $(:Balance, paramvec(θ)):Income]
+train, test ")
-    = (d println(-> "Test accuracy is stratifiedobs(first, d; p$(=accuracy(test_X, test_y))0.7))(")
-
-    shuffleobs(data))
+
+return model, weights, trainlosses, testlosses
-for feature end
-
-
-

Now we use this function to train the model, first using SGLD and then using Improper SGLD:

-
-
-Code -
results in numerics
+    μ, σ = train_logreg(; stepsrescale!(train[!, feature]; obsdim=100, opt=1)
+    SGLD(rescale!(test[!, feature], μ, σ; obsdim10.0, =10.0, 1)
+0.9))
-model, weights, trainlosses, testlosses end
+
+= results
-p1 prep_X(x) = plot(weights; labelgpu(=[Matrix(x)"Student" ')
+"Balance" prep_y(y) "Income" = "Intercept"], plot_titlegpu(=reshape(y, "SGLD")
-
-results 1, :))
+train_X, test_X = train_logreg(; stepsprep_X.((train[=:, features], test[100, opt:, features]))
+train_y, test_y == ImproperSGLD(prep_y.((train[2.0, :, target], test[0.01))
-model, weights, trainlosses, testlosses :, target]))
+train_set = results
-p2 = Flux.= DataLoader((train_X, train_y); batchsizeplot(weights; label==[100, shuffle"Student" ="Balance" false)
+
+
+

Finally, we create a small helper function that runs the training loop for a given optimiser opt and number of steps:

+
+
+Code +
"Income" function "Intercept"], plot_titletrain_logreg(; steps=::Int=1000, opt=Flux.Descent(2))
+    Random.seed!(1)
+
+    paramvec(θ) = reduce(hcat, cpu(θ))
+    model = gpu(Dense(length(features), 1, sigmoid))
+    θ = Flux.params(model)
+    θ₀ = paramvec(θ)
+
+    predict(x; thres=0.5) = model(x) .> thres
+    accuracy(x, y) = mean(cpu(predict(x)) .== cpu(y))
+
+    loss(yhat, y) = Flux.binarycrossentropy(yhat, y)
+    avg_loss(yhat, y) = mean(loss(yhat, y))
+    trainloss() = avg_loss(model(train_X), train_y)
+    testloss() = avg_loss(model(test_X), test_y)
+
+    trainlosses = [cpu(trainloss()); zeros(steps)]
+    testlosses = [cpu(testloss()); zeros(steps)]
+    weights = [cpu(θ₀); zeros(steps, length(θ₀))]
+
+    opt_state = Flux.setup(opt, model)
+
+    for t in 1:steps
+        for data in train_set
+            input, label = data
+
+            # Calculate the gradient of the objective
+            # with respect to the parameters within the model:
+            grads = Flux.gradient(model) do m
+                result = m(input)
+                loss(result, label)
+            end
+
+            Flux.update!(opt_state, model, grads[1])
+        end
+
+        # Bookkeeping
+        weights[t + 1, :] = cpu(paramvec(θ))
+        trainlosses[t + 1] = cpu(trainloss())
+        testlosses[t + 1] = cpu(testloss())
+    end
+
+    println("Final parameters are $(paramvec(θ))")
+    println("Test accuracy is $(accuracy(test_X, test_y))")
+
+    return model, weights, trainlosses, testlosses
+end
+
+
+

Now we use this function to train the model, first using SGLD and then using Improper SGLD:

+
+
+Code +
results = train_logreg(; steps=100, opt=SGLD(10.0, 10.0, 0.9))
+model, weights, trainlosses, testlosses = results
+p1 = plot(weights; label=["Student" "Balance" "Income" "Intercept"], plot_title="SGLD")
+
+results = train_logreg(; steps=100, opt=ImproperSGLD(2.0, 0.01))
+model, weights, trainlosses, testlosses = results
+p2 = plot(weights; label=["Student" "Balance" "Income" "Intercept"], plot_title="Improper SGLD")
 
@@ -1180,109 +1601,109 @@ Test accuracy is 0.9763333333333334
- + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - + - +
Figure 1: Training the logistic regression model using SGLD and Improper. Plots show the estimated coefficients over the course of training. @@ -1309,7 +1730,7 @@ Figure 2: The animation shows the last 250 draws from the marginal posterio
  1. UnconditionalSampler — samples from the unconditional distribution as in Grathwohl et al. (2020).
  2. ConditionalSampler — samples from the conditional distribution as in Grathwohl et al. (2020).
    3. -
  3. JointSampler — samples from the joint distribution as in (kelly2021directly?).
    4. +
  4. JointSampler — samples from the joint distribution as in Kelly, Zemel, and Grathwohl (2021).

Example: Joint Energy-Based Model

@@ -1859,2315 +2280,2315 @@ font-style: inherit;">plot(plt)
- + - + - + - + - - + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
@@ -4185,6 +4606,9 @@ font-style: inherit;">plot(plt)
Grathwohl, Will, Kuan-Chieh Wang, Joern-Henrik Jacobsen, David Duvenaud, Mohammad Norouzi, and Kevin Swersky. 2020. “Your Classifier Is Secretly an Energy Based Model and You Should Treat It Like One.” In International Conference on Learning Representations.
+
+Kelly, Jacob, Richard Zemel, and Will Grathwohl. 2021. “Directly Training Joint Energy-Based Models for Conditional Synthesis and Calibrated Prediction of Multi-Attribute Data.” https://arxiv.org/abs/2108.04227. +
Murphy, Kevin P. 2023. Probabilistic Machine Learning: Advanced Topics. MIT press.
@@ -4230,8 +4654,8 @@ Short demo of our conformal chatbot.

🤗 HuggingFace Model

The model can be loaded from HF straight into our running Julia session using the Transformers.jl package. Below we load the tokenizer tkr and the model mod. The tokenizer is used to convert the text into a sequence of integers, which is then fed into the model. The model outputs a hidden state, which is then fed into a classifier to get the logits for each class. Finally, the logits are then passed through a softmax function to get the corresponding predicted probabilities. Below we run a few queries through the model to see how it performs.

-
-
+
+
Code 
onecold(d)]

🔁 MLJ Interface

Since our package is interfaced to MLJ.jl, we need to define a wrapper model that conforms to the MLJ interface. In order to add the model for general use, we would probably go through MLJFlux.jl, but for this tutorial, we will make our life easy and simply overload the MLJBase.fit and MLJBase.predict methods. Since the model from HF is already pre-trained and we are not interested in further fine-tuning, we will simply return the model object in the MLJBase.fit method. The MLJBase.predict method will then take the model object and the query and return the predicted probabilities. We also need to define the MLJBase.target_scitype and MLJBase.predict_mode methods. The former tells MLJ what the output type of the model is, and the latter can be used to retrieve the label with the highest predicted probability.

-
-
+
+
Code 
predict(clf, fitresult, Xnew))
<

To test that everything is working as expected, we fit the model and generated predictions for a subset of the test data:

-
-
+
+
Code 
clf :top_n]);
-
  1.923436 seconds (8.61 M allocations: 631.348 MiB, 2.99% gc time, 84.31% compilation time)
+
  1.875274 seconds (8.61 M allocations: 631.254 MiB, 3.20% gc time, 87.70% compilation time)
@@ -4575,8 +4999,8 @@ font-style: inherit;">"dev/private/simple_inductive.jls", mach)Feed user input through conformal LLM and present the output to the user.
  • If the conformal prediction set includes more than one label, prompt the user to either refine their input or choose one of the options included in the set.
    • -
    -
    +
    +
    Code 
    mach end

    Below we show the output for two example queries. The first one is very ambiguous. As expected, the size of the prediction set is therefore large.

    -
    -
    +
    +
    Code 
    ambiguous_query 2]

    The more refined version of the prompt yields a smaller prediction set: less ambiguous prompts result in lower predictive uncertainty.

    -
    -
    +
    +
    Code 
    refined_query 
 
   Paving the Way Towards Low-Overhead Uncertainty Calibration
-  Patrick Altmeyer
   Severin Bratus
   Mark Ardman
   Adelina Cazacu
   Andrei Ionescu
   Ivan Makarov
+  Patrick Altmeyer
   https://www.taija.org/blog/posts/guest-students-laplace/
   “Optimal Brain
 Sharma, Apoorva, Navid Azizan, and Marco Pavone. 2021. “Sketching Curvature for Efficient Out-of-Distribution Detection for Deep Neural Networks.” arXiv. https://doi.org/10.48550/arXiv.2102.12567.
    -

    Citation

    BibTeX citation:
    @online{altmeyer2023,
-  author = {Altmeyer, Patrick and Bratus, Severin and Ardman, Mark and
-    Cazacu, Adelina and Ionescu, Andrei and Makarov, Ivan and Altmeyer,
-    Patrick},
+

    Citation

    BibTeX citation:
    @online{bratus2023,
+  author = {Bratus, Severin and Ardman, Mark and Cazacu, Adelina and
+    Ionescu, Andrei and Makarov, Ivan and Altmeyer, Patrick},
   title = {Paving the {Way} {Towards} {Low-Overhead} {Uncertainty}
     {Calibration}},
   date = {2023-07-04},
   url = {https://www.taija.org/blog/posts/guest-students-laplace/},
   langid = {en}
 }
-
    For attribution, please cite this work as:
    -Altmeyer, Patrick, Severin Bratus, Mark Ardman, Adelina Cazacu, Andrei -Ionescu, Ivan Makarov, and Patrick Altmeyer. 2023. “Paving the Way -Towards Low-Overhead Uncertainty Calibration.” July 4, 2023. https://www.taija.org/blog/posts/guest-students-laplace/. +
    For attribution, please cite this work as:
    +Bratus, Severin, Mark Ardman, Adelina Cazacu, Andrei Ionescu, Ivan +Makarov, and Patrick Altmeyer. 2023. “Paving the Way Towards +Low-Overhead Uncertainty Calibration.” July 4, 2023. https://www.taija.org/blog/posts/guest-students-laplace/.
    ]]> bayesian deep learning laplace approximation @@ -5153,8 +5576,8 @@ Interactive Version

    📈 Data

    Most machine learning workflows start with data. For illustrative purposes we will work with synthetic data. The helper function below can be used to generate some regression data.

    -
    -
    +
    +
    Code 
    end

    Figure 1 illustrates our observations (dots) along with the ground-truth mapping from inputs to outputs (line). We have defined that mapping as follows:

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    -
    +
    +
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    Figure 1: Some synthetic regression data. Observations are shown as dots. The ground-truth mapping from inputs to outputs is shown as a dashed line. @@ -6324,8 +6747,8 @@ Figure 1: Some synthetic regression data. Observations are shown as dots. T

    ConformalPrediction.jl is interfaced to MLJ.jl (Blaom et al. 2020): a comprehensive Machine Learning Framework for Julia. MLJ.jl provides a large and growing suite of popular machine learning models that can be used for supervised and unsupervised tasks. Conformal Prediction is a model-agnostic approach to uncertainty quantification, so it can be applied to any common supervised machine learning model.

    The interface to MLJ.jl therefore seems natural: any (supervised) MLJ.jl model can now be conformalized using ConformalPrediction.jl. By leveraging existing MLJ.jl functionality for common tasks like training, prediction and model evaluation, this package is light-weight and scalable. Now let’s see how all of that works …

    To start with, let’s split our data into a training and test set:

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 Figure 2: Point predictions for our machine learning model.
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    🔥 Conformalizing the Model
    
 
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 Figure 3: Prediction intervals for our conformalized machine learning model.
@@ -7369,8 +7792,8 @@ Figure 3: Prediction intervals for our conformalized machine learning model
 
    
 
    🧐 Evaluation
    
 
    To verify the marginal coverage property empirically we can look at the empirical coverage rate of our conformal predictor (see Section 3 of the tutorial for details). To this end our package provides a custom performance measure emp_coverage that is compatible with MLJ.jl model evaluation workflows. In particular, we will call evaluate! on our conformal model using emp_coverage as our performance metric. The resulting empirical coverage rate should then be close to the desired level of coverage.
    
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    ✅ ✅ ✅ Great! We got an empirical coverage rate that is slightly higher than desired 😁 … but why isn’t it exactly the same?

    @@ -7460,1055 +7883,1055 @@ Coverage per fold: [0.94, 0.928, 0.892, 0.874, 0.898, 0.922]     - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    Figure 4: Prediction intervals for our conformalized machine learning model applied to out-of-domain data. @@ -8593,7 +9016,7 @@ Conformalized prediction sets for a
    simple Deep Image Classifier.

    🎯 The Task at Hand

    The task at hand is to predict the labels of handwritten images of digits using the famous MNIST dataset (LeCun 1998). Importing this popular machine learning dataset in Julia is made remarkably easy through MLDatasets.jl:

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    :N]

    Figure 1 below shows a few random samples from the training data:

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    Figure 1: Random samples from the MNIST dataset. @@ -8701,7 +9124,7 @@ Figure 1: Random samples from the MNIST dataset.

    To model the mapping from image inputs to labels will rely on a simple Multi-Layer Perceptron (MLP). A great Julia library for Deep Learning is Flux.jl. But wait … doesn’t ConformalPrediction.jl work with models trained in MLJ.jl? That’s right, but fortunately there exists a Flux.jl interface to MLJ.jl, namely MLJFlux.jl. The interface is still in its early stages, but already very powerful and easily accessible for anyone (like myself) who is used to building Neural Networks in Flux.jl.

    In Flux.jl, you could build an MLP for this task as follows,

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    10)
 
    where (28,28) is just the input dimension (28x28 pixel images). Since we have ten digits, our output dimension is ten.1
    
 
    We can do the exact same thing in MLJFlux.jl as follows,
    
 
    
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    32, n_out)
 
    
 
    where here we rely on the @builder macro to make the transition from Flux.jl to MLJ.jl as seamless as possible. Finally, MLJFlux.jl already comes with a number of helper functions to define plain-vanilla networks. In this case, we will use the ImageClassifier with our custom builder and cross-entropy loss:
    
 
    
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    The generated instance clf is a model (in the MLJ.jl sense) so from this point on we can rely on standard MLJ.jl workflows. For example, we can wrap our model in data to create a machine and then evaluate it on a holdout set as follows:
    
 
    
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    🔥 Conformalizing the Network
    
 
    Since clf is a model, it is also compatible with our package: ConformalPrediction.jl. To conformalize our MLP, we therefore only need to call conformal_model(clf). Since the generated instance conf_model is also just a model, we can still rely on standard MLJ.jl workflows. Below we first wrap it in data and then fit it. Aaaand … we’re done! Let’s look at the results in the next section.
    
 
    
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    As for many other things, ConformalPrediction.jl taps into the existing functionality of MLJ.jl for model evaluation. In particular, we will see below how we can use the generic evaluate! method on our machine. To assess the correctness of our conformal predictor, we can compute the empirical coverage rate using the custom performance measure emp_coverage. With respect to model calibration we will look at the model’s conditional coverage. For adaptive, well-calibrated conformal models, conditional coverage is high. One general go-to measure for assessing conditional coverage is size-stratified coverage. The custom measure for this purpose is just called size_stratified_coverage, aliased by ssc.
    
 
    The code below implements the model evaluation using cross-validation. The Simple Inductive Classifier that we used above is not adaptive and hence the attained conditional coverage is low compared to the overall empirical coverage, which is close to , so in line with the desired coverage rate specified above.
    
 
    
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    _eval ")
    
 
    
 
    
 
    Evaluating over 6 folds:  33%[========>                ]  ETA: 0:00:05Evaluating over 6 folds:  50%[============>            ]  ETA: 0:00:03Evaluating over 6 folds:  67%[================>        ]  ETA: 0:00:02Evaluating over 6 folds:  83%[====================>    ]  ETA: 0:00:01Evaluating over 6 folds: 100%[=========================] Time: 0:00:05
-Empirical coverage: 0.959
-SSC: 0.791
    
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+SSC: 0.828
    PerformanceEvaluation object with these fields:
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 ┌──────────────────────────────────────────────┬───────────┬─────────────┬──────
 │ measure                                      │ operation │ measurement │ 1.9 ⋯
 ├──────────────────────────────────────────────┼───────────┼─────────────┼──────
-│ ConformalPrediction.emp_coverage             │ predict   │ 0.959       │ 0.0 ⋯
-│ ConformalPrediction.size_stratified_coverage │ predict   │ 0.791       │ 0.1 ⋯
+│ ConformalPrediction.emp_coverage             │ predict   │ 0.958       │ 0.0 ⋯
+│ ConformalPrediction.size_stratified_coverage │ predict   │ 0.828       │ 0.0 ⋯
 └──────────────────────────────────────────────┴───────────┴─────────────┴──────
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    We can attain higher adaptivity (SSC) when using adaptive prediction sets:

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    [ Info: Training machine(AdaptiveInductiveClassifier(model = ImageClassifier(builder = GenericBuilder(apply = #3), …), …), …).
-Optimising neural net:  18%[====>                    ]  ETA: 0:00:00Optimising neural net:  27%[======>                  ]  ETA: 0:00:01Optimising neural net:  36%[=========>               ]  ETA: 0:00:01Optimising neural net:  45%[===========>             ]  ETA: 0:00:00Optimising neural net:  55%[=============>           ]  ETA: 0:00:00Optimising neural net:  64%[===============>         ]  ETA: 0:00:00Optimising neural net:  73%[==================>      ]  ETA: 0:00:00Optimising neural net:  82%[====================>    ]  ETA: 0:00:00Optimising neural net:  91%[======================>  ]  ETA: 0:00:00Optimising neural net: 100%[=========================] Time: 0:00:00
-Evaluating over 6 folds:  33%[========>                ]  ETA: 0:00:03Evaluating over 6 folds:  50%[============>            ]  ETA: 0:00:02Evaluating over 6 folds:  67%[================>        ]  ETA: 0:00:02Evaluating over 6 folds:  83%[====================>    ]  ETA: 0:00:01Evaluating over 6 folds: 100%[=========================] Time: 0:00:05
-Empirical coverage: 0.996
-SSC: 0.983
    +Optimising neural net: 18%[====> ] ETA: 0:00:01Optimising neural net: 27%[======> ] ETA: 0:00:01Optimising neural net: 36%[=========> ] ETA: 0:00:01Optimising neural net: 45%[===========> ] ETA: 0:00:00Optimising neural net: 55%[=============> ] ETA: 0:00:00Optimising neural net: 64%[===============> ] ETA: 0:00:00Optimising neural net: 73%[==================> ] ETA: 0:00:00Optimising neural net: 82%[====================> ] ETA: 0:00:00Optimising neural net: 91%[======================> ] ETA: 0:00:00Optimising neural net: 100%[=========================] Time: 0:00:00 +Evaluating over 6 folds: 33%[========> ] ETA: 0:00:04Evaluating over 6 folds: 50%[============> ] ETA: 0:00:03Evaluating over 6 folds: 67%[================> ] ETA: 0:00:02Evaluating over 6 folds: 83%[====================> ] ETA: 0:00:01Evaluating over 6 folds: 100%[=========================] Time: 0:00:04 +Empirical coverage: 0.998 +SSC: 0.99     
    PerformanceEvaluation object with these fields:
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 ┌──────────────────────────────────────────────┬───────────┬─────────────┬──────
 │ measure                                      │ operation │ measurement │ 1.9 ⋯
 ├──────────────────────────────────────────────┼───────────┼─────────────┼──────
-│ ConformalPrediction.emp_coverage             │ predict   │ 0.996       │ 0.0 ⋯
-│ ConformalPrediction.size_stratified_coverage │ predict   │ 0.983       │ 0.0 ⋯
+│ ConformalPrediction.emp_coverage             │ predict   │ 0.998       │ 0.0 ⋯
+│ ConformalPrediction.size_stratified_coverage │ predict   │ 0.99        │ 0.0 ⋯
 └──────────────────────────────────────────────┴───────────┴─────────────┴──────
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    We can also have a look at the resulting set size for both approaches using a custom Plots.jl recipe (fig-setsize). In line with the above, the spread is wider for the adaptive approach, which reflects that “the procedure is effectively distinguishing between easy and hard inputs” (A. N. Angelopoulos and Bates 2022).

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    @@ -10582,8 +11016,8 @@ Note

    Split Conformal Classification

    We consider a simple binary classification problem. Let denote our feature-label pairs and let denote the mapping from features to labels. For illustration purposes we will use the moons dataset 🌙. Using MLJ.jl we first generate the data and split into into a training and test set:

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    MLJ.jl conventions. Using ConformalPrediction.jl we then wrap our atomic model in a conformal model using the standard API call conformal_model(model::Supervised; kwargs...). To train and predict from our conformal model we can then rely on the conventional MLJ.jl procedure again. In particular, we wrap our conformal model in data (turning it into a machine) and then fit it on the training set. Finally, we use our machine to predict the label for a new test sample Xtest:
    
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    The final predictions are set-valued. While the softmax output remains unchanged for the SimpleInductiveClassifier, the size of the prediction set depends on the chosen coverage rate, .
    
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    When specifying a coverage rate very close to one, the prediction set will typically include many (in some cases all) of the possible labels. Below, for example, both classes are included in the prediction set when setting the coverage rate equal to =1.0. This is intuitive, since high coverage quite literally requires that the true label is covered by the prediction set with high probability.
    
 
    
 
    
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    Conversely, for low coverage rates, prediction sets can also be empty. For a choice of =0.1, for example, the prediction set for our test sample is empty. This is a bit difficult to think about intuitively and I have not yet come across a satisfactory, intuitive interpretation.2 When the prediction set is empty, the predict call currently returns missing:
    
 
    
 
    
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    Figure 1 should provide some more intuition as to what exactly is happening here. It illustrates the effect of the chosen coverage rate on the predicted softmax output and the set size in the two-dimensional feature space. Contours are overlayed with the moon data points (including test data). The two samples highlighted in red,  and , have been manually added for illustration purposes. Let’s look at these one by one.
    
 
    Firstly, note that  (red cross) falls into a region of the domain that is characterized by high predictive uncertainty. It sits right at the bottom-right corner of our class-zero moon 🌜 (orange), a region that is almost entirely enveloped by our class-one moon 🌛 (green). For low coverage rates the prediction set for  is empty: on the left-hand side this is indicated by the missing contour for the softmax probability; on the right-hand side we can observe that the corresponding set size is indeed zero. For high coverage rates the prediction set includes both  and , indicative of the fact that the conformal classifier is uncertain about the true label.
    
 
    With respect to , we observe that while also sitting on the fringe of our class-zero moon, this sample populates a region that is not fully enveloped by data points from the opposite class. In this region, the underlying atomic classifier can be expected to be more certain about its predictions, but still not highly confident. How is this reflected by our corresponding conformal prediction sets?
    
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    Next, we need to specify the counterfactual generators we want to use. The package currently ships with two default generators that both need gradient access: firstly, the generic generator introduced by Wachter, Mittelstadt, and Russell (2017) and, secondly, a greedy generator introduced by Schut et al. (2021).
    
 
    The greedy generator is designed to be used with models that incorporate uncertainty in their predictions such as the deep ensemble introduced above. It works for probabilistic (Bayesian) models, because they only produce high-confidence predictions in regions of the feature domain that are populated by training samples. As long as the model is expressive enough and well-specified, counterfactuals in these regions will always be realistic and unambiguous since by construction they should look very similar to training samples. Other popular approaches to counterfactual explanations like REVISE (Joshi et al. 2019) and CLUE (Antorán et al. 2020) also play with this simple idea.
    
 
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    Explaining a torch model
    
 
    We will consider a simple MLP trained for a binary classification task. As before we first need to adapt this custom model for use with our package. The code below the two necessary steps - sub-typing and method extension. Logits are returned by the torch model and copied from the R environment into the Julia scope. Probabilities are then computed inside the Julia scope by passing the logits through the sigmoid function.
    
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     evaluated at the maximum a posteriori (MAP) estimate  amounts to a multi-variate Gaussian distribution. In particular, that Gaussian is centered around the MAP estimate with covariance equal to the inverse Hessian evaluated at the mode  (Murphy 2022).
    
 
    That is basically all there is to the story: if we have a good estimate of  we have an analytical expression for an (approximate) posterior over parameters. So let’s go ahead and start by run Bayesian Logistic regression using Flux.jl. We begin by loading some required packages including LaplaceRedux.jl. It ships with a helper function toy_data_linear that creates a toy data set composed of linearly separable samples evenly balanced across the two classes.
    
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+
    
+
    
 Code
 
    zip(xs,y);
    
 
    
 
    
 
    Then we proceed to prepare the single-layer neural network with weight decay. The term  determines the strength of the  penalty: we regularize parameters  more heavily for higher values. Equivalently, we can say that from the Bayesian perspective it governs the strength of the prior : a higher value of  indicates a higher conviction about our prior belief that , which is of course equivalent to regularizing more heavily. The exact choice of  for this toy example is somewhat arbitrary (it made for good visualizations below). Note that I have used  to denote our neural parameters to distinguish the case from Bayesian logistic regression, but we are in fact still solving the same problem.
    
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    nn weight_regularization();
    
 
    
 
    
 
    Before we apply Laplace approximation we train our model:
    
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+
    
 Code
 
    end
    
 
    
 
    
 
    Up until this point we have just followed the standard recipe for training a regularized artificial neural network in Flux.jl for a simple binary classification task. To compute the Laplace approximation using LaplaceRedux.jl we need just two more lines of code:
    
-
    
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+
    
+
    
 Code
 
    la fit!(la, data);
    
 
    
 
    
 
    Under the hood the Hessian is approximated through the empirical Fisher, which can be computed using only the gradients of our loss function  where  are training data (see NeurIPS 2021 paper for details). Finally, LaplaceRedux.jl ships with a function predict(𝑳::LaplaceRedux, X::AbstractArray; link_approx=:probit) that computes the posterior predictive using a probit approximation, much like we saw in the previous post. That function is used under the hood of the plot_contour function below to create the right panel of Figure 1. It visualizes the posterior predictive distribution in the 2D feature space. For comparison I have added the corresponding plugin estimate as well. Note how for the Laplace approximation the predicted probabilities fan out indicating that confidence decreases in regions scarce of data.
    
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+
    
+
    
 Code
 
    p_plugin 
 
    … to Bayesian Neural Networks
    
 
    Now let’s step it up a notch: we will repeat the exercise from above, but this time for data that is not linearly separable using a simple MLP instead of the single-layer neural network we used above. The code below is almost the same as above, so I will not go through the various steps again.
    
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+
    
+
    
 Code
 
    end
    
 
    
 
    
 
    Fitting the Laplace approximation is also analogous, but note that this we have added an argument: subset_of_weights=:last_layer. This specifies that we only want to use the parameters of the last layer of our MLP. While we could have used all of them (subset_of_weights=:all), Daxberger et al. (2021) find that the last-layer Laplace approximation produces satisfying results, while be computationally cheaper. Figure 2 demonstrates that once again the Laplace approximation yields a posterior predictive distribution that is more conservative than the over-confident plugin estimate.
    
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    la  and the neural network architecture.
    
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    zoom
-
 
 
 
@@ -254,7 +253,7 @@ 
    On this page
    
   
    Affiliation
    
   
     
    
-    
    Patrick Altmeyer 
    
+    
    Patrick Altmeyer  
    
   
    
   
    
         
    
@@ -309,8 +308,8 @@ 
    Counterfact
 
    
 
    Black-box models
    
 
    The code below loads relevant packages along with the MNIST data and pre-trained models.
    
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+
    
+
    
 Code
 
    # Load package, models and data:
 using CounterfactualExplanations, Flux
@@ -327,8 +326,8 @@ 
    Black-box models
    
 
  • Multiple dispatch: the package-internal functions logits and probs need to be extended through custom methods for the new model type.
    • 
 
 
    The following code implements these two steps first for the MLP and then for the deep ensemble.
    
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+
    
+
    
 Code
 
    using CounterfactualExplanations.Models
 import CounterfactualExplanations.Models: logits, probs
@@ -361,8 +360,8 @@ 
    Counterfactual g
 
    Next, we need to specify the counterfactual generators we want to use. The package currently ships with two default generators that both need gradient access: firstly, the generic generator introduced by Wachter, Mittelstadt, and Russell (2017) and, secondly, a greedy generator introduced by Schut et al. (2021).
    
 
    The greedy generator is designed to be used with models that incorporate uncertainty in their predictions such as the deep ensemble introduced above. It works for probabilistic (Bayesian) models, because they only produce high-confidence predictions in regions of the feature domain that are populated by training samples. As long as the model is expressive enough and well-specified, counterfactuals in these regions will always be realistic and unambiguous since by construction they should look very similar to training samples. Other popular approaches to counterfactual explanations like REVISE (Joshi et al. 2019) and CLUE (Antorán et al. 2020) also play with this simple idea.
    
 
    The following code instantiates the two generators for the problem at hand.
    
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+
    
+
    
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    generic = GenericGenerator(;loss=:logitcrossentropy)
 greedy = GreedyGenerator(;loss=:logitcrossentropy)
    
@@ -372,7 +371,7 @@ 
    Counterfactual g
 
    
 
    Explanations
    
 
    Once the model and counterfactual generator are specified, running counterfactual search is very easy using the package. For a given factual (x), target class (target) and data set (counterfactual_data), simply running
    
-
    
+
    
 
    generate_counterfactual(x, target, counterfactual_data, M, generic)
    
 
    
 
    will generate the results, in this case using the generic generator (generic) for the MLP (M). Since we have specified two different black-box models and two different counterfactual generators, we have four combinations of a model and a generator in total. For each of these combinations I have used the generate_counterfactual function to produce the results in Figure 1.
    
@@ -395,8 +394,8 @@ 
    Language interop
 
    
 
    Explaining a torch model
    
 
    We will consider a simple MLP trained for a binary classification task. As before we first need to adapt this custom model for use with our package. The code below the two necessary steps - sub-typing and method extension. Logits are returned by the torch model and copied from the R environment into the Julia scope. Probabilities are then computed inside the Julia scope by passing the logits through the sigmoid function.
    
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    using Flux
 using CounterfactualExplanations, CounterfactualExplanations.Models
@@ -434,8 +433,8 @@ 
    Explaining a You may have stumbled across the term respecify above: does it really seem like a good idea to just replace an existing function from our package? Surely not! There are certainly better ways to go about this, which we will consider when adding native support for Python and R models in future package releases. Which brings us to our final section …
    
 
    
 
    
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    import CounterfactualExplanations.Generators: ∂ℓ
 using LinearAlgebra
@@ -1015,7 +1014,7 @@ 
    Further reading 📚
    
   }
 });
 
-
 
     
diff --git a/docs/blog/posts/causal-recourse/index.html b/docs/blog/posts/causal-recourse/index.html
index 7b1005f..9418858 100644
--- a/docs/blog/posts/causal-recourse/index.html
+++ b/docs/blog/posts/causal-recourse/index.html
@@ -159,7 +159,6 @@
 
 
 
-
 
 
 
@@ -221,14 +220,16 @@ 
    On this page
    
   
  • Project Overview
   
    • 
+  
  • Usage
    • 
   
  • Conclusion
    • 
   
  • References
    • 
   
@@ -282,7 +283,13 @@ 
    On this page
    
 
 
    
 
    Introduction
    
-
    In recent years, the need for interpretable and explainable AI has surged, particularly in high-stakes domains. Counterfactual explanations provide a means to understand how changes to input features could alter the outcomes of machine learning models. This blog post presents a new tool in the CounterfactualExplanations.jl package, developed during my JSoC (Julia Summer of Code) project, which incorporates causal reasoning into counterfactual generation.
    
+
    In recent years, the need for interpretable and explainable AI has surged, particularly in high-stakes domains. Counterfactual explanations provide a means to understand how changes to input features could alter the outcomes of machine learning models. This blog post presents a new tool in the CounterfactualExplanations.jl package, developed during my JSoC (Julia Summer of Code) project, which incorporates causal reasoning into counterfactual generation.
    
+
    
+
    Testimonial
    
+
    
+
    This was an amazing experience, not just experience to contribute to two repositories simultaneously, but also to work with the mantainers of these repos. I learned a lot about the Julia language and the Julia community. This was possible because of the mentorship of Patrick Altmeyer (CounterfactualExplanations) and Moritz Schauer (CausalInference), who guided me throughout the project and are amazing researchers.
    
+
    
+
    
 
    
 
    
 
    Project Overview
    
@@ -291,18 +298,14 @@ 
    Project Overview
    
 
    Key Contributions
    
 
    During the project, I contributed to two key repositories:
    
 
      
-
    1. CounterfactualExplanations.jl: Developed a new tool for generating counterfactual explanations using causal information. This allows users to create smarter perturbations rather than random adjustments, ultimately providing more meaningful insights.
      2. 
-
    2. CausalInference.jl: Implemented a Structural Causal Model (SCM) structure that extracts information from data, laying the groundwork for the causal reasoning capabilities in CounterfactualExplanations.jl.
      3. 
+
    3. CounterfactualExplanations.jl: Developed a new tool for generating counterfactual explanations using causal information. This allows users to generate counterfactuals through causal interventions rather than minimal perturbations, ultimately providing more meaningful insights.
      4. 
+
    4. CausalInference.jl: Implemented a Structural Causal Model (SCM) structure that extracts information from data, laying the groundwork for the causal reasoning capabilities in CounterfactualExplanations.jl.
      5. 
 
    
-
    This was an amazing experience, not just experience contribute to two repositories simultaneously, but also to work with the mantainers of these repos. I learned a lot about the Julia language and the Julia community. This was possible because of the mentorship of Patrick Altmeyer (CounterfactualExplanations) and Moritz Schauer (CausalInference), who guided me throughout the project and are amazing researchers.
    
-
    
-
    
-
    The MINTGenerator
    
-
    In this project, we developed the MINTGenerator, a counterfactual generator based on the Recourse through Minimal Intervention (MINT) method proposed by Karimi, Schölkopf, and Valera (2021).
    
 
    
-
    
-
    Description
    
-
    The MINTGenerator incorporates causal reeasoning in algorithm recourse to achieve minimal interventions when generating a counterfactual explanation. In this sense, the main ideia is that just perturbating a black box model without taking into account the causal relations in the data can guide to misleading recommendations. Here we now shift to a perspective where every action/pertubation is an intervetion in the causal graph of the problem, thus the change is not made just in the intervened upon variable, but also in its childs in the causal structure. The generator utilizes a Structural Causal Model(SCM) to encode the variables in a way that causal effects are propagated and uses a generic gradient-based generator to create the search path, that is, any gradient-base generator (ECCo, REVISE, Watcher, …) can be used with the MINT SCM encoder to generate counterfactual samples in latent space for minimal intervetions algorithm recourse.
    
+
    
+
    Theoretical Background
    
+
    In this project, we developed a framework for the MINT Generator: a counterfactual generator based on the Recourse through Minimal Intervention (MINT) method proposed by Karimi, Schölkopf, and Valera (2021).
    
+
    The MINT Generator incorporates causal reasoning to achieve algorithmic recourse through minimal interventions. In this sense, the main idea is that just perturbating a black-box model without taking into account the causal relations in the data can lead to misleading recommendations. Here we now shift to a perspective where every feature pertubation is an intervetion in the causal graph of the problem. Leveraging causal relationships, interventions on causal parents automatially lead to potentially useful changes in their causal children. The generator utilizes a Structural Causal Model(SCM) to encode the variables in a way that causal effects are propagated and uses a generic gradient-based generator to create the search path. This has the benefit that any existing gradient-based generator, such as ECCo (Altmeyer et al. 2024), Watcher (Wachter, Mittelstadt, and Russell 2017), DiCE (Mothilal, Sharma, and Tan 2020), and more, can be used with the MINT SCM encoder to generate counterfactual through causal interventions.
    
 
    The MINT algorithm minimizes a loss function that combines the causal constraints of the SCM and the distance between the generated counterfactual and the original input. Since we want a gradient-based generator, we need to pass the constrained optimizaiton problem into an unconstrained one and we do this by using the Lagrangian. Initially, as defined in (Karimi, Schölkopf, and Valera 2021), we aim to aim to find the minimal cost set of actions \(A\) (in the form of structural interventions) that results in a counterfactual instance yielding the favorable output from \(h\),
    
 
    \[
 \begin{aligned}
@@ -333,9 +336,7 @@ 
    Description
    
 
    
 
    
 
    Implementation
    
-
    
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    CausalInference.jl
    
-
    In terms of implementation, we need to capture the causal relations from the data, that’s where CausalInference.jl comes in. However, before the project, the package did not have a SCM structure, in the sense that the methods just captured the topological Directed Acyclic Graph (DAG) that showed the causality ruling the data, that is, no causal structural equations were provided,
    
+
    As mentioned above, this project involved contributions to both CausalInference.jl and CounterfactualExplanations.jl. In this section, we will cover both of these. Before we begin, we load all necessary dependencies below:
    
 
    
 
    
 Code
@@ -348,90 +349,109 @@ 
    CausalInference.j
 using Plots
 using Random
 Random.seed!(1)
-using StatsBase
-
-N = 2000 # number of data points
-
-x = randn(N)
-v = x + randn(N)*0.25
-w = x + randn(N)*0.25
-z = v + w + randn(N)*0.25
-s = z + randn(N)*0.25
-
-df = (x=x, v=v, w=w, z=z, s=s)
-
-est_g, score = ges(df; penalty=1.0, parallel=true)
-
-plt = graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)], size=(500,500), nodesize=0.1, fontsize=25)
-savefig(plt, "www/intro.png")
-display(plt)
    
+using StatsBase
    
+
    
+
    
+
    
+
    Causal Inference
    
+
    In terms of implementation, we need to capture the causal relations from the data, which is where CausalInference.jl comes in. However, before the project, the package did not have a SCM structure, in the sense that the methods just captured the topological Directed Acyclic Graph (DAG) that showed the causality governing the data. There was previously no way to transform graphs into structural causal models.
    
+
    Consider the following synthetic data:
    
+
    
+
    
+Code
+
    N = 2000 # number of data points
+
+x = randn(N)
+v = x + randn(N)*0.25
+w = x + randn(N)*0.25
+z = v + w + randn(N)*0.25
+s = z + randn(N)*0.25
+df = (x=x, v=v, w=w, z=z, s=s)
    
+
    
+
    
+
    Using CausalInference.jl, we can use the ges method for the causal discovery (Chickering 2003) and plot the resulting DAG Figure 1:
    
+
    
+
    
+Code
+
    est_g, score = ges(df; penalty=1.0, parallel=true)
+
+plt = graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)], size=(500,500), nodesize=0.1, fontsize=25)
+savefig(plt, "www/intro.png")
+display(plt)
    
 
    
 
    
 
    ┌ Warning: Only one thread available
 └ @ CausalInference ~/.julia/packages/CausalInference/ozcj8/src/ges.jl:52
    
 
    
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+Figure 1: A simple example of a causal graph.
+
    
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    So, our goal was given the DAG provided by the ges method in the causal discovery (Chickering 2003), generate equations that rules each of these causal relations, represented in the DAG as directed edges. The SCM is the union of the DAG and these causal equations, that is, the SCM is a tuple \((G, \mathbf{f})\), where \(G\) is the DAG and \(\mathbf{f}\) is the set of functions that generates the value of each variable given its parents.
    
-
    Our solution for constructing the structural causal equations was to assume that the data was generated by a linear model, ie, the causal relations were linear. For the DAG provided in the code example we derive
    
+
    
+
    Given the DAG in Figure 1, our goal is to recover the equations that define the underlying causal relations. The SCM is the union of the DAG and these causal equations: formally, it can be represented as a tuple \((G, \mathbf{f})\), where \(G\) is the DAG and \(\mathbf{f}\) is the set of functions that generates the value of each variable given its parents.
    
+
    Our solution for constructing the structural causal equations was to assume that the data was generated by a linear model, which in this simple synthetic example actually corresponds to the ground truth. For the DAG provided in the code example we derive
    
 
    \[ v = \mathcal{b}_v \]
    
 
    \[ x = \mathcal{a}_{v \to x} v + \mathcal{b}_x \]
    
 
    \[ w = \mathcal{a}_{x \to w} x + \mathcal{b}_w \]
    
 
    \[ z = \mathcal{a}_{v \to z} v+ \mathcal{a}_{w \to z} w + \mathcal{b}_z \]
    
 
    \[ s = \mathcal{a}_{z \to s} z + \mathcal{b}_s \]
    
 
    and that’s the tricky thing, as we can see these causal equations are different than the ones that generated the data, but they are the ones that respect the causal system obtained from the obtained DAG. Here \(\mathcal{b}_i\) and \(\mathcal{a}_{i \to j}\) are the intercept term and the coefficient obtained from the linear regression, respectively. To correctly solve the linear regression respecting the dependencies of the causal graph, we use topological_sort_by_dfs from Graphs.jl.
    
-
    Now, with the SCM structure in hand, we see that the representation could be a struct containing the DAG and the coefficients/intercepts of the causal equations, this maps exactly the tuple \((G, \mathbf{f})\) that we defined. However, since we need these equations to be differentiable, we need to define a function that takes the SCM and returns the value of the variable given its parents and using just the coefficients and the DAG, lead to errors, because AutoDiff does not deal well with functions that are conditioned (if statements). So, we need to define a way to retrieve the system of causal equations in a smooth way and that’s where the causal_effects matrix comes to the rescue.
    
+
    Now, with the SCM structure at hand, we see that the representation could be a struct containing the DAG and the coefficients/intercepts of the causal equations, which corresponds exactly the tuple \((G, \mathbf{f})\) that we defined. A technical difficulty is that since we aim for gradient-based counterfactual generation, we need to define a differentiable function that takes the SCM and applies the encoded causal relationships to all variables. That is where the causal_effects matrix comes to the rescue.
    
 
    Let the factual vector of features be denoted as:
    
 
    \[
 \mathbf{x}_F =
@@ -490,55 +510,161 @@ 
    CausalInference.j
 \]
    
 
    This equation shows how each counterfactual variable \(x_{SCF_i}\) is generated as a linear combination of the factual inputs \(x_{F_j}\) based on the causal effects matrix, with an intercept term \(b_i\) added for each variable.
    
 
    One can note that the orphan nodes, that is, the nodes that do not have parents in the DAG, are going to be equal to the intercept term \(\mathcal{b}_\hat{o}\). The intuition behind this is that when we do the linear regression, variables that have no causal parents are just equal to the unconditional mean of the variable, i.e, we get \(x_{SCF_\hat{o}} = \mathbb{E}(x_\hat{o})\). Because of this, in some cases a better understanding of the regression is needed, so the residuals are also part of the SCM structure,
    
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+
    
 
    
 Code
-
    struct SCM
-    variables::Vector{String}
-    coefficients::Vector{Vector{Float64}}
-    residuals::Vector{Vector{Float64}}
-    dag::DiGraph
-    causal_effects::Matrix{Float64}
-end
    
+
    struct SCM
+    variables::Vector{String}
+    coefficients::Vector{Vector{Float64}}
+    residuals::Vector{Vector{Float64}}
+    dag::DiGraph
+    causal_effects::Matrix{Float64}
+end
    
 
    
 
    
 
    
 
    
 
    CounterfactualExplanations.jl
    
-
    Now, we need to go into the optimization problem previously described. We seek to minimize the lagrangian function we defined where now we have a differentiable function. The standard way to implement generators in CounterfactualExplanations.jl is to use AutoDiff exactly using composable functions in the lagrangian. The definition of \(\mathcal{L_{\texttt{MINT}}}\) is in the same shape of the the others gradient-based generators in the package, so the optimization is straightforward. However, we needed some way to pass the \(x_F\) into the \(x_{SCF}\) and that’s where transformer.jl comes in. This is where InputTransformers are defined in the package and in some way this is what we are doing, we are passing our factual to the “latent” causal space of the counterfactual. Our first step is to create a new kind of InputTransformer that is the SCM itself,
    
-
    
+
    Next, we will dive to go into the optimization problem previously described in Section 2.2. Recall that we seek to minimize the Lagrangian function we defined where we now have a differentiable function. The standard way to implement generators in CounterfactualExplanations.jl is to use autodifferentiation to solve this Lagrangian. The definition of \(\mathcal{L_{\texttt{MINT}}}\) above is just an unconstrained objective function, much like with any other gradient-based generator in the package, so the optimization is straightforward (see docs for more details on gradient-based generators).
    
+
    A challenge was to find a way to pass the \(x_F\) into the \(x_{SCF}\). For the time being, we have decided to extend an existing feature of the package, namely InputTransformers: they can be used to transform features, for example, through standardization. All existing InputTransformers work under the premise of encoding features into some latent representation, searching counterfactuals in that latent space, and finally decoding latent features back into the original feature space. In some way, this is also what we are doing here: we are passing our factual to the “latent” causal space of the counterfactual.
    
+
    Our first step is to create a new kind of InputTransformer for the SCM:
    
+
    
+
    
+Code
+
    const TypedInputTransformer = Union{
+    Type{<:StatsBase.AbstractDataTransform},
+    Type{<:MultivariateStats.AbstractDimensionalityReduction},
+    Type{<:GenerativeModels.AbstractGenerativeModel},
+    Type{<:CausalInference.SCM} # The SCM transfromer
+}
    
+
    
+
    
+
    Next, we need a way to actually apply train this transformer. This is done by “overloading” the fit_transformer method,
    
+
    
 
    
 Code
-
    const TypedInputTransformer = Union{
-    Type{<:StatsBase.AbstractDataTransform},
-    Type{<:MultivariateStats.AbstractDimensionalityReduction},
-    Type{<:GenerativeModels.AbstractGenerativeModel},
-    Type{<:CausalInference.SCM} # The SCM transfromer
-}
    
+
    function fit_transformer(
+    data::CounterfactualData, input_encoder::Type{<:CausalInference.SCM}; kwargs...
+)
+    t = Tables.table(transpose(data.X))
+    est_g, score = CausalInference.ges(t; penalty=1.0, parallel=true)
+    est_dag = CausalInference.pdag2dag!(est_g)
+    scm = CausalInference.estimate_equations(t, est_dag)
+    return scm
+end
    
 
    
 
    
-
    and then we need a way to create this transformer, that’s where we “overload” fit_transformer using CausalInferece.jl,
    
-
    
+
    which takes an input dataset and then relies on CausalInference.jl for causal discovery.
    
+
    We are getting there … but one implementation challenge is still left: how can we use the learned SCM during the counterfactual search?
    
+
    Our idea was simple: during each gradient-step, just apply the SCM to all features of the counterfactual. Implementation-wise, this boiled down to overloading the decode_array function, which handles the actual decoding step for all InputTransformers:
    
+
    
 
    
 Code
-
    function fit_transformer(
-    data::CounterfactualData, input_encoder::Type{<:CausalInference.SCM}; kwargs...
-)
-    t = Tables.table(transpose(data.X))
-    est_g, score = CausalInference.ges(t; penalty=1.0, parallel=true)
-    est_dag = CausalInference.pdag2dag!(est_g)
-    scm = CausalInference.estimate_equations(t, est_dag)
-    return scm
-end
    
+
    function decode_array(data::CounterfactualData, dt::CausalInference.SCM, x::AbstractArray)
+    return run_causal_effects(dt, x)
+end
+
+function run_causal_effects(scm::CausalInference.SCM, x::AbstractArray)
+    return scm.causal_effects[:, 1:(end - 1)] * x + scm.causal_effects[:, end] # bias
+end
    
 
    
 
    
-
    … We are getting there! However, now comes the hardest part, where this is placed?
    
+
    Here we are! Using this approach, gradient computations explicitly take the causal graph into account. We can now rely on standard workflows for gradient-based generators to solve a different minimization problem that incorporate causal effects.
    
+
    
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+
    
+
+
    
+
    
+Concrete Generator Type
+
    
+
    
+
    
+
    One piece that is still missing here is to implement a concrete generator type of the MINT Generator (#466). That will make it easier for users to use the MINT Generator in the same way as all of our other counterfactual generators. This step has been postponed, because it hinges on an a larger development task (#435).
    
+
    
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+
    Limitations and Future Work
    
+
    Altough the range of lines of code was not tremendous, the hard work was. The merged code does not show every research and development I was guided during this time by the mentors. For example, initially we were trying a different approach to work with differentiation inside the CounterfactualExplanations.jl package, where the code always broke 😅. But, without this obstacle, we could not have in mind a possible future work where the run_causal_effects function could be more flexible. For example, as we said, the variables without causal parents are been assigned just to the unconditional mean, but in terms of counterfactuals theory, maybe using just the factual feature would be more realistic. But to do this we would need to work in the causal_effects_matrix and this was part of my work creating transformable_features for the SCM where we would probably need to use ignore_derivatives() from Zygote.jl.
    
+
    
+
    
+Code
+
    function transformable_features(
+    counterfactual_data::CounterfactualData, input_encoder::Type{CausalInference.SCM}
+)
+    g = counterfactual_data.input_encoder.dag
+    child_causal_nodes = [v for v in vertices(g) if indegree(g, v) >= 1]
+    return child_causal_nodes
+end
    
+
    
+
    
+
    Another direction of future work is that the current implementation of the MINT Generator is limited to linear causal relations. One could extend this to non-linear causal relations, such as those found in neural networks. Additionally, the we could shift the paradigm to use Bayesian Inference to generate the causal equations. This work would be a new extension in CausalInference.jl.
    
+
    
+
    
+
    Github PRs and Issues
    
+
    In the following links, you can find the PRs and issues that were opened and closed during the project. They show some kind of history of the work developed:
    
+
    Causal Inference:
    
+
+
    CounterfactualExplanations:
    
+
+
    And one that still open:
    
+
 
    
 
    
+
    
+
    Usage
    
+
    The MINT algorithm can be implemented using the GenericGenerator and the SCM encoder, that we implement using CausalInference.jl package. The following code snippet shows how to use the MINT algorithm to generate counterfactuals using any gradient-based generator:
    
+
    
+
    
+Code
+
    using CausalInference
+using CounterfactualExplanations
+using CounterfactualExplanations.DataPreprocessing: fit_transformer
+using Tables
+
+N = 2000
+df = (
+    x = randn(N), 
+    v = randn(N) .^ 2 + randn(N) * 0.25, 
+    w = cos.(randn(N)) + randn(N) * 0.25, 
+    z = randn(N) .^ 2 + cos.(randn(N)) + randn(N) * 0.25 + randn(N) * 0.25, 
+    s = sin.(randn(N) .^ 2 + cos.(randn(N)) + randn(N) * 0.25 + randn(N) * 0.25) + randn(N) * 0.25
+)
+y_lab = rand(0:2, N)
+counterfactual_data_scm = CounterfactualData(Tables.matrix(df; transpose=true), y_lab)
+
+M = fit_model(counterfactual_data_scm, :Linear)
+chosen = rand(findall(predict_label(M, counterfactual_data_scm) .== 1))
+x = select_factual(counterfactual_data_scm, chosen)
+
+data_scm = deepcopy(counterfactual_data_scm)
+data_scm.input_encoder = fit_transformer(data_scm, CausalInference.SCM)
+
+ce = generate_counterfactual(x, 2, data_scm, M, GenericGenerator(); initialization=:identity)
    
+
    
+
    
+
    For further usage reference access the MINT official documentation.
    
 
    
 
    
 
    Conclusion
    
-
+
    During this project, I had the opportunity to contribute to both the XAI and Julia communities, where I implemented a SOTA method that used causal information to generate counterfactual explanations (Karimi, Schölkopf, and Valera 2021). It was an amazing experience to work with incredible mentors and the community. I would like to once again thank Patrick and Moritz for all their guidance, as well as Jacob Zelko and JuliaHUB for all their support. I learned a lot about the Julia language and the Julia community, and I witnessed firsthand the benefits of Open Source. In fact, it was Open Source that made it possible to contribute to two repositories simultaneously. This experience of working locally on CounterfactualExplanations.jl and CausalInference.jl was invaluable, as it allowed me to truly understand how things work under the hood.
    
+
    I hope that the MINT Generator can be useful to the community and that the package continues to be improved in the future. Contributing to a more trustworthy Artificial Intelligence has always been a goal of mine, and even though my contribution may be small, I feel proud to have achieved something meaningful. My wish is to continue contributing to the responsible use of AI. I am very grateful for this opportunity, and I look forward to continuing to contribute to the community. 🚀🚀🚀
    
 
    
 
    
 
@@ -550,22 +676,31 @@ 
    Conclusion
    
 
    
 
 
    References
    
+
    
+Altmeyer, Patrick, Mojtaba Farmanbar, Arie van Deursen, and Cynthia CS Liem. 2024. “Faithful Model Explanations Through Energy-Constrained Conformal Counterfactuals.” In Proceedings of the AAAI Conference on Artificial Intelligence, 38:10829–37. 10.
+
    
 
    
 Chickering, David Maxwell. 2003. “Optimal Structure Identification with Greedy Search.” J. Mach. Learn. Res. 3 (null): 507–54. https://doi.org/10.1162/153244303321897717.
 
    
 
    
 Karimi, Amir-Hossein, Bernhard Schölkopf, and Isabel Valera. 2021. “Algorithmic Recourse: From Counterfactual Explanations to Interventions.” In Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency, 353–62. FAccT ’21. New York, NY, USA: Association for Computing Machinery. https://doi.org/10.1145/3442188.3445899.
 
    
-
    Citation
    BibTeX citation:
    @online{altmeyer2024,
-  author = {Altmeyer, Patrick and Luiz Franco, Jorge},
+
    
+Mothilal, Ramaravind K, Amit Sharma, and Chenhao Tan. 2020. “Explaining Machine Learning Classifiers Through Diverse Counterfactual Explanations.” In Proceedings of the 2020 Conference on Fairness, Accountability, and Transparency, 607–17. https://doi.org/10.1145/3351095.3372850.
+
    
+
    
+Wachter, Sandra, Brent Mittelstadt, and Chris Russell. 2017. “Counterfactual Explanations Without Opening the Black Box: Automated Decisions and the GDPR.” Harv. JL & Tech. 31: 841. https://doi.org/10.2139/ssrn.3063289.
+
    
+
    Citation
    BibTeX citation:
    @online{luiz_franco2024,
+  author = {Luiz Franco, Jorge},
   title = {When {Causality} Meets {Recourse}},
   date = {2024-09-17},
   url = {https://www.taija.org/blog/posts/causal-recourse/},
   langid = {en}
 }
-
    For attribution, please cite this work as:
    
-Altmeyer, Patrick, and Jorge Luiz Franco. 2024. “When Causality
-Meets Recourse.” September 17, 2024. https://www.taija.org/blog/posts/causal-recourse/.
+
    For attribution, please cite this work as:
    +Luiz Franco, Jorge. 2024. “When Causality Meets Recourse.” +September 17, 2024. https://www.taija.org/blog/posts/causal-recourse/.
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a/docs/blog/posts/conformal-image-classifier/index.html b/docs/blog/posts/conformal-image-classifier/index.html index 79798a7..6ca6ed5 100644 --- a/docs/blog/posts/conformal-image-classifier/index.html +++ b/docs/blog/posts/conformal-image-classifier/index.html @@ -159,7 +159,6 @@ - @@ -252,7 +251,7 @@

    On this page

    Affiliation
    -

    Patrick Altmeyer

    +

    Patrick Altmeyer

    @@ -296,7 +295,7 @@

    On this page

    🎯 The Task at Hand

    The task at hand is to predict the labels of handwritten images of digits using the famous MNIST dataset (LeCun 1998). Importing this popular machine learning dataset in Julia is made remarkably easy through MLDatasets.jl:

    -
    +
    Code 
    using MLDatasets
 N = 1000
@@ -307,7 +306,7 @@ 
    🎯 The Task at Hand
    
 
    Figure 1 below shows a few random samples from the training data:
    
 
    
-
    
+
    
 Code
 
    using MLJ
 using Images
@@ -320,7 +319,7 @@ 
    🎯 The Task at Hand
    
 
    
 
    
-
+
 
    
 
    
 Figure 1: Random samples from the MNIST dataset.
@@ -334,7 +333,7 @@ 
    🚧 Building the Net
 
    To model the mapping from image inputs to labels will rely on a simple Multi-Layer Perceptron (MLP). A great Julia library for Deep Learning is Flux.jl. But wait … doesn’t ConformalPrediction.jl work with models trained in MLJ.jl? That’s right, but fortunately there exists a Flux.jl interface to MLJ.jl, namely MLJFlux.jl. The interface is still in its early stages, but already very powerful and easily accessible for anyone (like myself) who is used to building Neural Networks in Flux.jl.
    
 
    In Flux.jl, you could build an MLP for this task as follows,
    
 
    
-
    
+
    
 Code
 
    using Flux
 
@@ -348,7 +347,7 @@ 
    🚧 Building the Net
 
    where (28,28) is just the input dimension (28x28 pixel images). Since we have ten digits, our output dimension is ten.1
    
 
    We can do the exact same thing in MLJFlux.jl as follows,
    
 
    
-
    
+
    
 Code
 
    using MLJFlux
 
@@ -361,7 +360,7 @@ 
    🚧 Building the Net
 
    
 
    where here we rely on the @builder macro to make the transition from Flux.jl to MLJ.jl as seamless as possible. Finally, MLJFlux.jl already comes with a number of helper functions to define plain-vanilla networks. In this case, we will use the ImageClassifier with our custom builder and cross-entropy loss:
    
 
    
-
    
+
    
 Code
 
    ImageClassifier = @load ImageClassifier
 clf = ImageClassifier(
@@ -373,7 +372,7 @@ 
    🚧 Building the Net
 
    
 
    The generated instance clf is a model (in the MLJ.jl sense) so from this point on we can rely on standard MLJ.jl workflows. For example, we can wrap our model in data to create a machine and then evaluate it on a holdout set as follows:
    
 
    
-
    
+
    
 Code
 
    mach = machine(clf, X, y)
 
@@ -391,7 +390,7 @@ 
    🚧 Building the Net
 
    🔥 Conformalizing the Network
    
 
    Since clf is a model, it is also compatible with our package: ConformalPrediction.jl. To conformalize our MLP, we therefore only need to call conformal_model(clf). Since the generated instance conf_model is also just a model, we can still rely on standard MLJ.jl workflows. Below we first wrap it in data and then fit it. Aaaand … we’re done! Let’s look at the results in the next section.
    
 
    
-
    
+
    
 Code
 
    using ConformalPrediction
 conf_model = conformal_model(clf; method=:simple_inductive, coverage=.95)
@@ -416,27 +415,27 @@ 
    📊 Results
    
 
 
 
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 📊 Results
    
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+" transform="translate(118, 47)">
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+  
+    
+  
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+
+📊 Results
    
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-
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transform="translate(1318, 47)"> - - - - - - - - - - +
    (a) Randomly selected prediction sets of size \(|C|=1\). @@ -824,157 +825,166 @@

    📊 Results

    - + - + - + - + - + - + - + - + - + 📊 Results

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    iAEAAEgSxAAAACQJYgAAAJIEMQAAAEmCGAAAgCRBDAAAQJIgBgAAIEkQAwAAkCSIAQAASBLEAAAA JAliAAAAkgQxAAAASYIYAACAJEEMAABAkiAGAAAgSRADAACQJIgBAABIEsQAAAAkCWIAAACSBDEA AABJghgAAIAkQQwAAECSIAYAACBJEAMAAJAkiAEAAEgSxAAAACQJYgAAAJIEMQAAAEmCGAAAgCRB -DAAAQJIgBgAAIEkQAwAAkCSIAQAASBLEAAAAJAliAAAAkgQxAAAASYIYAACAJEEMAABAkiAGAAAg -SRADAACQJIgBAABIEsQAAAAkCWIAAACSBDEAAABJghgAAIAkQQwAAECSIAYAACBJEAMAAJAkiAEA -AEgSxAAAACQJYgAAAJIEMQAAAEmCGAAAgCRBDAAAQJIgBgAAIEkQAwAAkCSIAQAASBLEAAAAJAli -AAAAkgQxAAAASYIYAACAJEEMAABAkiAGAAAgSRADAACQJIgBAABIEsQAAAAkCWIAAACSBDEAAABJ -ghgAAIAkQQwAAECSIAYAACBJEAMAAJAkiAEAAEgSxAAAACQJYgAAAJIEMQAAAEmCGAAAgCRBDAAA -QNI6PQAAAJ5br746vWDz8cfTC5aj11+fnnBh99ln0xP2fvppegF/wYUYAACAJEEMAABAkiAGAAAg -SRADAACQJIgBAABIEsQAAAAkCWIAAACSBDEAAABJghgAAIAkQQwAAECSIAYAACBJEAMAAJAkiAEA -AEgSxAAAACQJYgAAAJIEMQAAAEmCGAAAgCRBDAAAQJIgBgAAIEkQAwAAkCSIAQAASBLEAAAAJAli -AAAAkgQxAAAASYIYAACAJEEMAABAkiAGAAAgSRADAACQJIgBAABIEsQAAAAkCWIAAACSBDEAAABJ -6/QAAAD42y5fnl6w9+mn0ws2V69OL1h2jx9PT9j8+uv0Ap4DLsQAAAAkCWIAAACSBDEAAABJghgA +DAAAQJIgBgAAIEkQAwAAkCSIAQAASBLEAAAAJAliAAAAkgQxAAAASYIYAACApH8DA1CrS+fsAJ8A +AAAASUVORK5CYII= +" transform="translate(1318, 47)"> +

    Counterfact

    Black-box models

    The code below loads relevant packages along with the MNIST data and pre-trained models.

    -
    +
    # Load package, models and data:
 using CounterfactualExplanations, Flux
 using CounterfactualExplanations.Data: mnist_data, mnist_model, mnist_ensemble
@@ -185,7 +185,7 @@ 
    Black-box models
    
 
  • Multiple dispatch: the package-internal functions logits and probs need to be extended through custom methods for the new model type.
    • 
 
 
    The following code implements these two steps first for the MLP and then for the deep ensemble.
    
-
    
+
    
 
    using CounterfactualExplanations.Models
 import CounterfactualExplanations.Models: logits, probs
 # MLP:
@@ -216,7 +216,7 @@ 
    Counterfactual g
 
    Next, we need to specify the counterfactual generators we want to use. The package currently ships with two default generators that both need gradient access: firstly, the generic generator introduced by @wachter2017counterfactual and, secondly, a greedy generator introduced by @schut2021generating.
    
 
    The greedy generator is designed to be used with models that incorporate uncertainty in their predictions such as the deep ensemble introduced above. It works for probabilistic (Bayesian) models, because they only produce high-confidence predictions in regions of the feature domain that are populated by training samples. As long as the model is expressive enough and well-specified, counterfactuals in these regions will always be realistic and unambiguous since by construction they should look very similar to training samples. Other popular approaches to counterfactual explanations like REVISE [@joshi2019realistic] and CLUE [@antoran2020getting] also play with this simple idea.
    
 
    The following code instantiates the two generators for the problem at hand.
    
-
    
+
    
 
    generic = GenericGenerator(;loss=:logitcrossentropy)
 greedy = GreedyGenerator(;loss=:logitcrossentropy)
    
 
    
@@ -224,7 +224,7 @@ 
    Counterfactual g
 
    
 
    Explanations
    
 
    Once the model and counterfactual generator are specified, running counterfactual search is very easy using the package. For a given factual (x), target class (target) and data set (counterfactual_data), simply running
    
-
    
+
    
 
    generate_counterfactual(x, target, counterfactual_data, M, generic)
    
 
    
 
    will generate the results, in this case using the generic generator (generic) for the MLP (M). Since we have specified two different black-box models and two different counterfactual generators, we have four combinations of a model and a generator in total. For each of these combinations I have used the generate_counterfactual function to produce the results in Figure 1.
    
@@ -247,7 +247,7 @@ 
    Language interop
 
    
 
    Explaining a torch model
    
 
    We will consider a simple MLP trained for a binary classification task. As before we first need to adapt this custom model for use with our package. The code below the two necessary steps - sub-typing and method extension. Logits are returned by the torch model and copied from the R environment into the Julia scope. Probabilities are then computed inside the Julia scope by passing the logits through the sigmoid function.
    
-
    
+
    
 
    using Flux
 using CounterfactualExplanations, CounterfactualExplanations.Models
 import CounterfactualExplanations.Models: logits, probs # import functions in order to extend
@@ -283,7 +283,7 @@ 
    Explaining a You may have stumbled across the term respecify above: does it really seem like a good idea to just replace an existing function from our package? Surely not! There are certainly better ways to go about this, which we will consider when adding native support for Python and R models in future package releases. Which brings us to our final section …
    
 
    
 
    
-
    
+
    
 
    import CounterfactualExplanations.Generators: ∂ℓ
 using LinearAlgebra
 
diff --git a/profile/blog/posts/causal-recourse/bib.bib b/profile/blog/posts/causal-recourse/bib.bib
new file mode 100644
index 0000000..29127ef
--- /dev/null
+++ b/profile/blog/posts/causal-recourse/bib.bib
@@ -0,0 +1,3464 @@
+@Article{ges2003,
+author = {Chickering, David Maxwell},
+title = {Optimal structure identification with greedy search},
+year = {2003},
+issue_date = {3/1/2003},
+publisher = {JMLR.org},
+volume = {3},
+number = {null},
+issn = {1532-4435},
+url = {https://doi.org/10.1162/153244303321897717},
+doi = {10.1162/153244303321897717},
+abstract = {In this paper we prove the so-called "Meek Conjecture". In particular, we show that if a DAG H is an independence map of another DAG G, then there exists a finite sequence of edge additions and covered edge reversals in G such that (1) after each edge modification H remains an independence map of G and (2) after all modifications G =H. As shown by Meek (1997), this result has an important consequence for Bayesian approaches to learning Bayesian networks from data: in the limit of large sample size, there exists a two-phase greedy search algorithm that---when applied to a particular sparsely-connected search space---provably identifies a perfect map of the generative distribution if that perfect map is a DAG. We provide a new implementation of the search space, using equivalence classes as states, for which all operators used in the greedy search can be scored efficiently using local functions of the nodes in the domain. Finally, using both synthetic and real-world datasets, we demonstrate that the two-phase greedy approach leads to good solutions when learning with finite sample sizes.},
+journal = {J. Mach. Learn. Res.},
+month = {mar},
+pages = {507–554},
+numpages = {48}
+}
+
+@InProceedings{karimi2021,
+author = {Karimi, Amir-Hossein and Sch\"{o}lkopf, Bernhard and Valera, Isabel},
+title = {Algorithmic Recourse: from Counterfactual Explanations to Interventions},
+year = {2021},
+isbn = {9781450383097},
+publisher = {Association for Computing Machinery},
+address = {New York, NY, USA},
+url = {https://doi.org/10.1145/3442188.3445899},
+doi = {10.1145/3442188.3445899},
+abstract = {As machine learning is increasingly used to inform consequential decision-making (e.g., pre-trial bail and loan approval), it becomes important to explain how the system arrived at its decision, and also suggest actions to achieve a favorable decision. Counterfactual explanations -"how the world would have (had) to be different for a desirable outcome to occur"- aim to satisfy these criteria. Existing works have primarily focused on designing algorithms to obtain counterfactual explanations for a wide range of settings. However, it has largely been overlooked that ultimately, one of the main objectives is to allow people to act rather than just understand. In layman's terms, counterfactual explanations inform an individual where they need to get to, but not how to get there. In this work, we rely on causal reasoning to caution against the use of counterfactual explanations as a recommendable set of actions for recourse. Instead, we propose a shift of paradigm from recourse via nearest counterfactual explanations to recourse through minimal interventions, shifting the focus from explanations to interventions.},
+booktitle = {Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency},
+pages = {353–362},
+numpages = {10},
+keywords = {algorithmic recourse, causal inference, consequential recommendations, contrastive explanations, counterfactual explanations, explainable artificial intelligence, minimal interventions},
+location = {Virtual Event, Canada},
+series = {FAccT '21}
+}
+
+@Book{pearl2009book,
+author = {Pearl, Judea},
+title = {Causality: Models, Reasoning and Inference},
+year = {2009},
+isbn = {052189560X},
+publisher = {Cambridge University Press},
+address = {USA},
+edition = {2nd},
+abstract = {Written by one of the preeminent researchers in the field, this book provides a comprehensive exposition of modern analysis of causation. It shows how causality has grown from a nebulous concept into a mathematical theory with significant applications in the fields of statistics, artificial intelligence, economics, philosophy, cognitive science, and the health and social sciences. Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections and statistical associations. The book will open the way for including causal analysis in the standard curricula of statistics, artificial intelligence, business, epidemiology, social sciences, and economics. Students in these fields will find natural models, simple inferential procedures, and precise mathematical definitions of causal concepts that traditional texts have evaded or made unduly complicated. The first edition of Causality has led to a paradigmatic change in the way that causality is treated in statistics, philosophy, computer science, social science, and economics. Cited in more than 3,000 scientific publications, it continues to liberate scientists from the traditional molds of statistical thinking. In this revised edition, Judea Pearl elucidates thorny issues, answers readers' questions, and offers a panoramic view of recent advances in this field of research. Causality will be of interests to students and professionals in a wide variety of fields. Anyone who wishes to elucidate meaningful relationships from data, predict effects of actions and policies, assess explanations of reported events, or form theories of causal understanding and causal speech will find this book stimulating and invaluable.}
+}
+
+@TechReport{xu2022conformal,
+  author      = {Xu, Chen and Xie, Yao},
+  date        = {2022-06},
+  institution = {arXiv},
+  title       = {Conformal prediction set for time-series},
+  doi         = {10.48550/arXiv.2206.07851},
+  note        = {arXiv:2206.07851 [cs, stat] type: article},
+  url         = {http://arxiv.org/abs/2206.07851},
+  urldate     = {2023-07-22},
+  abstract    = {When building either prediction intervals for regression (with real-valued response) or prediction sets for classification (with categorical responses), uncertainty quantification is essential to studying complex machine learning methods. In this paper, we develop Ensemble Regularized Adaptive Prediction Set (ERAPS) to construct prediction sets for time-series (with categorical responses), based on the prior work of [Xu and Xie, 2021]. In particular, we allow unknown dependencies to exist within features and responses that arrive in sequence. Method-wise, ERAPS is a distribution-free and ensemble-based framework that is applicable for arbitrary classifiers. Theoretically, we bound the coverage gap without assuming data exchangeability and show asymptotic set convergence. Empirically, we demonstrate valid marginal and conditional coverage by ERAPS, which also tends to yield smaller prediction sets than competing methods.},
+  annotation  = {Comment: Strongly accepted by the Workshop on Distribution-Free Uncertainty Quantification at ICML 2022},
+  file        = {arXiv Fulltext PDF:https\://arxiv.org/pdf/2206.07851.pdf:application/pdf},
+  keywords    = {Statistics - Machine Learning, Computer Science - Machine Learning, Statistics - Methodology},
+}
+
+@Article{kingma2014adam,
+  author  = {Kingma, Diederik P and Ba, Jimmy},
+  title   = {Adam: A method for stochastic optimization},
+  journal = {arXiv preprint arXiv:1412.6980},
+  year    = {2014},
+}
+
+@Misc{xiao2017fashion,
+  author        = {Han Xiao and Kashif Rasul and Roland Vollgraf},
+  title         = {Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms},
+  eprint        = {1708.07747},
+  archiveprefix = {arXiv},
+  primaryclass  = {cs.LG},
+  year          = {2017},
+}
+
+@Online{mw2023fidelity,
+  author       = {Merriam-Webster},
+  title        = {"Fidelity"},
+  url          = {https://www.merriam-webster.com/dictionary/fidelity},
+  language     = {en},
+  organization = {Merriam-Webster},
+  urldate      = {2023-03-23},
+  abstract     = {the quality or state of being faithful; accuracy in details : exactness; the degree to which an electronic device (such as a record player, radio, or television) accurately reproduces its effect (such as sound or picture)… See the full definition},
+}
+
+@InProceedings{altmeyer2023endogenous,
+  author       = {Altmeyer, Patrick and Angela, Giovan and Buszydlik, Aleksander and Dobiczek, Karol and van Deursen, Arie and Liem, Cynthia CS},
+  booktitle    = {2023 IEEE Conference on Secure and Trustworthy Machine Learning (SaTML)},
+  title        = {Endogenous Macrodynamics in Algorithmic Recourse},
+  organization = {IEEE},
+  pages        = {418--431},
+  year         = {2023},
+}
+
+%% This BibTeX bibliography file was created using BibDesk.
+%% https://bibdesk.sourceforge.io/
+
+%% Created for Patrick Altmeyer at 2022-12-13 12:58:22 +0100 
+
+
+%% Saved with string encoding Unicode (UTF-8) 
+
+
+
+@Article{abadie2002instrumental,
+  author        = {Abadie, Alberto and Angrist, Joshua and Imbens, Guido},
+  title         = {Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings},
+  doi           = {10.2139/ssrn.195733},
+  number        = {1},
+  pages         = {91--117},
+  volume        = {70},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Econometrica : journal of the Econometric Society},
+  shortjournal  = {Econometrica},
+  year          = {2002},
+}
+
+@Article{abadie2003economic,
+  author        = {Abadie, Alberto and Gardeazabal, Javier},
+  title         = {The Economic Costs of Conflict: {{A}} Case Study of the {{Basque Country}}},
+  number        = {1},
+  pages         = {113--132},
+  volume        = {93},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {American economic review},
+  year          = {2003},
+}
+
+@InProceedings{ackerman2021machine,
+  author        = {Ackerman, Samuel and Dube, Parijat and Farchi, Eitan and Raz, Orna and Zalmanovici, Marcel},
+  booktitle     = {2021 {{IEEE}}/{{ACM Third International Workshop}} on {{Deep Learning}} for {{Testing}} and {{Testing}} for {{Deep Learning}} ({{DeepTest}})},
+  title         = {Machine {{Learning Model Drift Detection Via Weak Data Slices}}},
+  doi           = {10.1109/deeptest52559.2021.00007},
+  pages         = {1--8},
+  publisher     = {{IEEE}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2021},
+}
+
+@Article{allen2017referencedependent,
+  author        = {Allen, Eric J and Dechow, Patricia M and Pope, Devin G and Wu, George},
+  title         = {Reference-Dependent Preferences: {{Evidence}} from Marathon Runners},
+  doi           = {10.3386/w20343},
+  number        = {6},
+  pages         = {1657--1672},
+  volume        = {63},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Management Science},
+  year          = {2017},
+}
+
+@Article{altmeyer2018option,
+  author        = {Altmeyer, Patrick and Grapendal, Jacob Daniel and Pravosud, Makar and Quintana, Gand Derry},
+  title         = {Option Pricing in the {{Heston}} Stochastic Volatility Model: An Empirical Evaluation},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2018},
+}
+
+@Article{altmeyer2021deep,
+  author        = {Altmeyer, Patrick and Agusti, Marc and Vidal-Quadras Costa, Ignacio},
+  title         = {Deep {{Vector Autoregression}} for {{Macroeconomic Data}}},
+  url           = {https://thevoice.bse.eu/wp-content/uploads/2021/07/ds21-project-agusti-et-al.pdf},
+  bdsk-url-1    = {https://thevoice.bse.eu/wp-content/uploads/2021/07/ds21-project-agusti-et-al.pdf},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2021},
+}
+
+@Book{altmeyer2021deepvars,
+  author        = {Altmeyer, Patrick},
+  title         = {Deepvars: {{Deep Vector Autoregession}}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2021},
+}
+
+@Misc{altmeyer2022counterfactualexplanations,
+  author        = {Altmeyer, Patrick},
+  title         = {{{CounterfactualExplanations}}.Jl - a {{Julia}} Package for {{Counterfactual Explanations}} and {{Algorithmic Recourse}}},
+  url           = {https://github.com/pat-alt/CounterfactualExplanations.jl},
+  bdsk-url-1    = {https://github.com/pat-alt/CounterfactualExplanations.jl},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2022},
+}
+
+@Software{altmeyerCounterfactualExplanationsJlJulia2022,
+  author        = {Altmeyer, Patrick},
+  title         = {{{CounterfactualExplanations}}.Jl - a {{Julia}} Package for {{Counterfactual Explanations}} and {{Algorithmic Recourse}}},
+  url           = {https://github.com/pat-alt/CounterfactualExplanations.jl},
+  version       = {0.1.2},
+  bdsk-url-1    = {https://github.com/pat-alt/CounterfactualExplanations.jl},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2022},
+}
+
+@Misc{angelopoulos2021gentle,
+  author        = {Anastasios N. Angelopoulos and Stephen Bates},
+  title         = {A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification},
+  eprint        = {2107.07511},
+  archiveprefix = {arXiv},
+  primaryclass  = {cs.LG},
+  year          = {2022},
+}
+
+@Misc{angelopoulos2022uncertainty,
+  author        = {Angelopoulos, Anastasios and Bates, Stephen and Malik, Jitendra and Jordan, Michael I.},
+  title         = {Uncertainty {{Sets}} for {{Image Classifiers}} Using {{Conformal Prediction}}},
+  eprint        = {2009.14193},
+  eprinttype    = {arxiv},
+  abstract      = {Convolutional image classifiers can achieve high predictive accuracy, but quantifying their uncertainty remains an unresolved challenge, hindering their deployment in consequential settings. Existing uncertainty quantification techniques, such as Platt scaling, attempt to calibrate the network's probability estimates, but they do not have formal guarantees. We present an algorithm that modifies any classifier to output a predictive set containing the true label with a user-specified probability, such as 90\%. The algorithm is simple and fast like Platt scaling, but provides a formal finite-sample coverage guarantee for every model and dataset. Our method modifies an existing conformal prediction algorithm to give more stable predictive sets by regularizing the small scores of unlikely classes after Platt scaling. In experiments on both Imagenet and Imagenet-V2 with ResNet-152 and other classifiers, our scheme outperforms existing approaches, achieving coverage with sets that are often factors of 5 to 10 smaller than a stand-alone Platt scaling baseline.},
+  archiveprefix = {arXiv},
+  bdsk-url-1    = {http://arxiv.org/abs/2009.14193},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  file          = {:/Users/FA31DU/Zotero/storage/5BYIRBR2/Angelopoulos et al. - 2022 - Uncertainty Sets for Image Classifiers using Confo.pdf:;:/Users/FA31DU/Zotero/storage/2QJAKFKV/2009.html:},
+  keywords      = {Computer Science - Computer Vision and Pattern Recognition, Mathematics - Statistics Theory, Statistics - Machine Learning},
+  month         = sep,
+  number        = {arXiv:2009.14193},
+  primaryclass  = {cs, math, stat},
+  publisher     = {{arXiv}},
+  year          = {2022},
+}
+
+@Article{angelucci2009indirect,
+  author        = {Angelucci, Manuela and De Giorgi, Giacomo},
+  title         = {Indirect Effects of an Aid Program: How Do Cash Transfers Affect Ineligibles' Consumption?},
+  doi           = {10.1257/aer.99.1.486},
+  number        = {1},
+  pages         = {486--508},
+  volume        = {99},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {American economic review},
+  year          = {2009},
+}
+
+@Article{angrist1990lifetime,
+  author        = {Angrist, Joshua D},
+  title         = {Lifetime Earnings and the {{Vietnam}} Era Draft Lottery: Evidence from Social Security Administrative Records},
+  pages         = {313--336},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {The American Economic Review},
+  year          = {1990},
+}
+
+@Unpublished{antoran2020getting,
+  author        = {Antor{\'a}n, Javier and Bhatt, Umang and Adel, Tameem and Weller, Adrian and Hern{\'a}ndez-Lobato, Jos{\'e} Miguel},
+  title         = {Getting a Clue: {{A}} Method for Explaining Uncertainty Estimates},
+  archiveprefix = {arXiv},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  eprint        = {2006.06848},
+  eprinttype    = {arxiv},
+  year          = {2020},
+}
+
+@Article{arcones1992bootstrap,
+  author        = {Arcones, Miguel A and Gine, Evarist},
+  title         = {On the Bootstrap of {{U}} and {{V}} Statistics},
+  pages         = {655--674},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {The Annals of Statistics},
+  year          = {1992},
+}
+
+@Article{ariely2003coherent,
+  author        = {Ariely, Dan and Loewenstein, George and Prelec, Drazen},
+  title         = {``{{Coherent}} Arbitrariness'': {{Stable}} Demand Curves without Stable Preferences},
+  doi           = {10.1017/cbo9780511618031.014},
+  number        = {1},
+  pages         = {73--106},
+  volume        = {118},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {The Quarterly journal of economics},
+  year          = {2003},
+}
+
+@Article{ariely2006tom,
+  author        = {Ariely, Dan and Loewenstein, George and Prelec, Drazen},
+  title         = {Tom {{Sawyer}} and the Construction of Value},
+  doi           = {10.1017/cbo9780511618031.015},
+  number        = {1},
+  pages         = {1--10},
+  volume        = {60},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of Economic Behavior \& Organization},
+  year          = {2006},
+}
+
+@Article{arrieta2020explainable,
+  author        = {Arrieta, Alejandro Barredo and Diaz-Rodriguez, Natalia and Del Ser, Javier and Bennetot, Adrien and Tabik, Siham and Barbado, Alberto and Garcia, Salvador and Gil-Lopez, Sergio and Molina, Daniel and Benjamins, Richard and others},
+  title         = {Explainable {{Artificial Intelligence}} ({{XAI}}): {{Concepts}}, Taxonomies, Opportunities and Challenges toward Responsible {{AI}}},
+  doi           = {10.1016/j.inffus.2019.12.012},
+  pages         = {82--115},
+  volume        = {58},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Information Fusion},
+  year          = {2020},
+}
+
+@Article{auer2002finitetime,
+  author        = {Auer, Peter and Cesa-Bianchi, Nicolo and Fischer, Paul},
+  title         = {Finite-Time Analysis of the Multiarmed Bandit Problem},
+  number        = {2},
+  pages         = {235--256},
+  volume        = {47},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Machine learning},
+  year          = {2002},
+}
+
+@Article{barabasi2016network,
+  author        = {Barab{\'a}si, Albert-L{\'a}szl{\'o}},
+  title         = {Network {{Science}}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Network Science},
+  year          = {2016},
+}
+
+@Unpublished{bastounis2021mathematics,
+  author        = {Bastounis, Alexander and Hansen, Anders C and Vla{\v c}i{\'c}, Verner},
+  title         = {The Mathematics of Adversarial Attacks in {{AI}}--{{Why}} Deep Learning Is Unstable despite the Existence of Stable Neural Networks},
+  archiveprefix = {arXiv},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  eprint        = {2109.06098},
+  eprinttype    = {arxiv},
+  year          = {2021},
+}
+
+@Article{bechara1997deciding,
+  author        = {Bechara, Antoine and Damasio, Hanna and Tranel, Daniel and Damasio, Antonio R},
+  title         = {Deciding Advantageously before Knowing the Advantageous Strategy},
+  doi           = {10.7551/mitpress/3077.003.0044},
+  number        = {5304},
+  pages         = {1293--1295},
+  volume        = {275},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Science (New York, N.Y.)},
+  shortjournal  = {Science},
+  year          = {1997},
+}
+
+@Book{berlinet2011reproducing,
+  author        = {Berlinet, Alain and Thomas-Agnan, Christine},
+  title         = {Reproducing Kernel {{Hilbert}} Spaces in Probability and Statistics},
+  doi           = {10.1007/978-1-4419-9096-9},
+  publisher     = {{Springer Science \& Business Media}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2011},
+}
+
+@Misc{bernanke1990federal,
+  author        = {Bernanke, Ben S},
+  title         = {The Federal Funds Rate and the Channels of Monetary Transnission},
+  doi           = {10.3386/w3487},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  publisher     = {{National Bureau of Economic Research Cambridge, Mass., USA}},
+  year          = {1990},
+}
+
+@Article{besbes2014stochastic,
+  author        = {Besbes, Omar and Gur, Yonatan and Zeevi, Assaf},
+  title         = {Stochastic Multi-Armed-Bandit Problem with Non-Stationary Rewards},
+  pages         = {199--207},
+  volume        = {27},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Advances in neural information processing systems},
+  year          = {2014},
+}
+
+@Article{bholat2020impact,
+  author        = {Bholat, D and Gharbawi, M and Thew, O},
+  title         = {The {{Impact}} of {{Covid}} on {{Machine Learning}} and {{Data Science}} in {{UK Banking}}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Bank of England Quarterly Bulletin, Q4},
+  year          = {2020},
+}
+
+@Book{bishop2006pattern,
+  author        = {Bishop, Christopher M},
+  title         = {Pattern Recognition and Machine Learning},
+  publisher     = {{springer}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2006},
+}
+
+@Article{blaom2020mlj,
+  author        = {Blaom, Anthony D. and Kiraly, Franz and Lienart, Thibaut and Simillides, Yiannis and Arenas, Diego and Vollmer, Sebastian J.},
+  title         = {{{MLJ}}: {{A Julia}} Package for Composable Machine Learning},
+  doi           = {10.21105/joss.02704},
+  issn          = {2475-9066},
+  number        = {55},
+  pages         = {2704},
+  urldate       = {2022-10-27},
+  volume        = {5},
+  abstract      = {Blaom et al., (2020). MLJ: A Julia package for composable machine learning. Journal of Open Source Software, 5(55), 2704, https://doi.org/10.21105/joss.02704},
+  bdsk-url-1    = {https://joss.theoj.org/papers/10.21105/joss.02704},
+  bdsk-url-2    = {https://doi.org/10.21105/joss.02704},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  file          = {:/Users/FA31DU/Zotero/storage/7AY87FGP/Blaom et al. - 2020 - MLJ A Julia package for composable machine learni.pdf:;:/Users/FA31DU/Zotero/storage/D69YSMVF/joss.html:},
+  journal       = {Journal of Open Source Software},
+  langid        = {english},
+  month         = nov,
+  shorttitle    = {{{MLJ}}},
+  year          = {2020},
+}
+
+@InProceedings{blundell2015weight,
+  author        = {Blundell, Charles and Cornebise, Julien and Kavukcuoglu, Koray and Wierstra, Daan},
+  booktitle     = {International Conference on Machine Learning},
+  title         = {Weight Uncertainty in Neural Network},
+  pages         = {1613--1622},
+  publisher     = {{PMLR}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2015},
+}
+
+@Article{borch2022machine,
+  author        = {Borch, Christian},
+  title         = {Machine Learning, Knowledge Risk, and Principal-Agent Problems in Automated Trading},
+  doi           = {10.1016/j.techsoc.2021.101852},
+  pages         = {101852},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Technology in Society},
+  year          = {2022},
+}
+
+@Article{borisov2022deep,
+  author    = {Borisov, Vadim and Leemann, Tobias and Se{\ss}ler, Kathrin and Haug, Johannes and Pawelczyk, Martin and Kasneci, Gjergji},
+  title     = {Deep neural networks and tabular data: A survey},
+  journal   = {IEEE Transactions on Neural Networks and Learning Systems},
+  publisher = {IEEE},
+  year      = {2022},
+}
+
+@Article{bramoulle2009identification,
+  author        = {Bramoull{\'e}, Yann and Djebbari, Habiba and Fortin, Bernard},
+  title         = {Identification of Peer Effects through Social Networks},
+  doi           = {10.2139/ssrn.965818},
+  number        = {1},
+  pages         = {41--55},
+  volume        = {150},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of econometrics},
+  year          = {2009},
+}
+
+@Article{bramoulle2020peer,
+  author        = {Bramoull{\'e}, Yann and Djebbari, Habiba and Fortin, Bernard},
+  title         = {Peer Effects in Networks: {{A}} Survey},
+  doi           = {10.2139/ssrn.3534495},
+  pages         = {603--629},
+  volume        = {12},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Annual Review of Economics},
+  year          = {2020},
+}
+
+@Unpublished{branco2015survey,
+  author        = {Branco, Paula and Torgo, Luis and Ribeiro, Rita},
+  title         = {A Survey of Predictive Modelling under Imbalanced Distributions},
+  archiveprefix = {arXiv},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  eprint        = {1505.01658},
+  eprinttype    = {arxiv},
+  year          = {2015},
+}
+
+@Book{brock1991nonlinear,
+  author        = {Brock, William Allen and Brock, William A and Hsieh, David Arthur and LeBaron, Blake Dean and Brock, William E},
+  title         = {Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence},
+  doi           = {10.2307/2234554},
+  publisher     = {{MIT press}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {1991},
+}
+
+@InProceedings{buolamwini2018gender,
+  author        = {Buolamwini, Joy and Gebru, Timnit},
+  booktitle     = {Conference on Fairness, Accountability and Transparency},
+  title         = {Gender Shades: {{Intersectional}} Accuracy Disparities in Commercial Gender Classification},
+  pages         = {77--91},
+  publisher     = {{PMLR}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2018},
+}
+
+@Unpublished{bussmann2020neural,
+  author        = {Bussmann, Bart and Nys, Jannes and Latr{\'e}, Steven},
+  title         = {Neural {{Additive Vector Autoregression Models}} for {{Causal Discovery}} in {{Time Series Data}}},
+  archiveprefix = {arXiv},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  eprint        = {2010.09429},
+  eprinttype    = {arxiv},
+  year          = {2020},
+}
+
+@Report{card1993minimum,
+  author        = {Card, David and Krueger, Alan B},
+  title         = {Minimum Wages and Employment: {{A}} Case Study of the Fast Food Industry in {{New Jersey}} and {{Pennsylvania}}},
+  doi           = {10.3386/w4509},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  school        = {{National Bureau of Economic Research}},
+  year          = {1993},
+}
+
+@InProceedings{carlini2017evaluating,
+  author        = {Carlini, Nicholas and Wagner, David},
+  booktitle     = {2017 Ieee Symposium on Security and Privacy (Sp)},
+  title         = {Towards Evaluating the Robustness of Neural Networks},
+  doi           = {10.1109/sp.2017.49},
+  pages         = {39--57},
+  publisher     = {{IEEE}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2017},
+}
+
+@Article{carlisle2019racist,
+  author        = {Carlisle, M.},
+  title         = {Racist Data Destruction? - a {{Boston}} Housing Dataset Controversy},
+  url           = {https://medium.com/@docintangible/racist-data-destruction-113e3eff54a8},
+  bdsk-url-1    = {https://medium.com/@docintangible/racist-data-destruction-113e3eff54a8},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2019},
+}
+
+@Article{carrell2009does,
+  author        = {Carrell, Scott E and Fullerton, Richard L and West, James E},
+  title         = {Does Your Cohort Matter? {{Measuring}} Peer Effects in College Achievement},
+  doi           = {10.3386/w14032},
+  number        = {3},
+  pages         = {439--464},
+  volume        = {27},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of Labor Economics},
+  year          = {2009},
+}
+
+@Article{carrell2013natural,
+  author        = {Carrell, Scott E and Sacerdote, Bruce I and West, James E},
+  title         = {From Natural Variation to Optimal Policy? {{The}} Importance of Endogenous Peer Group Formation},
+  doi           = {10.3982/ecta10168},
+  number        = {3},
+  pages         = {855--882},
+  volume        = {81},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Econometrica : journal of the Econometric Society},
+  shortjournal  = {Econometrica},
+  year          = {2013},
+}
+
+@Article{carrizosa2021generating,
+  author        = {Carrizosa, Emilio and Ramırez-Ayerbe, Jasone and Romero, Dolores},
+  title         = {Generating {{Collective Counterfactual Explanations}} in {{Score-Based Classification}} via {{Mathematical Optimization}}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2021},
+}
+
+@Article{cascarino2022explainable,
+  author        = {Cascarino, Giuseppe and Moscatelli, Mirko and Parlapiano, Fabio},
+  title         = {Explainable {{Artificial Intelligence}}: Interpreting Default Forecasting Models Based on {{Machine Learning}}},
+  doi           = {10.2139/ssrn.4090707},
+  number        = {674},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Bank of Italy Occasional Paper},
+  year          = {2022},
+}
+
+@Article{chandola2009anomaly,
+  author        = {Chandola, Varun and Banerjee, Arindam and Kumar, Vipin},
+  title         = {Anomaly Detection: {{A}} Survey},
+  number        = {3},
+  pages         = {1--58},
+  volume        = {41},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {ACM computing surveys (CSUR)},
+  year          = {2009},
+}
+
+@Article{chapelle2011empirical,
+  author        = {Chapelle, Olivier and Li, Lihong},
+  title         = {An Empirical Evaluation of Thompson Sampling},
+  pages         = {2249--2257},
+  volume        = {24},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Advances in neural information processing systems},
+  year          = {2011},
+}
+
+@Article{chetty2011adjustment,
+  author        = {Chetty, Raj and Friedman, John N and Olsen, Tore and Pistaferri, Luigi},
+  title         = {Adjustment Costs, Firm Responses, and Micro vs. Macro Labor Supply Elasticities: {{Evidence}} from {{Danish}} Tax Records},
+  doi           = {10.3386/w15617},
+  number        = {2},
+  pages         = {749--804},
+  volume        = {126},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {The quarterly journal of economics},
+  year          = {2011},
+}
+
+@Article{cortes1995supportvector,
+  author        = {Cortes, Corinna and Vapnik, Vladimir},
+  title         = {Support-Vector Networks},
+  number        = {3},
+  pages         = {273--297},
+  volume        = {20},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Machine learning},
+  year          = {1995},
+}
+
+@Article{crawford2019variable,
+  author        = {Crawford, Lorin and Flaxman, Seth R and Runcie, Daniel E and West, Mike},
+  title         = {Variable Prioritization in Nonlinear Black Box Methods: {{A}} Genetic Association Case Study},
+  doi           = {10.1214/18-aoas1222},
+  number        = {2},
+  pages         = {958},
+  volume        = {13},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {The annals of applied statistics},
+  year          = {2019},
+}
+
+@InProceedings{dai2022counterfactual,
+  author        = {Dai, Xinyue and Keane, Mark T and Shalloo, Laurence and Ruelle, Elodie and Byrne, Ruth MJ},
+  title         = {Counterfactual Explanations for Prediction and Diagnosis in Xai},
+  doi           = {10.1145/3514094.3534144},
+  eventtitle    = {Proceedings of the 2022 {{AAAI}}/{{ACM Conference}} on {{AI}}, {{Ethics}}, and {{Society}}},
+  pages         = {215--226},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2022},
+}
+
+@Article{danielsson2021artificial,
+  author        = {Danielsson, Jon and Macrae, Robert and Uthemann, Andreas},
+  title         = {Artificial Intelligence and Systemic Risk},
+  pages         = {106290},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of Banking \& Finance},
+  year          = {2021},
+}
+
+@Article{daxberger2021laplace,
+  author        = {Daxberger, Erik and Kristiadi, Agustinus and Immer, Alexander and Eschenhagen, Runa and Bauer, Matthias and Hennig, Philipp},
+  title         = {Laplace {{Redux-Effortless Bayesian Deep Learning}}},
+  volume        = {34},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Advances in Neural Information Processing Systems},
+  year          = {2021},
+}
+
+@Article{dehejia1999causal,
+  author        = {Dehejia, Rajeev H and Wahba, Sadek},
+  title         = {Causal Effects in Nonexperimental Studies: {{Reevaluating}} the Evaluation of Training Programs},
+  doi           = {10.1080/01621459.1999.10473858},
+  number        = {448},
+  pages         = {1053--1062},
+  volume        = {94},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of the American statistical Association},
+  year          = {1999},
+}
+
+@Article{dell2010persistent,
+  author        = {Dell, Melissa},
+  title         = {The Persistent Effects of {{Peru}}'s Mining Mita},
+  doi           = {10.2139/ssrn.1596425},
+  number        = {6},
+  pages         = {1863--1903},
+  volume        = {78},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Econometrica : journal of the Econometric Society},
+  shortjournal  = {Econometrica},
+  year          = {2010},
+}
+
+@Article{denhengst2020reinforcement,
+  author        = {den Hengst, Floris and Grua, Eoin Martino and el Hassouni, Ali and Hoogendoorn, Mark},
+  title         = {Reinforcement Learning for Personalization: {{A}} Systematic Literature Review},
+  doi           = {10.3233/ds-200028},
+  issue         = {Preprint},
+  pages         = {1--41},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Data Science},
+  options       = {useprefix=true},
+  year          = {2020},
+}
+
+@Article{deoliveira2021framework,
+  author        = {de Oliveira, Raphael Mazzine Barbosa and Martens, David},
+  title         = {A Framework and Benchmarking Study for Counterfactual Generating Methods on Tabular Data},
+  doi           = {10.3390/app11167274},
+  number        = {16},
+  pages         = {7274},
+  volume        = {11},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Applied Sciences},
+  options       = {useprefix=true},
+  year          = {2021},
+}
+
+@InProceedings{dombrowski2021diffeomorphic,
+  author        = {Dombrowski, Ann-Kathrin and Gerken, Jan E and Kessel, Pan},
+  booktitle     = {{{ICML Workshop}} on {{Invertible Neural Networks}}, {{Normalizing Flows}}, and {{Explicit Likelihood Models}}},
+  title         = {Diffeomorphic Explanations with Normalizing Flows},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2021},
+}
+
+@InProceedings{dorffner1996neural,
+  author        = {Dorffner, Georg},
+  booktitle     = {Neural Network World},
+  title         = {Neural Networks for Time Series Processing},
+  publisher     = {{Citeseer}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {1996},
+}
+
+@Article{epstein1979stability,
+  author        = {Epstein, Seymour},
+  title         = {The Stability of Behavior: {{I}}. {{On}} Predicting Most of the People Much of the Time.},
+  doi           = {10.1037/0022-3514.37.7.1097},
+  number        = {7},
+  pages         = {1097},
+  volume        = {37},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of personality and social psychology},
+  year          = {1979},
+}
+
+@Online{barocas2022fairness,
+  author        = {Solon Barocas and Moritz Hardt and Arvind Narayanan},
+  title         = {Fairness and Machine Learning},
+  url           = {https://fairmlbook.org/index.html},
+  urldate       = {2022-11-08},
+  bdsk-url-1    = {https://fairmlbook.org/index.html},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  month         = dec,
+  year          = {2022},
+}
+
+@Article{falk2006clean,
+  author        = {Falk, Armin and Ichino, Andrea},
+  title         = {Clean Evidence on Peer Effects},
+  doi           = {10.1086/497818},
+  number        = {1},
+  pages         = {39--57},
+  volume        = {24},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of labor economics},
+  year          = {2006},
+}
+
+@Unpublished{fan2020interpretability,
+  author        = {Fan, Fenglei and Xiong, Jinjun and Wang, Ge},
+  title         = {On Interpretability of Artificial Neural Networks},
+  archiveprefix = {arXiv},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  eprint        = {2001.02522},
+  eprinttype    = {arxiv},
+  year          = {2020},
+}
+
+@Article{fang2011dynamic,
+  author        = {Fang, Hanming and Gavazza, Alessandro},
+  title         = {Dynamic Inefficiencies in an Employment-Based Health Insurance System: {{Theory}} and Evidence},
+  number        = {7},
+  pages         = {3047--77},
+  volume        = {101},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {American Economic Review},
+  year          = {2011},
+}
+
+@Article{fehr2000cooperation,
+  author        = {Fehr, Ernst and Gachter, Simon},
+  title         = {Cooperation and Punishment in Public Goods Experiments},
+  doi           = {10.2139/ssrn.203194},
+  number        = {4},
+  pages         = {980--994},
+  volume        = {90},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {American Economic Review},
+  year          = {2000},
+}
+
+@Article{fix1951important,
+  author        = {Fix, E and Hodges, J},
+  title         = {An Important Contribution to Nonparametric Discriminant Analysis and Density Estimation},
+  number        = {57},
+  pages         = {233--238},
+  volume        = {3},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {International Statistical Review},
+  year          = {1951},
+}
+
+@Book{friedman2008monetary,
+  author        = {Friedman, Milton and Schwartz, Anna Jacobson},
+  title         = {A Monetary History of the {{United States}}, 1867-1960},
+  publisher     = {{Princeton University Press}},
+  volume        = {14},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2008},
+}
+
+@InProceedings{gal2016dropout,
+  author        = {Gal, Yarin and Ghahramani, Zoubin},
+  booktitle     = {International Conference on Machine Learning},
+  title         = {Dropout as a Bayesian Approximation: {{Representing}} Model Uncertainty in Deep Learning},
+  pages         = {1050--1059},
+  publisher     = {{PMLR}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2016},
+}
+
+@InProceedings{gal2017deep,
+  author        = {Gal, Yarin and Islam, Riashat and Ghahramani, Zoubin},
+  booktitle     = {International {{Conference}} on {{Machine Learning}}},
+  title         = {Deep Bayesian Active Learning with Image Data},
+  pages         = {1183--1192},
+  publisher     = {{PMLR}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2017},
+}
+
+@Article{galizzi2019external,
+  author        = {Galizzi, Matteo M and Navarro-Martinez, Daniel},
+  title         = {On the External Validity of Social Preference Games: A Systematic Lab-Field Study},
+  doi           = {10.1287/mnsc.2017.2908},
+  number        = {3},
+  pages         = {976--1002},
+  volume        = {65},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Management Science},
+  year          = {2019},
+}
+
+@Article{gama2014survey,
+  author        = {Gama, Jo{\~a}o and {\v Z}liobait{\.e}, Indr{\.e} and Bifet, Albert and Pechenizkiy, Mykola and Bouchachia, Abdelhamid},
+  title         = {A Survey on Concept Drift Adaptation},
+  number        = {4},
+  pages         = {1--37},
+  volume        = {46},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {ACM computing surveys (CSUR)},
+  year          = {2014},
+}
+
+@Unpublished{garivier2008upperconfidence,
+  author        = {Garivier, Aur{\'e}lien and Moulines, Eric},
+  title         = {On Upper-Confidence Bound Policies for Non-Stationary Bandit Problems},
+  archiveprefix = {arXiv},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  eprint        = {0805.3415},
+  eprinttype    = {arxiv},
+  year          = {2008},
+}
+
+@Book{gelman2013bayesian,
+  author        = {Gelman, Andrew and Carlin, John B and Stern, Hal S and Dunson, David B and Vehtari, Aki and Rubin, Donald B},
+  title         = {Bayesian Data Analysis},
+  publisher     = {{CRC press}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2013},
+}
+
+@Article{gilbert1998immune,
+  author        = {Gilbert, Daniel T and Pinel, Elizabeth C and Wilson, Timothy D and Blumberg, Stephen J and Wheatley, Thalia P},
+  title         = {Immune Neglect: A Source of Durability Bias in Affective Forecasting.},
+  doi           = {10.1037/0022-3514.75.3.617},
+  number        = {3},
+  pages         = {617},
+  volume        = {75},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of personality and social psychology},
+  year          = {1998},
+}
+
+@Article{gneezy2006uncertainty,
+  author        = {Gneezy, Uri and List, John A and Wu, George},
+  title         = {The Uncertainty Effect: {{When}} a Risky Prospect Is Valued Less than Its Worst Possible Outcome},
+  doi           = {10.1093/qje/121.4.1283},
+  number        = {4},
+  pages         = {1283--1309},
+  volume        = {121},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {The Quarterly Journal of Economics},
+  year          = {2006},
+}
+
+@InCollection{goan2020bayesian,
+  author        = {Goan, Ethan and Fookes, Clinton},
+  booktitle     = {Case {{Studies}} in {{Applied Bayesian Data Science}}},
+  title         = {Bayesian {{Neural Networks}}: {{An Introduction}} and {{Survey}}},
+  doi           = {10.1007/978-3-030-42553-1_3},
+  pages         = {45--87},
+  publisher     = {{Springer}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2020},
+}
+
+@Article{goldsmith-pinkham2013social,
+  author        = {Goldsmith-Pinkham, Paul and Imbens, Guido W},
+  title         = {Social Networks and the Identification of Peer Effects},
+  number        = {3},
+  pages         = {253--264},
+  volume        = {31},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of Business \& Economic Statistics},
+  year          = {2013},
+}
+
+@Unpublished{goodfellow2014explaining,
+  author        = {Goodfellow, Ian J and Shlens, Jonathon and Szegedy, Christian},
+  title         = {Explaining and Harnessing Adversarial Examples},
+  archiveprefix = {arXiv},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  eprint        = {1412.6572},
+  eprinttype    = {arxiv},
+  year          = {2014},
+}
+
+@Book{goodfellow2016deep,
+  author        = {Goodfellow, Ian and Bengio, Yoshua and Courville, Aaron},
+  title         = {Deep {{Learning}}},
+  publisher     = {{MIT Press}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2016},
+}
+
+@Article{goodfriend2005incredible,
+  author        = {Goodfriend, Marvin and King, Robert G},
+  title         = {The Incredible {{Volcker}} Disinflation},
+  doi           = {10.3386/w11562},
+  number        = {5},
+  pages         = {981--1015},
+  volume        = {52},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of Monetary Economics},
+  year          = {2005},
+}
+
+@Article{graham2017econometric,
+  author        = {Graham, Bryan S},
+  title         = {An Econometric Model of Network Formation with Degree Heterogeneity},
+  doi           = {10.1920/wp.cem.2017.0817},
+  number        = {4},
+  pages         = {1033--1063},
+  volume        = {85},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Econometrica : journal of the Econometric Society},
+  shortjournal  = {Econometrica},
+  year          = {2017},
+}
+
+@Article{greene2012econometric,
+  author        = {Greene, William H},
+  title         = {Econometric Analysis, 71e},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Stern School of Business, New York University},
+  year          = {2012},
+}
+
+@Article{grether1979economic,
+  author        = {Grether, David M and Plott, Charles R},
+  title         = {Economic Theory of Choice and the Preference Reversal Phenomenon},
+  doi           = {10.1017/cbo9780511618031.006},
+  number        = {4},
+  pages         = {623--638},
+  volume        = {69},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {The American Economic Review},
+  year          = {1979},
+}
+
+@Article{gretton2012kernel,
+  author        = {Gretton, Arthur and Borgwardt, Karsten M and Rasch, Malte J and Sch{\"o}lkopf, Bernhard and Smola, Alexander},
+  title         = {A Kernel Two-Sample Test},
+  number        = {1},
+  pages         = {723--773},
+  volume        = {13},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {The Journal of Machine Learning Research},
+  year          = {2012},
+}
+
+@Unpublished{griffith2020name,
+  author        = {Griffith, Alan},
+  date          = {2020-08-01},
+  title         = {Name {{Your Friends}}, but {{Only Five}}? {{The Importance}} of {{Censoring}} in {{Peer Effects Estimates}} Using {{Social Network Data}}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  doi           = {10.1086/717935},
+  year          = {2020},
+}
+
+@Unpublished{grinsztajn2022why,
+  author        = {Grinsztajn, L{\'e}o and Oyallon, Edouard and Varoquaux, Ga{\"e}l},
+  title         = {Why Do Tree-Based Models Still Outperform Deep Learning on Tabular Data?},
+  archiveprefix = {arXiv},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  eprint        = {2207.08815},
+  eprinttype    = {arxiv},
+  year          = {2022},
+}
+
+@Misc{group2020detailed,
+  author        = {Group, Open COVID-19 Data Working},
+  title         = {Detailed {{Epidemiological Data}} from the {{COVID-19 Outbreak}}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2020},
+}
+
+@InProceedings{gupta2011thompson,
+  author        = {Gupta, Neha and Granmo, Ole-Christoffer and Agrawala, Ashok},
+  booktitle     = {2011 10th {{International Conference}} on {{Machine Learning}} and {{Applications}} and {{Workshops}}},
+  title         = {Thompson Sampling for Dynamic Multi-Armed Bandits},
+  doi           = {10.1109/icmla.2011.144},
+  pages         = {484--489},
+  publisher     = {{IEEE}},
+  volume        = {1},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2011},
+}
+
+@Book{hamilton2020time,
+  author        = {Hamilton, James Douglas},
+  title         = {Time Series Analysis},
+  publisher     = {{Princeton university press}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2020},
+}
+
+@Article{hamon2020robustness,
+  author        = {Hamon, Ronan and Junklewitz, Henrik and Sanchez, Ignacio},
+  title         = {Robustness and Explainability of Artificial Intelligence},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Publications Office of the European Union},
+  year          = {2020},
+}
+
+@Article{hamzacebi2008improving,
+  author        = {Hamza{\c c}ebi, Co{\c s}kun},
+  title         = {Improving Artificial Neural Networks' Performance in Seasonal Time Series Forecasting},
+  doi           = {10.1016/j.ins.2008.07.024},
+  number        = {23},
+  pages         = {4550--4559},
+  volume        = {178},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Information Sciences},
+  year          = {2008},
+}
+
+@InProceedings{hanneke2007bound,
+  author        = {Hanneke, Steve},
+  booktitle     = {Proceedings of the 24th International Conference on {{Machine}} Learning},
+  title         = {A Bound on the Label Complexity of Agnostic Active Learning},
+  doi           = {10.1145/1273496.1273541},
+  pages         = {353--360},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2007},
+}
+
+@Article{hansen2020virtue,
+  author        = {Hansen, Kristian Bondo},
+  title         = {The Virtue of Simplicity: {{On}} Machine Learning Models in Algorithmic Trading},
+  doi           = {10.1177/2053951720926558},
+  number        = {1},
+  pages         = {2053951720926558},
+  volume        = {7},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Big Data \& Society},
+  year          = {2020},
+}
+
+@Article{hartland2006multiarmed,
+  author        = {Hartland, C{\'e}dric and Gelly, Sylvain and Baskiotis, Nicolas and Teytaud, Olivier and Sebag, Michele},
+  title         = {Multi-Armed Bandit, Dynamic Environments and Meta-Bandits},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2006},
+}
+
+@Article{heckman1985alternative,
+  author        = {Heckman, James J and Robb Jr, Richard},
+  title         = {Alternative Methods for Evaluating the Impact of Interventions: {{An}} Overview},
+  number        = {1-2},
+  pages         = {239--267},
+  volume        = {30},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of econometrics},
+  year          = {1985},
+}
+
+@Article{hershfield2011increasing,
+  author        = {Hershfield, Hal E and Goldstein, Daniel G and Sharpe, William F and Fox, Jesse and Yeykelis, Leo and Carstensen, Laura L and Bailenson, Jeremy N},
+  title         = {Increasing Saving Behavior through Age-Progressed Renderings of the Future Self},
+  doi           = {10.1509/jmkr.48.spl.s23},
+  issue         = {SPL},
+  pages         = {S23--S37},
+  volume        = {48},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of Marketing Research},
+  year          = {2011},
+}
+
+@InProceedings{ho1995random,
+  author        = {Ho, Tin Kam},
+  booktitle     = {Proceedings of 3rd International Conference on Document Analysis and Recognition},
+  title         = {Random Decision Forests},
+  doi           = {10.1109/ICDAR.1995.598994},
+  pages         = {278--282},
+  publisher     = {{IEEE}},
+  volume        = {1},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {1995},
+}
+
+@Article{hochreiter1997long,
+  author        = {Hochreiter, Sepp and Schmidhuber, J{\"u}rgen},
+  title         = {Long Short-Term Memory},
+  number        = {8},
+  pages         = {1735--1780},
+  volume        = {9},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Neural computation},
+  year          = {1997},
+}
+
+@Unpublished{hoff2021bayesoptimal,
+  author        = {Hoff, Peter},
+  title         = {Bayes-Optimal Prediction with Frequentist Coverage Control},
+  url           = {10.3150/22-bej1484},
+  archiveprefix = {arXiv},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  doi           = {10.3150/22-bej1484},
+  eprint        = {2105.14045},
+  eprinttype    = {arxiv},
+  file          = {:/Users/FA31DU/Zotero/storage/IQK27WVA/Hoff - 2021 - Bayes-optimal prediction with frequentist coverage.pdf:;:/Users/FA31DU/Zotero/storage/K8EAZA25/2105.html:},
+  year          = {2021},
+}
+
+@Misc{hoffman1994german,
+  author        = {Hoffman, Hans},
+  title         = {German {{Credit Data}}},
+  url           = {https://archive.ics.uci.edu/ml/datasets/statlog+(german+credit+data)},
+  bdsk-url-1    = {https://archive.ics.uci.edu/ml/datasets/statlog+(german+credit+data)},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {https://archive.ics.uci.edu/ml/datasets/statlog+(german+credit+data)},
+  year          = {1994},
+}
+
+@Online{hoffmanGermanCreditData1994,
+  author        = {Hoffman, Hans},
+  title         = {German {{Credit Data}}},
+  url           = {https://archive.ics.uci.edu/ml/datasets/statlog+(german+credit+data)},
+  bdsk-url-1    = {https://archive.ics.uci.edu/ml/datasets/statlog+(german+credit+data)},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {1994},
+}
+
+@Unpublished{houlsby2011bayesian,
+  author        = {Houlsby, Neil and Husz{\'a}r, Ferenc and Ghahramani, Zoubin and Lengyel, M{\'a}t{\'e}},
+  title         = {Bayesian Active Learning for Classification and Preference Learning},
+  archiveprefix = {arXiv},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  eprint        = {1112.5745},
+  eprinttype    = {arxiv},
+  year          = {2011},
+}
+
+@Article{hsee1996evaluability,
+  author        = {Hsee, Christopher K},
+  title         = {The Evaluability Hypothesis: {{An}} Explanation for Preference Reversals between Joint and Separate Evaluations of Alternatives},
+  doi           = {10.1006/obhd.1996.0077},
+  number        = {3},
+  pages         = {247--257},
+  url           = {10.1006/obhd.1996.0077},
+  volume        = {67},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Organizational behavior and human decision processes},
+  year          = {1996},
+}
+
+@Article{hsee2004music,
+  author        = {Hsee, Christopher K and Rottenstreich, Yuval},
+  title         = {Music, Pandas, and Muggers: On the Affective Psychology of Value.},
+  doi           = {10.1017/cbo9780511618031.033},
+  number        = {1},
+  pages         = {23},
+  url           = {10.1017/cbo9780511618031.033},
+  volume        = {133},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of Experimental Psychology: General},
+  year          = {2004},
+}
+
+@Article{hsieh2016social,
+  author        = {Hsieh, Chih-Sheng and Lee, Lung Fei},
+  title         = {A Social Interactions Model with Endogenous Friendship Formation and Selectivity},
+  doi           = {10.1002/jae.2426},
+  number        = {2},
+  pages         = {301--319},
+  volume        = {31},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of Applied Econometrics},
+  year          = {2016},
+}
+
+@Unpublished{immer2020improving,
+  author        = {Immer, Alexander and Korzepa, Maciej and Bauer, Matthias},
+  title         = {Improving Predictions of Bayesian Neural Networks via Local Linearization},
+  archiveprefix = {arXiv},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  eprint        = {2008.08400},
+  eprinttype    = {arxiv},
+  year          = {2020},
+}
+
+@Unpublished{innes2018fashionable,
+  author        = {Innes, Michael and Saba, Elliot and Fischer, Keno and Gandhi, Dhairya and Rudilosso, Marco Concetto and Joy, Neethu Mariya and Karmali, Tejan and Pal, Avik and Shah, Viral},
+  title         = {Fashionable Modelling with Flux},
+  archiveprefix = {arXiv},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  eprint        = {1811.01457},
+  eprinttype    = {arxiv},
+  year          = {2018},
+}
+
+@Article{innes2018flux,
+  author        = {Innes, Mike},
+  title         = {Flux: {{Elegant}} Machine Learning with {{Julia}}},
+  doi           = {10.21105/joss.00602},
+  number        = {25},
+  pages         = {602},
+  volume        = {3},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of Open Source Software},
+  year          = {2018},
+}
+
+@Unpublished{ish-horowicz2019interpreting,
+  author        = {Ish-Horowicz, Jonathan and Udwin, Dana and Flaxman, Seth and Filippi, Sarah and Crawford, Lorin},
+  title         = {Interpreting Deep Neural Networks through Variable Importance},
+  archiveprefix = {arXiv},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  eprint        = {1901.09839},
+  eprinttype    = {arxiv},
+  year          = {2019},
+}
+
+@InProceedings{jabbari2017fairness,
+  author        = {Jabbari, Shahin and Joseph, Matthew and Kearns, Michael and Morgenstern, Jamie and Roth, Aaron},
+  booktitle     = {International {{Conference}} on {{Machine Learning}}},
+  title         = {Fairness in Reinforcement Learning},
+  pages         = {1617--1626},
+  publisher     = {{PMLR}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2017},
+}
+
+@Article{jackson2007meeting,
+  author        = {Jackson, Matthew O and Rogers, Brian W},
+  title         = {Meeting Strangers and Friends of Friends: {{How}} Random Are Social Networks?},
+  doi           = {10.1257/aer.97.3.890},
+  number        = {3},
+  pages         = {890--915},
+  volume        = {97},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {American Economic Review},
+  year          = {2007},
+}
+
+@Unpublished{jeanneret2022diffusion,
+  author        = {Jeanneret, Guillaume and Simon, Lo{\"\i}c and Jurie, Fr{\'e}d{\'e}ric},
+  title         = {Diffusion {{Models}} for {{Counterfactual Explanations}}},
+  archiveprefix = {arXiv},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  eprint        = {2203.15636},
+  eprinttype    = {arxiv},
+  year          = {2022},
+}
+
+@Article{johansson2005failure,
+  author        = {Johansson, Petter and Hall, Lars and Sikstr{\"o}m, Sverker and Olsson, Andreas},
+  title         = {Failure to Detect Mismatches between Intention and Outcome in a Simple Decision Task},
+  doi           = {10.1126/science.1111709},
+  number        = {5745},
+  pages         = {116--119},
+  volume        = {310},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Science (New York, N.Y.)},
+  shortjournal  = {Science},
+  year          = {2005},
+}
+
+@Article{johnsson2021estimation,
+  author        = {Johnsson, Ida and Moon, Hyungsik Roger},
+  title         = {Estimation of Peer Effects in Endogenous Social Networks: {{Control}} Function Approach},
+  doi           = {10.2139/ssrn.3043404},
+  number        = {2},
+  pages         = {328--345},
+  volume        = {103},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Review of Economics and Statistics},
+  year          = {2021},
+}
+
+@Article{jolliffe2003modified,
+  author        = {Jolliffe, Ian T and Trendafilov, Nickolay T and Uddin, Mudassir},
+  title         = {A Modified Principal Component Technique Based on the {{LASSO}}},
+  doi           = {10.1198/1061860032148},
+  number        = {3},
+  pages         = {531--547},
+  volume        = {12},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of computational and Graphical Statistics},
+  year          = {2003},
+}
+
+@Article{joseph2021forecasting,
+  author        = {Joseph, Andreas and Kalamara, Eleni and Kapetanios, George and Potjagailo, Galina},
+  title         = {Forecasting Uk Inflation Bottom Up},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2021},
+}
+
+@Misc{joshi2019realistic,
+  author        = {Shalmali Joshi and Oluwasanmi Koyejo and Warut Vijitbenjaronk and Been Kim and Joydeep Ghosh},
+  title         = {Towards Realistic Individual Recourse and Actionable Explanations in Black-Box Decision Making Systems},
+  eprint        = {1907.09615},
+  archiveprefix = {arXiv},
+  primaryclass  = {cs.LG},
+  year          = {2019},
+}
+
+@Unpublished{jospin2020handson,
+  author        = {Jospin, Laurent Valentin and Buntine, Wray and Boussaid, Farid and Laga, Hamid and Bennamoun, Mohammed},
+  title         = {Hands-on {{Bayesian Neural Networks}}--a {{Tutorial}} for {{Deep Learning Users}}},
+  archiveprefix = {arXiv},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  doi           = {10.1109/mci.2022.3155327},
+  eprint        = {2007.06823},
+  eprinttype    = {arxiv},
+  year          = {2020},
+}
+
+@Misc{kaggle2011give,
+  author        = {Kaggle},
+  title         = {Give Me Some Credit, {{Improve}} on the State of the Art in Credit Scoring by Predicting the Probability That Somebody Will Experience Financial Distress in the next Two Years.},
+  howpublished  = {https://www.kaggle.com/c/GiveMeSomeCredit},
+  note          = {Accessed: 2023-12-14},
+  url           = {https://www.kaggle.com/c/GiveMeSomeCredit},
+  bdsk-url-1    = {https://www.kaggle.com/c/GiveMeSomeCredit},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  publisher     = {{Kaggle}},
+  year          = {2011},
+}
+
+@online{kagglecompetitionGiveMeCredit,
+	author = {Kaggle Competition},
+	date-added = {2022-12-13 12:58:01 +0100},
+	date-modified = {2022-12-13 12:58:01 +0100},
+	title = {Give Me Some Credit, {{Improve}} on the State of the Art in Credit Scoring by Predicting the Probability That Somebody Will Experience Financial Distress in the next Two Years.},
+	url = {https://www.kaggle.com/c/GiveMeSomeCredit},
+	bdsk-url-1 = {https://www.kaggle.com/c/GiveMeSomeCredit}}
+
+@Article{kahneman1979prospect,
+  author        = {Kahneman, Daniel and Tversky, Amos},
+  title         = {Prospect {{Theory}}: {{An Analysis}} of {{Decision}} under {{Risk}}},
+  pages         = {263--291},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Econometrica: Journal of the Econometric Society},
+  year          = {1979},
+}
+
+@Article{kahneman1990experimental,
+  author        = {Kahneman, Daniel and Knetsch, Jack L and Thaler, Richard H},
+  title         = {Experimental Tests of the Endowment Effect and the {{Coase}} Theorem},
+  doi           = {10.1017/cbo9781139175197.009},
+  number        = {6},
+  pages         = {1325--1348},
+  volume        = {98},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of political Economy},
+  year          = {1990},
+}
+
+@Article{kahneman1992reference,
+  author        = {Kahneman, Daniel},
+  title         = {Reference Points, Anchors, Norms, and Mixed Feelings},
+  doi           = {10.1016/0749-5978(92)90015-y},
+  number        = {2},
+  pages         = {296--312},
+  volume        = {51},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Organizational behavior and human decision processes},
+  year          = {1992},
+}
+
+@Unpublished{karimi2020algorithmic,
+  author        = {Karimi, Amir-Hossein and Von K{\"u}gelgen, Julius and Sch{\"o}lkopf, Bernhard and Valera, Isabel},
+  title         = {Algorithmic Recourse under Imperfect Causal Knowledge: A Probabilistic Approach},
+  archiveprefix = {arXiv},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  eprint        = {2006.06831},
+  eprinttype    = {arxiv},
+  year          = {2020},
+}
+
+@Misc{karimi2020survey,
+  author        = {Amir-Hossein Karimi and Gilles Barthe and Bernhard Schölkopf and Isabel Valera},
+  title         = {A survey of algorithmic recourse: definitions, formulations, solutions, and prospects},
+  eprint        = {2010.04050},
+  archiveprefix = {arXiv},
+  primaryclass  = {cs.LG},
+  year          = {2021},
+}
+
+@InProceedings{karimi2021algorithmic,
+  author        = {Karimi, Amir-Hossein and Sch{\"o}lkopf, Bernhard and Valera, Isabel},
+  booktitle     = {Proceedings of the 2021 {{ACM Conference}} on {{Fairness}}, {{Accountability}}, and {{Transparency}}},
+  title         = {Algorithmic Recourse: From Counterfactual Explanations to Interventions},
+  pages         = {353--362},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2021},
+}
+
+@InProceedings{kaur2020interpreting,
+  author        = {Kaur, Harmanpreet and Nori, Harsha and Jenkins, Samuel and Caruana, Rich and Wallach, Hanna and Wortman Vaughan, Jennifer},
+  booktitle     = {Proceedings of the 2020 {{CHI}} Conference on Human Factors in Computing Systems},
+  title         = {Interpreting Interpretability: Understanding Data Scientists' Use of Interpretability Tools for Machine Learning},
+  doi           = {10.1145/3313831.3376219},
+  pages         = {1--14},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2020},
+}
+
+@Article{kehoe2021defence,
+  author        = {Kehoe, Aidan and Wittek, Peter and Xue, Yanbo and Pozas-Kerstjens, Alejandro},
+  title         = {Defence against Adversarial Attacks Using Classical and Quantum-Enhanced {{Boltzmann}} Machines},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Machine Learning: Science and Technology},
+  year          = {2021},
+}
+
+@Unpublished{kendall2017what,
+  author        = {Kendall, Alex and Gal, Yarin},
+  title         = {What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?},
+  archiveprefix = {arXiv},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  eprint        = {1703.04977},
+  eprinttype    = {arxiv},
+  year          = {2017},
+}
+
+@Article{kihoro2004seasonal,
+  author        = {Kihoro, J and Otieno, RO and Wafula, C},
+  title         = {Seasonal Time Series Forecasting: {{A}} Comparative Study of {{ARIMA}} and {{ANN}} Models},
+  doi           = {10.4314/ajst.v5i2.15330},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2004},
+}
+
+@Book{kilian2017structural,
+  author        = {Kilian, Lutz and L{\"u}tkepohl, Helmut},
+  title         = {Structural Vector Autoregressive Analysis},
+  publisher     = {{Cambridge University Press}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2017},
+}
+
+@Article{kirsch2019batchbald,
+  author        = {Kirsch, Andreas and Van Amersfoort, Joost and Gal, Yarin},
+  title         = {Batchbald: {{Efficient}} and Diverse Batch Acquisition for Deep Bayesian Active Learning},
+  pages         = {7026--7037},
+  volume        = {32},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Advances in neural information processing systems},
+  year          = {2019},
+}
+
+@Unpublished{kuiper2021exploring,
+  author        = {Kuiper, Ouren and van den Berg, Martin and van den Burgt, Joost and Leijnen, Stefan},
+  title         = {Exploring {{Explainable AI}} in the {{Financial Sector}}: {{Perspectives}} of {{Banks}} and {{Supervisory Authorities}}},
+  archiveprefix = {arXiv},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  doi           = {10.1007/978-3-030-93842-0_6},
+  eprint        = {2111.02244},
+  eprinttype    = {arxiv},
+  year          = {2021},
+}
+
+@Article{kydland1982time,
+  author        = {Kydland, Finn E and Prescott, Edward C},
+  title         = {Time to Build and Aggregate Fluctuations},
+  pages         = {1345--1370},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Econometrica: Journal of the Econometric Society},
+  year          = {1982},
+}
+
+@Unpublished{lachapelle2019gradientbased,
+  author        = {Lachapelle, S{\'e}bastien and Brouillard, Philippe and Deleu, Tristan and Lacoste-Julien, Simon},
+  title         = {Gradient-Based Neural Dag Learning},
+  archiveprefix = {arXiv},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  eprint        = {1906.02226},
+  eprinttype    = {arxiv},
+  year          = {2019},
+}
+
+@InProceedings{lakkaraju2020how,
+  author        = {Lakkaraju, Himabindu and Bastani, Osbert},
+  booktitle     = {Proceedings of the {{AAAI}}/{{ACM Conference}} on {{AI}}, {{Ethics}}, and {{Society}}},
+  title         = {" {{How}} Do {{I}} Fool You?" {{Manipulating User Trust}} via {{Misleading Black Box Explanations}}},
+  pages         = {79--85},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2020},
+}
+
+@InProceedings{lakkaraju2020how,
+  author        = {Lakkaraju, Himabindu and Bastani, Osbert},
+  booktitle     = {Proceedings of the {{AAAI}}/{{ACM Conference}} on {{AI}}, {{Ethics}}, and {{Society}}},
+  title         = {" {{How Do I Fool You}}?" {{Manipulating User Trust}} via {{Misleading Black Box Explanations}}},
+  pages         = {79--85},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2020},
+}
+
+@Article{lakshminarayanan2016simple,
+  author  = {Lakshminarayanan, Balaji and Pritzel, Alexander and Blundell, Charles},
+  title   = {Simple and scalable predictive uncertainty estimation using deep ensembles},
+  volume  = {30},
+  journal = {Advances in neural information processing systems},
+  year    = {2017},
+}
+
+@Unpublished{laugel2017inverse,
+  author        = {Laugel, Thibault and Lesot, Marie-Jeanne and Marsala, Christophe and Renard, Xavier and Detyniecki, Marcin},
+  title         = {Inverse Classification for Comparison-Based Interpretability in Machine Learning},
+  archiveprefix = {arXiv},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  eprint        = {1712.08443},
+  eprinttype    = {arxiv},
+  shortjournal  = {arXiv preprint arXiv:1712.08443},
+  year          = {2017},
+}
+
+@Thesis{lawrence2001variational,
+  author        = {Lawrence, Neil David},
+  title         = {Variational Inference in Probabilistic Models},
+  type          = {phdthesis},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  school        = {{University of Cambridge}},
+  year          = {2001},
+}
+
+@Misc{lecun1998mnist,
+  author       = {LeCun, Yann},
+  title        = {The MNIST database of handwritten digits},
+  howpublished = {http://yann.lecun.com/exdb/mnist/},
+  note         = {Accessed: 2024-01-10},
+  year         = {1998},
+}
+
+@Article{lee2003best,
+  author        = {Lee, Lung-fei},
+  title         = {Best Spatial Two-Stage Least Squares Estimators for a Spatial Autoregressive Model with Autoregressive Disturbances},
+  doi           = {10.1081/etc-120025891},
+  number        = {4},
+  pages         = {307--335},
+  volume        = {22},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Econometric Reviews},
+  year          = {2003},
+}
+
+@Article{lerner2013financial,
+  author        = {Lerner, Jennifer S and Li, Ye and Weber, Elke U},
+  title         = {The Financial Costs of Sadness},
+  doi           = {10.1177/0956797612450302},
+  number        = {1},
+  pages         = {72--79},
+  volume        = {24},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Psychological science},
+  year          = {2013},
+}
+
+@Article{list2004neoclassical,
+  author        = {List, John A},
+  title         = {Neoclassical Theory versus Prospect Theory: {{Evidence}} from the Marketplace},
+  doi           = {10.3386/w9736},
+  number        = {2},
+  pages         = {615--625},
+  volume        = {72},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Econometrica : journal of the Econometric Society},
+  shortjournal  = {Econometrica},
+  year          = {2004},
+}
+
+@Article{lucas1976econometric,
+  author        = {Lucas, JR},
+  title         = {Econometric Policy Evaluation: A Critique `, in {{K}}. {{Brunner}} and {{A Meltzer}}, {{The Phillips}} Curve and Labor Markets, {{North Holland}}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {1976},
+}
+
+@InProceedings{lundberg2017unified,
+  author        = {Lundberg, Scott M and Lee, Su-In},
+  booktitle     = {Proceedings of the 31st International Conference on Neural Information Processing Systems},
+  title         = {A Unified Approach to Interpreting Model Predictions},
+  pages         = {4768--4777},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2017},
+}
+
+@Book{lutkepohl2005new,
+  author        = {L{\"u}tkepohl, Helmut},
+  title         = {New Introduction to Multiple Time Series Analysis},
+  publisher     = {{Springer Science \& Business Media}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2005},
+}
+
+@Article{madrian2001power,
+  author        = {Madrian, Brigitte C and Shea, Dennis F},
+  title         = {The Power of Suggestion: {{Inertia}} in 401 (k) Participation and Savings Behavior},
+  doi           = {10.3386/w7682},
+  number        = {4},
+  pages         = {1149--1187},
+  volume        = {116},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {The Quarterly journal of economics},
+  year          = {2001},
+}
+
+@Book{manning2008introduction,
+  author        = {Manning, Christopher D and Sch{\"u}tze, Hinrich and Raghavan, Prabhakar},
+  title         = {Introduction to Information Retrieval},
+  publisher     = {{Cambridge university press}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2008},
+}
+
+@Software{manokhin2022awesome,
+  author       = {Manokhin, Valery},
+  title        = {Awesome Conformal Prediction},
+  doi          = {10.5281/zenodo.6467205},
+  howpublished = {https://doi.org/10.5281/zenodo.6467205},
+  note         = {Accessed: 2023-12-24},
+  url          = {https://doi.org/10.5281/zenodo.6467205},
+  version      = {v1.0.0},
+  month        = apr,
+  publisher    = {Zenodo},
+  year         = {2022},
+}
+
+@Article{manski1993identification,
+  author        = {Manski, Charles F},
+  title         = {Identification of Endogenous Social Effects: {{The}} Reflection Problem},
+  doi           = {10.2307/2298123},
+  number        = {3},
+  pages         = {531--542},
+  volume        = {60},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {The review of economic studies},
+  year          = {1993},
+}
+
+@Article{markle2018goals,
+  author        = {Markle, Alex and Wu, George and White, Rebecca and Sackett, Aaron},
+  title         = {Goals as Reference Points in Marathon Running: {{A}} Novel Test of Reference Dependence},
+  doi           = {10.2139/ssrn.2523510},
+  number        = {1},
+  pages         = {19--50},
+  volume        = {56},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of Risk and Uncertainty},
+  year          = {2018},
+}
+
+@Article{masini2021machine,
+  author        = {Masini, Ricardo P and Medeiros, Marcelo C and Mendes, Eduardo F},
+  title         = {Machine Learning Advances for Time Series Forecasting},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of Economic Surveys},
+  year          = {2021},
+}
+
+@Article{mccracken2016fredmd,
+  author        = {McCracken, Michael W and Ng, Serena},
+  title         = {{{FRED-MD}}: {{A}} Monthly Database for Macroeconomic Research},
+  doi           = {10.20955/wp.2015.012},
+  number        = {4},
+  pages         = {574--589},
+  volume        = {34},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of Business \& Economic Statistics},
+  year          = {2016},
+}
+
+@Article{mcculloch1990logical,
+  author        = {McCulloch, Warren S and Pitts, Walter},
+  title         = {A Logical Calculus of the Ideas Immanent in Nervous Activity},
+  number        = {1},
+  pages         = {99--115},
+  volume        = {52},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Bulletin of mathematical biology},
+  year          = {1990},
+}
+
+@Article{migut2015visualizing,
+  author        = {Migut, MA and Worring, Marcel and Veenman, Cor J},
+  title         = {Visualizing Multi-Dimensional Decision Boundaries in {{2D}}},
+  doi           = {10.1007/s10618-013-0342-x},
+  number        = {1},
+  pages         = {273--295},
+  volume        = {29},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Data Mining and Knowledge Discovery},
+  year          = {2015},
+}
+
+@Article{miller2019explanation,
+  author        = {Miller, Tim},
+  title         = {Explanation in Artificial Intelligence: {{Insights}} from the Social Sciences},
+  doi           = {10.1016/j.artint.2018.07.007},
+  pages         = {1--38},
+  volume        = {267},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Artificial intelligence},
+  year          = {2019},
+}
+
+@InProceedings{miller2020strategic,
+  author        = {Miller, John and Milli, Smitha and Hardt, Moritz},
+  booktitle     = {Proceedings of the 37th {{International Conference}} on {{Machine Learning}}},
+  title         = {Strategic {{Classification}} Is {{Causal Modeling}} in {{Disguise}}},
+  eventtitle    = {International {{Conference}} on {{Machine Learning}}},
+  pages         = {6917--6926},
+  publisher     = {{PMLR}},
+  url           = {https://proceedings.mlr.press/v119/miller20b.html},
+  urldate       = {2022-11-03},
+  abstract      = {Consequential decision-making incentivizes individuals to strategically adapt their behavior to the specifics of the decision rule. While a long line of work has viewed strategic adaptation as gaming and attempted to mitigate its effects, recent work has instead sought to design classifiers that incentivize individuals to improve a desired quality. Key to both accounts is a cost function that dictates which adaptations are rational to undertake. In this work, we develop a causal framework for strategic adaptation. Our causal perspective clearly distinguishes between gaming and improvement and reveals an important obstacle to incentive design. We prove any procedure for designing classifiers that incentivize improvement must inevitably solve a non-trivial causal inference problem. We show a similar result holds for designing cost functions that satisfy the requirements of previous work. With the benefit of hindsight, our results show much of the prior work on strategic classification is causal modeling in disguise.},
+  bdsk-url-1    = {https://proceedings.mlr.press/v119/miller20b.html},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  file          = {:/Users/FA31DU/Zotero/storage/46I2QMPI/Miller et al. - 2020 - Strategic Classification is Causal Modeling in Dis.pdf:;:/Users/FA31DU/Zotero/storage/NWREET6B/Miller et al. - 2020 - Strategic Classification is Causal Modeling in Dis.pdf:},
+  issn          = {2640-3498},
+  langid        = {english},
+  month         = nov,
+  year          = {2020},
+}
+
+@Article{mischel1988nature,
+  author        = {Mischel, Walter and Shoda, Yuichi and Peake, Philip K},
+  title         = {The Nature of Adolescent Competencies Predicted by Preschool Delay of Gratification.},
+  doi           = {10.1037/0022-3514.54.4.687},
+  number        = {4},
+  pages         = {687},
+  volume        = {54},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of personality and social psychology},
+  year          = {1988},
+}
+
+@InProceedings{mittelstadt2019explaining,
+  author        = {Mittelstadt, Brent and Russell, Chris and Wachter, Sandra},
+  booktitle     = {Proceedings of the Conference on Fairness, Accountability, and Transparency},
+  title         = {Explaining Explanations in {{AI}}},
+  doi           = {10.1145/3287560.3287574},
+  pages         = {279--288},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2019},
+}
+
+@Book{molnar2022interpretable,
+  author   = {Christoph Molnar},
+  title    = {Interpretable Machine Learning},
+  edition  = {2},
+  subtitle = {A Guide for Making Black Box Models Explainable},
+  url      = {https://christophm.github.io/interpretable-ml-book},
+  year     = {2022},
+}
+
+@Book{morgan2015counterfactuals,
+  author        = {Morgan, Stephen L and Winship, Christopher},
+  title         = {Counterfactuals and Causal Inference},
+  publisher     = {{Cambridge University Press}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2015},
+}
+
+@Article{mosteller1951experimental,
+  author        = {Mosteller, Frederick and Nogee, Philip},
+  title         = {An Experimental Measurement of Utility},
+  number        = {5},
+  pages         = {371--404},
+  volume        = {59},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of Political Economy},
+  year          = {1951},
+}
+
+@InProceedings{mothilal2020explaining,
+  author        = {Mothilal, Ramaravind K and Sharma, Amit and Tan, Chenhao},
+  booktitle     = {Proceedings of the 2020 {{Conference}} on {{Fairness}}, {{Accountability}}, and {{Transparency}}},
+  title         = {Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations},
+  doi           = {10.1145/3351095.3372850},
+  pages         = {607--617},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2020},
+}
+
+@Book{murphy2012machine,
+  author        = {Murphy, Kevin P},
+  title         = {Machine Learning: A Probabilistic Perspective},
+  publisher     = {{MIT press}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2012},
+}
+
+@Book{murphy2012machine,
+  author        = {Murphy, Kevin P},
+  title         = {Machine Learning: {{A}} Probabilistic Perspective},
+  publisher     = {{MIT press}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2012},
+}
+
+@Book{murphy2022probabilistic,
+  author        = {Murphy, Kevin P},
+  title         = {Probabilistic {{Machine Learning}}: {{An}} Introduction},
+  publisher     = {{MIT Press}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2022},
+}
+
+@Article{nagel1995unraveling,
+  author        = {Nagel, Rosemarie},
+  title         = {Unraveling in Guessing Games: {{An}} Experimental Study},
+  number        = {5},
+  pages         = {1313--1326},
+  volume        = {85},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {The American Economic Review},
+  year          = {1995},
+}
+
+@Unpublished{navarro-martinez2021bridging,
+  author        = {Navarro-Martinez, Daniel and Wang, Xinghua},
+  title         = {Bridging the Gap between the Lab and the Field: {{Dictator}} Games and Donations},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2021},
+}
+
+@InProceedings{nelson2015evaluating,
+  author        = {Nelson, Kevin and Corbin, George and Anania, Mark and Kovacs, Matthew and Tobias, Jeremy and Blowers, Misty},
+  booktitle     = {2015 {{IEEE Symposium}} on {{Computational Intelligence}} for {{Security}} and {{Defense Applications}} ({{CISDA}})},
+  title         = {Evaluating Model Drift in Machine Learning Algorithms},
+  doi           = {10.1109/cisda.2015.7208643},
+  pages         = {1--8},
+  publisher     = {{IEEE}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2015},
+}
+
+@Book{nocedal2006numerical,
+  author        = {Nocedal, Jorge and Wright, Stephen},
+  title         = {Numerical Optimization},
+  publisher     = {{Springer Science \& Business Media}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2006},
+}
+
+@Misc{oecd2021artificial,
+  author        = {{OECD}},
+  title         = {Artificial {{Intelligence}}, {{Machine Learning}} and {{Big Data}} in {{Finance}}: {{Opportunities}}, {{Challenges}} and {{Implications}} for {{Policy Makers}}},
+  url           = {https://www.oecd.org/finance/financial-markets/Artificial-intelligence-machine-learning-big-data-in-finance.pdf},
+  bdsk-url-1    = {https://www.oecd.org/finance/financial-markets/Artificial-intelligence-machine-learning-big-data-in-finance.pdf},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2021},
+}
+
+@Online{oecdArtificialIntelligenceMachine2021,
+  author        = {{OECD}},
+  title         = {Artificial {{Intelligence}}, {{Machine Learning}} and {{Big Data}} in {{Finance}}: {{Opportunities}}, {{Challenges}} and {{Implications}} for {{Policy Makers}}},
+  url           = {https://www.oecd.org/finance/financial-markets/Artificial-intelligence-machine-learning-big-data-in-finance.pdf},
+  bdsk-url-1    = {https://www.oecd.org/finance/financial-markets/Artificial-intelligence-machine-learning-big-data-in-finance.pdf},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  publisher     = {{OECD}},
+  year          = {2021},
+}
+
+@Book{oneil2016weapons,
+  author        = {O'Neil, Cathy},
+  title         = {Weapons of Math Destruction: {{How}} Big Data Increases Inequality and Threatens Democracy},
+  publisher     = {{Crown}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2016},
+}
+
+@Article{pace1997sparse,
+  author        = {Pace, R Kelley and Barry, Ronald},
+  title         = {Sparse Spatial Autoregressions},
+  doi           = {10.1016/s0167-7152(96)00140-x},
+  number        = {3},
+  pages         = {291--297},
+  volume        = {33},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Statistics \& Probability Letters},
+  year          = {1997},
+}
+
+@Unpublished{parr2018matrix,
+  author        = {Parr, Terence and Howard, Jeremy},
+  title         = {The Matrix Calculus You Need for Deep Learning},
+  archiveprefix = {arXiv},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  eprint        = {1802.01528},
+  eprinttype    = {arxiv},
+  year          = {2018},
+}
+
+@Misc{pawelczyk2021carla,
+  author        = {Martin Pawelczyk and Sascha Bielawski and Johannes van den Heuvel and Tobias Richter and Gjergji Kasneci},
+  title         = {CARLA: A Python Library to Benchmark Algorithmic Recourse and Counterfactual Explanation Algorithms},
+  eprint        = {2108.00783},
+  archiveprefix = {arXiv},
+  primaryclass  = {cs.LG},
+  year          = {2021},
+}
+
+@Book{pearl2018book,
+  author        = {Pearl, Judea and Mackenzie, Dana},
+  title         = {The Book of Why: The New Science of Cause and Effect},
+  publisher     = {{Basic books}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2018},
+}
+
+@Article{pearl2019seven,
+  author        = {Pearl, Judea},
+  title         = {The Seven Tools of Causal Inference, with Reflections on Machine Learning},
+  doi           = {10.1145/3241036},
+  number        = {3},
+  pages         = {54--60},
+  volume        = {62},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Communications of the ACM},
+  year          = {2019},
+}
+
+@Article{pedregosa2011scikitlearn,
+  author        = {Pedregosa, Fabian and Varoquaux, Ga{\"e}l and Gramfort, Alexandre and Michel, Vincent and Thirion, Bertrand and Grisel, Olivier and Blondel, Mathieu and Prettenhofer, Peter and Weiss, Ron and Dubourg, Vincent and others},
+  title         = {Scikit-Learn: {{Machine}} Learning in {{Python}}},
+  pages         = {2825--2830},
+  volume        = {12},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {the Journal of machine Learning research},
+  year          = {2011},
+}
+
+@Book{perry2010economic,
+  author        = {Perry, George L and Tobin, James},
+  title         = {Economic {{Events}}, {{Ideas}}, and {{Policies}}: The 1960s and After},
+  doi           = {10.5860/choice.38-4002},
+  publisher     = {{Brookings Institution Press}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2010},
+}
+
+@Article{pfaff2008var,
+  author        = {Pfaff, Bernhard and others},
+  title         = {{{VAR}}, {{SVAR}} and {{SVEC}} Models: {{Implementation}} within {{R}} Package Vars},
+  number        = {4},
+  pages         = {1--32},
+  volume        = {27},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of Statistical Software},
+  year          = {2008},
+}
+
+@Book{pindyck2014microeconomics,
+  author        = {Pindyck, Robert S and Rubinfeld, Daniel L},
+  title         = {Microeconomics},
+  publisher     = {{Pearson Education}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2014},
+}
+
+@Article{pope2011numbers,
+  author        = {Pope, Devin and Simonsohn, Uri},
+  title         = {Round Numbers as Goals: {{Evidence}} from Baseball, {{SAT}} Takers, and the Lab},
+  number        = {1},
+  pages         = {71--79},
+  volume        = {22},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Psychological science},
+  year          = {2011},
+}
+
+@InProceedings{poyiadzi2020face,
+  author        = {Poyiadzi, Rafael and Sokol, Kacper and Santos-Rodriguez, Raul and De Bie, Tijl and Flach, Peter},
+  booktitle     = {Proceedings of the {{AAAI}}/{{ACM Conference}} on {{AI}}, {{Ethics}}, and {{Society}}},
+  title         = {{{FACE}}: {{Feasible}} and Actionable Counterfactual Explanations},
+  pages         = {344--350},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2020},
+}
+
+@Article{qu2015estimating,
+  author        = {Qu, Xi and Lee, Lung-fei},
+  title         = {Estimating a Spatial Autoregressive Model with an Endogenous Spatial Weight Matrix},
+  doi           = {10.1016/j.jeconom.2014.08.008},
+  number        = {2},
+  pages         = {209--232},
+  volume        = {184},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of Econometrics},
+  year          = {2015},
+}
+
+@Article{rabanser2019failing,
+  author        = {Rabanser, Stephan and G{\"u}nnemann, Stephan and Lipton, Zachary},
+  title         = {Failing Loudly: {{An}} Empirical Study of Methods for Detecting Dataset Shift},
+  volume        = {32},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Advances in Neural Information Processing Systems},
+  year          = {2019},
+}
+
+@Unpublished{raghunathan2019adversarial,
+  author        = {Raghunathan, Aditi and Xie, Sang Michael and Yang, Fanny and Duchi, John C and Liang, Percy},
+  title         = {Adversarial Training Can Hurt Generalization},
+  archiveprefix = {arXiv},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  eprint        = {1906.06032},
+  eprinttype    = {arxiv},
+  year          = {2019},
+}
+
+@Unpublished{raj2017taming,
+  author        = {Raj, Vishnu and Kalyani, Sheetal},
+  title         = {Taming Non-Stationary Bandits: {{A Bayesian}} Approach},
+  archiveprefix = {arXiv},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  eprint        = {1707.09727},
+  eprinttype    = {arxiv},
+  year          = {2017},
+}
+
+@InProceedings{rasmussen2003gaussian,
+  author        = {Rasmussen, Carl Edward},
+  booktitle     = {Summer School on Machine Learning},
+  title         = {Gaussian Processes in Machine Learning},
+  pages         = {63--71},
+  publisher     = {{Springer}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2003},
+}
+
+@InProceedings{ribeiro2016why,
+  author        = {Ribeiro, Marco Tulio and Singh, Sameer and Guestrin, Carlos},
+  booktitle     = {Proceedings of the 22nd {{ACM SIGKDD}} International Conference on Knowledge Discovery and Data Mining},
+  title         = {"{{Why}} Should I Trust You?" {{Explaining}} the Predictions of Any Classifier},
+  pages         = {1135--1144},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2016},
+}
+
+@Article{romer1989does,
+  author        = {Romer, Christina D and Romer, David H},
+  title         = {Does Monetary Policy Matter? {{A}} New Test in the Spirit of {{Friedman}} and {{Schwartz}}},
+  doi           = {10.3386/w2966},
+  pages         = {121--170},
+  volume        = {4},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {NBER macroeconomics annual},
+  year          = {1989},
+}
+
+@Article{rudin2019stop,
+  author        = {Rudin, Cynthia},
+  title         = {Stop Explaining Black Box Machine Learning Models for High Stakes Decisions and Use Interpretable Models Instead},
+  doi           = {10.1038/s42256-019-0048-x},
+  number        = {5},
+  pages         = {206--215},
+  volume        = {1},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Nature Machine Intelligence},
+  year          = {2019},
+}
+
+@Article{sacerdote2001peer,
+  author        = {Sacerdote, Bruce},
+  title         = {Peer Effects with Random Assignment: {{Results}} for {{Dartmouth}} Roommates},
+  doi           = {10.3386/w7469},
+  number        = {2},
+  pages         = {681--704},
+  volume        = {116},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {The Quarterly journal of economics},
+  year          = {2001},
+}
+
+@Article{sadinle2019least,
+  author        = {Sadinle, Mauricio and Lei, Jing and Wasserman, Larry},
+  title         = {Least Ambiguous Set-Valued Classifiers with Bounded Error Levels},
+  doi           = {10.1080/01621459.2017.1395341},
+  number        = {525},
+  pages         = {223--234},
+  volume        = {114},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  file          = {:/Users/FA31DU/Zotero/storage/YXQ8N76A/Sadinle et al. - 2019 - Least ambiguous set-valued classifiers with bounde.pdf:;:/Users/FA31DU/Zotero/storage/ZHB56F3V/01621459.2017.html:},
+  journal       = {Journal of the American Statistical Association},
+  publisher     = {{Taylor \& Francis}},
+  year          = {2019},
+}
+
+@InProceedings{satopaa2011finding,
+  author        = {Satopaa, Ville and Albrecht, Jeannie and Irwin, David and Raghavan, Barath},
+  booktitle     = {2011 31st International Conference on Distributed Computing Systems Workshops},
+  title         = {Finding a" Kneedle" in a Haystack: {{Detecting}} Knee Points in System Behavior},
+  doi           = {10.1109/icdcsw.2011.20},
+  pages         = {166--171},
+  publisher     = {{IEEE}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2011},
+}
+
+@InProceedings{schut2021generating,
+  author        = {Schut, Lisa and Key, Oscar and Mc Grath, Rory and Costabello, Luca and Sacaleanu, Bogdan and Gal, Yarin and others},
+  booktitle     = {International {{Conference}} on {{Artificial Intelligence}} and {{Statistics}}},
+  title         = {Generating {{Interpretable Counterfactual Explanations By Implicit Minimisation}} of {{Epistemic}} and {{Aleatoric Uncertainties}}},
+  pages         = {1756--1764},
+  publisher     = {{PMLR}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2021},
+}
+
+@Book{schutze2008introduction,
+  author        = {Sch{\"u}tze, Hinrich and Manning, Christopher D and Raghavan, Prabhakar},
+  title         = {Introduction to Information Retrieval},
+  publisher     = {{Cambridge University Press Cambridge}},
+  volume        = {39},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2008},
+}
+
+@Article{shafir1993reasonbased,
+  author        = {Shafir, Eldar and Simonson, Itamar and Tversky, Amos},
+  title         = {Reason-Based Choice},
+  number        = {1-2},
+  pages         = {11--36},
+  volume        = {49},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Cognition},
+  year          = {1993},
+}
+
+@Article{simonson1989choice,
+  author        = {Simonson, Itamar},
+  title         = {Choice Based on Reasons: {{The}} Case of Attraction and Compromise Effects},
+  doi           = {10.1086/209205},
+  number        = {2},
+  pages         = {158--174},
+  volume        = {16},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of consumer research},
+  year          = {1989},
+}
+
+@Article{sims1986are,
+  author        = {Sims, Christopher A and others},
+  title         = {Are Forecasting Models Usable for Policy Analysis?},
+  doi           = {10.21034/qr.1011},
+  issue         = {Win},
+  pages         = {2--16},
+  volume        = {10},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Quarterly Review},
+  year          = {1986},
+}
+
+@InProceedings{slack2020fooling,
+  author        = {Slack, Dylan and Hilgard, Sophie and Jia, Emily and Singh, Sameer and Lakkaraju, Himabindu},
+  booktitle     = {Proceedings of the {{AAAI}}/{{ACM Conference}} on {{AI}}, {{Ethics}}, and {{Society}}},
+  title         = {Fooling Lime and Shap: {{Adversarial}} Attacks on Post Hoc Explanation Methods},
+  pages         = {180--186},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2020},
+}
+
+@Article{slack2021counterfactual,
+  author        = {Slack, Dylan and Hilgard, Anna and Lakkaraju, Himabindu and Singh, Sameer},
+  title         = {Counterfactual Explanations Can Be Manipulated},
+  volume        = {34},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Advances in Neural Information Processing Systems},
+  year          = {2021},
+}
+
+@Article{slovic1974who,
+  author        = {Slovic, Paul and Tversky, Amos},
+  title         = {Who Accepts {{Savage}}'s Axiom?},
+  number        = {6},
+  pages         = {368--373},
+  volume        = {19},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Behavioral science},
+  year          = {1974},
+}
+
+@Misc{spooner2021counterfactual,
+  author        = {Thomas Spooner and Danial Dervovic and Jason Long and Jon Shepard and Jiahao Chen and Daniele Magazzeni},
+  title         = {Counterfactual Explanations for Arbitrary Regression Models},
+  eprint        = {2106.15212},
+  archiveprefix = {arXiv},
+  primaryclass  = {cs.LG},
+  year          = {2021},
+}
+
+@Article{srivastava2014dropout,
+  author        = {Srivastava, Nitish and Hinton, Geoffrey and Krizhevsky, Alex and Sutskever, Ilya and Salakhutdinov, Ruslan},
+  title         = {Dropout: A Simple Way to Prevent Neural Networks from Overfitting},
+  number        = {1},
+  pages         = {1929--1958},
+  volume        = {15},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {The journal of machine learning research},
+  year          = {2014},
+}
+
+@Unpublished{stanton2022bayesian,
+  author        = {Stanton, Samuel and Maddox, Wesley and Wilson, Andrew Gordon},
+  title         = {Bayesian {{Optimization}} with {{Conformal Coverage Guarantees}}},
+  archiveprefix = {arXiv},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  eprint        = {2210.12496},
+  eprinttype    = {arxiv},
+  file          = {:/Users/FA31DU/Zotero/storage/XFGZAB9J/Stanton et al. - 2022 - Bayesian Optimization with Conformal Coverage Guar.pdf:;:/Users/FA31DU/Zotero/storage/RPWYDPVW/2210.html:},
+  year          = {2022},
+}
+
+@Article{sturm2014simple,
+  author        = {Sturm, Bob L},
+  title         = {A Simple Method to Determine If a Music Information Retrieval System Is a ``Horse''},
+  doi           = {10.1109/tmm.2014.2330697},
+  number        = {6},
+  pages         = {1636--1644},
+  volume        = {16},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {IEEE Transactions on Multimedia},
+  year          = {2014},
+}
+
+@Article{sunstein2003libertarian,
+  author        = {Sunstein, Cass R and Thaler, Richard H},
+  title         = {Libertarian Paternalism Is Not an Oxymoron},
+  doi           = {10.1017/cbo9780511618031.039},
+  pages         = {1159--1202},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {The University of Chicago Law Review},
+  year          = {2003},
+}
+
+@Book{sutton2018reinforcement,
+  author        = {Sutton, Richard S and Barto, Andrew G},
+  title         = {Reinforcement Learning: {{An}} Introduction},
+  publisher     = {{MIT press}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2018},
+}
+
+@Unpublished{szegedy2013intriguing,
+  author        = {Szegedy, Christian and Zaremba, Wojciech and Sutskever, Ilya and Bruna, Joan and Erhan, Dumitru and Goodfellow, Ian and Fergus, Rob},
+  title         = {Intriguing Properties of Neural Networks},
+  archiveprefix = {arXiv},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  eprint        = {1312.6199},
+  eprinttype    = {arxiv},
+  year          = {2013},
+}
+
+@Article{thaler1981empirical,
+  author        = {Thaler, Richard},
+  title         = {Some Empirical Evidence on Dynamic Inconsistency},
+  doi           = {10.1016/0165-1765(81)90067-7},
+  number        = {3},
+  pages         = {201--207},
+  volume        = {8},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Economics letters},
+  year          = {1981},
+}
+
+@Article{thaler2004more,
+  author        = {Thaler, Richard H and Benartzi, Shlomo},
+  title         = {Save More Tomorrow{\texttrademark}: {{Using}} Behavioral Economics to Increase Employee Saving},
+  doi           = {10.1086/380085},
+  number        = {S1},
+  pages         = {S164--S187},
+  volume        = {112},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of political Economy},
+  year          = {2004},
+}
+
+@Article{tversky1981framing,
+  author        = {Tversky, Amos and Kahneman, Daniel},
+  title         = {The Framing of Decisions and the Psychology of Choice},
+  doi           = {10.1007/978-1-4613-2391-4_2},
+  number        = {4481},
+  pages         = {453--458},
+  volume        = {211},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Science (New York, N.Y.)},
+  shortjournal  = {science},
+  year          = {1981},
+}
+
+@Article{ungemach2011how,
+  author        = {Ungemach, Christoph and Stewart, Neil and Reimers, Stian},
+  title         = {How Incidental Values from the Environment Affect Decisions about Money, Risk, and Delay},
+  doi           = {10.1177/0956797610396225},
+  number        = {2},
+  pages         = {253--260},
+  volume        = {22},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Psychological Science},
+  year          = {2011},
+}
+
+@Article{upadhyay2021robust,
+  author  = {Upadhyay, Sohini and Joshi, Shalmali and Lakkaraju, Himabindu},
+  title   = {Towards robust and reliable algorithmic recourse},
+  pages   = {16926--16937},
+  volume  = {34},
+  journal = {Advances in Neural Information Processing Systems},
+  year    = {2021},
+}
+
+@InProceedings{ustun2019actionable,
+  author        = {Ustun, Berk and Spangher, Alexander and Liu, Yang},
+  booktitle     = {Proceedings of the {{Conference}} on {{Fairness}}, {{Accountability}}, and {{Transparency}}},
+  title         = {Actionable Recourse in Linear Classification},
+  doi           = {10.1145/3287560.3287566},
+  pages         = {10--19},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2019},
+}
+
+@Article{vanboven2000egocentric,
+  author        = {Van Boven, Leaf and Dunning, David and Loewenstein, George},
+  title         = {Egocentric Empathy Gaps between Owners and Buyers: Misperceptions of the Endowment Effect.},
+  doi           = {10.1037/0022-3514.79.1.66},
+  number        = {1},
+  pages         = {66},
+  volume        = {79},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of personality and social psychology},
+  year          = {2000},
+}
+
+@Book{varshney2022trustworthy,
+  author        = {Varshney, Kush R.},
+  title         = {Trustworthy {{Machine Learning}}},
+  publisher     = {{Independently Published}},
+  address       = {{Chappaqua, NY, USA}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2022},
+}
+
+@Misc{verma2020counterfactual,
+  author        = {Sahil Verma and Varich Boonsanong and Minh Hoang and Keegan E. Hines and John P. Dickerson and Chirag Shah},
+  title         = {Counterfactual Explanations and Algorithmic Recourses for Machine Learning: A Review},
+  eprint        = {2010.10596},
+  archiveprefix = {arXiv},
+  primaryclass  = {cs.LG},
+  year          = {2022},
+}
+
+@Article{verstyuk2020modeling,
+  author        = {Verstyuk, Sergiy},
+  title         = {Modeling Multivariate Time Series in Economics: {{From}} Auto-Regressions to Recurrent Neural Networks},
+  doi           = {10.2139/ssrn.3589337},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Available at SSRN 3589337},
+  year          = {2020},
+}
+
+@Article{wachter2017counterfactual,
+  author        = {Wachter, Sandra and Mittelstadt, Brent and Russell, Chris},
+  title         = {Counterfactual Explanations without Opening the Black Box: {{Automated}} Decisions and the {{GDPR}}},
+  doi           = {10.2139/ssrn.3063289},
+  pages         = {841},
+  volume        = {31},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Harv. JL \& Tech.},
+  year          = {2017},
+}
+
+@Article{wang2018optimal,
+  author        = {Wang, HaiYing and Zhu, Rong and Ma, Ping},
+  title         = {Optimal Subsampling for Large Sample Logistic Regression},
+  number        = {522},
+  pages         = {829--844},
+  volume        = {113},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Journal of the American Statistical Association},
+  year          = {2018},
+}
+
+@Book{wasserman2006all,
+  author        = {Wasserman, Larry},
+  title         = {All of Nonparametric Statistics},
+  publisher     = {{Springer Science \& Business Media}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2006},
+}
+
+@Book{wasserman2013all,
+  author        = {Wasserman, Larry},
+  title         = {All of Statistics: A Concise Course in Statistical Inference},
+  publisher     = {{Springer Science \& Business Media}},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  year          = {2013},
+}
+
+@Article{widmer1996learning,
+  author        = {Widmer, Gerhard and Kubat, Miroslav},
+  title         = {Learning in the Presence of Concept Drift and Hidden Contexts},
+  doi           = {10.1007/bf00116900},
+  number        = {1},
+  pages         = {69--101},
+  volume        = {23},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Machine learning},
+  year          = {1996},
+}
+
+@Misc{wilson2020case,
+  author        = {Andrew Gordon Wilson},
+  title         = {The Case for Bayesian Deep Learning},
+  eprint        = {2001.10995},
+  archiveprefix = {arXiv},
+  primaryclass  = {cs.LG},
+  year          = {2020},
+}
+
+@Article{witten2009penalized,
+  author        = {Witten, Daniela M and Tibshirani, Robert and Hastie, Trevor},
+  title         = {A Penalized Matrix Decomposition, with Applications to Sparse Principal Components and Canonical Correlation Analysis},
+  doi           = {10.1093/biostatistics/kxp008},
+  number        = {3},
+  pages         = {515--534},
+  volume        = {10},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Biostatistics (Oxford, England)},
+  shortjournal  = {Biostatistics},
+  year          = {2009},
+}
+
+@Article{xu2020epidemiological,
+  author        = {Xu, Bo and Gutierrez, Bernardo and Mekaru, Sumiko and Sewalk, Kara and Goodwin, Lauren and Loskill, Alyssa and Cohn, Emily and Hswen, Yulin and Hill, Sarah C. and Cobo, Maria M and Zarebski, Alexander and Li, Sabrina and Wu, Chieh-Hsi and Hulland, Erin and Morgan, Julia and Wang, Lin and O'Brien, Katelynn and Scarpino, Samuel V. and Brownstein, John S. and Pybus, Oliver G. and Pigott, David M. and Kraemer, Moritz U. G.},
+  title         = {Epidemiological Data from the {{COVID-19}} Outbreak, Real-Time Case Information},
+  doi           = {doi.org/10.1038/s41597-020-0448-0},
+  number        = {106},
+  volume        = {7},
+  bdsk-url-1    = {https://doi.org/10.1038/s41597-020-0448-0},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Scientific Data},
+  year          = {2020},
+}
+
+@Article{yeh2009comparisons,
+  author        = {Yeh, I-Cheng and Lien, Che-hui},
+  title         = {The Comparisons of Data Mining Techniques for the Predictive Accuracy of Probability of Default of Credit Card Clients},
+  doi           = {10.1016/j.eswa.2007.12.020},
+  number        = {2},
+  pages         = {2473--2480},
+  volume        = {36},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Expert systems with applications},
+  year          = {2009},
+}
+
+@Article{zhang1998forecasting,
+  author        = {Zhang, Guoqiang and Patuwo, B Eddy and Hu, Michael Y},
+  title         = {Forecasting with Artificial Neural Networks:: {{The}} State of the Art},
+  number        = {1},
+  pages         = {35--62},
+  volume        = {14},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {International journal of forecasting},
+  year          = {1998},
+}
+
+@Article{zhang2003time,
+  author        = {Zhang, G Peter},
+  title         = {Time Series Forecasting Using a Hybrid {{ARIMA}} and Neural Network Model},
+  doi           = {10.1016/s0925-2312(01)00702-0},
+  pages         = {159--175},
+  volume        = {50},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {Neurocomputing},
+  year          = {2003},
+}
+
+@Unpublished{zheng2018dags,
+  author        = {Zheng, Xun and Aragam, Bryon and Ravikumar, Pradeep and Xing, Eric P},
+  title         = {Dags with No Tears: {{Continuous}} Optimization for Structure Learning},
+  archiveprefix = {arXiv},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  eprint        = {1803.01422},
+  eprinttype    = {arxiv},
+  year          = {2018},
+}
+
+@Article{zhu2015optimal,
+  author        = {Zhu, Rong and Ma, Ping and Mahoney, Michael W and Yu, Bin},
+  title         = {Optimal Subsampling Approaches for Large Sample Linear Regression},
+  pages         = {arXiv--1509},
+  date-added    = {2022-12-13 12:58:01 +0100},
+  date-modified = {2022-12-13 12:58:01 +0100},
+  journal       = {arXiv},
+  year          = {2015},
+}
+
+@Article{barber2021predictive,
+  author    = {Barber, Rina Foygel and Candès, Emmanuel J. and Ramdas, Aaditya and Tibshirani, Ryan J.},
+  title     = {Predictive inference with the jackknife+},
+  doi       = {10.1214/20-AOS1965},
+  issn      = {0090-5364, 2168-8966},
+  number    = {1},
+  pages     = {486--507},
+  urldate   = {2022-12-13},
+  volume    = {49},
+  abstract  = {This paper introduces the jackknife+, which is a novel method for constructing predictive confidence intervals. Whereas the jackknife outputs an interval centered at the predicted response of a test point, with the width of the interval determined by the quantiles of leave-one-out residuals, the jackknife+ also uses the leave-one-out predictions at the test point to account for the variability in the fitted regression function. Assuming exchangeable training samples, we prove that this crucial modification permits rigorous coverage guarantees regardless of the distribution of the data points, for any algorithm that treats the training points symmetrically. Such guarantees are not possible for the original jackknife and we demonstrate examples where the coverage rate may actually vanish. Our theoretical and empirical analysis reveals that the jackknife and the jackknife+ intervals achieve nearly exact coverage and have similar lengths whenever the fitting algorithm obeys some form of stability. Further, we extend the jackknife+ to \$K\$-fold cross validation and similarly establish rigorous coverage properties. Our methods are related to cross-conformal prediction proposed by Vovk (Ann. Math. Artif. Intell. 74 (2015) 9–28) and we discuss connections.},
+  file      = {:Barber2021 - Predictive Inference with the Jackknife+.pdf:PDF},
+  journal   = {The Annals of Statistics},
+  keywords  = {62F40, 62G08, 62G09, conformal inference, cross-validation, distribution-free, jackknife, leave-one-out, stability},
+  month     = feb,
+  publisher = {Institute of Mathematical Statistics},
+  year      = {2021},
+}
+
+@TechReport{chouldechova2018frontiers,
+  author        = {Chouldechova, Alexandra and Roth, Aaron},
+  title         = {The {Frontiers} of {Fairness} in {Machine} {Learning}},
+  doi           = {10.48550/arXiv.1810.08810},
+  eprint        = {1810.08810},
+  note          = {arXiv:1810.08810 [cs, stat] type: article},
+  abstract      = {The last few years have seen an explosion of academic and popular interest in algorithmic fairness. Despite this interest and the volume and velocity of work that has been produced recently, the fundamental science of fairness in machine learning is still in a nascent state. In March 2018, we convened a group of experts as part of a CCC visioning workshop to assess the state of the field, and distill the most promising research directions going forward. This report summarizes the findings of that workshop. Along the way, it surveys recent theoretical work in the field and points towards promising directions for research.},
+  archiveprefix = {arxiv},
+  file          = {:chouldechova2018frontiers - The Frontiers of Fairness in Machine Learning.pdf:PDF},
+  keywords      = {Computer Science - Machine Learning, Computer Science - Data Structures and Algorithms, Computer Science - Computer Science and Game Theory, Statistics - Machine Learning},
+  month         = oct,
+  school        = {arXiv},
+  year          = {2018},
+}
+
+@Misc{pawelczyk2022probabilistically,
+  author        = {Martin Pawelczyk and Teresa Datta and Johannes van-den-Heuvel and Gjergji Kasneci and Himabindu Lakkaraju},
+  title         = {Probabilistically Robust Recourse: Navigating the Trade-offs between Costs and Robustness in Algorithmic Recourse},
+  eprint        = {2203.06768},
+  archiveprefix = {arXiv},
+  primaryclass  = {cs.LG},
+  year          = {2023},
+}
+
+@Misc{stutz2022learning,
+  author        = {David Stutz and Krishnamurthy and Dvijotham and Ali Taylan Cemgil and Arnaud Doucet},
+  title         = {Learning Optimal Conformal Classifiers},
+  eprint        = {2110.09192},
+  archiveprefix = {arXiv},
+  primaryclass  = {cs.LG},
+  year          = {2022},
+}
+
+@InProceedings{grathwohl2020your,
+  author    = {Grathwohl, Will and Wang, Kuan-Chieh and Jacobsen, Joern-Henrik and Duvenaud, David and Norouzi, Mohammad and Swersky, Kevin},
+  booktitle = {International Conference on Learning Representations},
+  title     = {Your classifier is secretly an energy based model and you should treat it like one},
+  year      = {2020},
+}
+
+@Book{murphy2023probabilistic,
+  author    = {Murphy, Kevin P},
+  title     = {Probabilistic machine learning: Advanced topics},
+  publisher = {MIT press},
+  year      = {2023},
+}
+
+@InProceedings{artelt2021evaluating,
+  author       = {Artelt, Andr{\'e} and Vaquet, Valerie and Velioglu, Riza and Hinder, Fabian and Brinkrolf, Johannes and Schilling, Malte and Hammer, Barbara},
+  booktitle    = {2021 IEEE Symposium Series on Computational Intelligence (SSCI)},
+  title        = {Evaluating robustness of counterfactual explanations},
+  organization = {IEEE},
+  pages        = {01--09},
+  year         = {2021},
+}
+
+@Article{guidotti2022counterfactual,
+  author    = {Guidotti, Riccardo},
+  title     = {Counterfactual explanations and how to find them: literature review and benchmarking},
+  pages     = {1--55},
+  journal   = {Data Mining and Knowledge Discovery},
+  publisher = {Springer},
+  year      = {2022},
+}
+
+@Misc{mahajan2019preserving,
+  author        = {Divyat Mahajan and Chenhao Tan and Amit Sharma},
+  title         = {Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifiers},
+  eprint        = {1912.03277},
+  archiveprefix = {arXiv},
+  primaryclass  = {cs.LG},
+  year          = {2020},
+}
+
+@TechReport{antoran2023sampling,
+  author      = {Antorán, Javier and Padhy, Shreyas and Barbano, Riccardo and Nalisnick, Eric and Janz, David and Hernández-Lobato, José Miguel},
+  date        = {2023-03},
+  institution = {arXiv},
+  title       = {Sampling-based inference for large linear models, with application to linearised {Laplace}},
+  note        = {arXiv:2210.04994 [cs, stat] type: article},
+  url         = {http://arxiv.org/abs/2210.04994},
+  urldate     = {2023-03-25},
+  abstract    = {Large-scale linear models are ubiquitous throughout machine learning, with contemporary application as surrogate models for neural network uncertainty quantification; that is, the linearised Laplace method. Alas, the computational cost associated with Bayesian linear models constrains this method's application to small networks, small output spaces and small datasets. We address this limitation by introducing a scalable sample-based Bayesian inference method for conjugate Gaussian multi-output linear models, together with a matching method for hyperparameter (regularisation) selection. Furthermore, we use a classic feature normalisation method (the g-prior) to resolve a previously highlighted pathology of the linearised Laplace method. Together, these contributions allow us to perform linearised neural network inference with ResNet-18 on CIFAR100 (11M parameters, 100 outputs x 50k datapoints), with ResNet-50 on Imagenet (50M parameters, 1000 outputs x 1.2M datapoints) and with a U-Net on a high-resolution tomographic reconstruction task (2M parameters, 251k output{\textasciitilde}dimensions).},
+  annotation  = {Comment: Published at ICLR 2023. This latest Arxiv version is extended with a demonstration of the proposed methods on the Imagenet dataset},
+  file        = {arXiv Fulltext PDF:https\://arxiv.org/pdf/2210.04994.pdf:application/pdf},
+  keywords    = {Statistics - Machine Learning, Computer Science - Artificial Intelligence, Computer Science - Machine Learning},
+}
+
+@Misc{altmeyer2022conformal,
+  author   = {Altmeyer, Patrick},
+  date     = {2022-10},
+  title    = {{Conformal} {Prediction} in {Julia}},
+  language = {en},
+  url      = {https://www.paltmeyer.com/blog/posts/conformal-prediction/},
+  urldate  = {2023-03-27},
+  abstract = {A (very) gentle introduction to Conformal Prediction in Julia using my new package ConformalPrediction.jl.},
+}
+
+@InProceedings{welling2011bayesian,
+  author       = {Welling, Max and Teh, Yee W},
+  booktitle    = {Proceedings of the 28th international conference on machine learning (ICML-11)},
+  title        = {Bayesian learning via stochastic gradient Langevin dynamics},
+  organization = {Citeseer},
+  pages        = {681--688},
+  year         = {2011},
+}
+
+@Article{gill2010circular,
+  author    = {Gill, Jeff and Hangartner, Dominik},
+  title     = {Circular data in political science and how to handle it},
+  number    = {3},
+  pages     = {316--336},
+  volume    = {18},
+  journal   = {Political Analysis},
+  publisher = {Cambridge University Press},
+  year      = {2010},
+}
+
+@InProceedings{liu2022goggle,
+  author    = {Liu, Tennison and Qian, Zhaozhi and Berrevoets, Jeroen and van der Schaar, Mihaela},
+  booktitle = {The Eleventh International Conference on Learning Representations},
+  title     = {GOGGLE: Generative modelling for tabular data by learning relational structure},
+  year      = {2022},
+}
+
+@Misc{du2019implicit,
+  author        = {Yilun Du and Igor Mordatch},
+  title         = {Implicit Generation and Generalization in Energy-Based Models},
+  eprint        = {1903.08689},
+  archiveprefix = {arXiv},
+  primaryclass  = {cs.LG},
+  year          = {2020},
+}
+
+@InProceedings{krizhevsky2009learning,
+  author     = {Krizhevsky, A.},
+  date       = {2009},
+  title      = {Learning {Multiple} {Layers} of {Features} from {Tiny} {Images}},
+  url        = {https://www.semanticscholar.org/paper/Learning-Multiple-Layers-of-Features-from-Tiny-Krizhevsky/5d90f06bb70a0a3dced62413346235c02b1aa086},
+  urldate    = {2023-06-21},
+  abstract   = {Groups at MIT and NYU have collected a dataset of millions of tiny colour images from the web. It is, in principle, an excellent dataset for unsupervised training of deep generative models, but previous researchers who have tried this have found it dicult to learn a good set of lters from the images. We show how to train a multi-layer generative model that learns to extract meaningful features which resemble those found in the human visual cortex. Using a novel parallelization algorithm to distribute the work among multiple machines connected on a network, we show how training such a model can be done in reasonable time. A second problematic aspect of the tiny images dataset is that there are no reliable class labels which makes it hard to use for object recognition experiments. We created two sets of reliable labels. The CIFAR-10 set has 6000 examples of each of 10 classes and the CIFAR-100 set has 600 examples of each of 100 non-overlapping classes. Using these labels, we show that object recognition is signicantly improved by pre-training a layer of features on a large set of unlabeled tiny images.},
+  annotation = {[TLDR] It is shown how to train a multi-layer generative model that learns to extract meaningful features which resemble those found in the human visual cortex, using a novel parallelization algorithm to distribute the work among multiple machines connected on a network.},
+  file       = {Semantic Scholar Link:https\://www.semanticscholar.org/paper/Learning-Multiple-Layers-of-Features-from-Tiny-Krizhevsky/5d90f06bb70a0a3dced62413346235c02b1aa086:text/html;Full Text PDF:http\://www.cs.toronto.edu/~kriz/learning-features-2009-TR.pdf:application/pdf},
+}
+
+@Misc{becker1996adult,
+  author    = {Barry Becker, Ronny Kohavi},
+  date      = {1996},
+  title     = {Adult},
+  doi       = {10.24432/C5XW20},
+  note      = {Type: dataset},
+  url       = {https://archive.ics.uci.edu/dataset/2},
+  urldate   = {2023-06-21},
+  publisher = {UCI Machine Learning Repository},
+}
+
+@InProceedings{tolomei2017interpretable,
+  author     = {Tolomei, Gabriele and Silvestri, Fabrizio and Haines, Andrew and Lalmas, Mounia},
+  booktitle  = {Proceedings of the 23rd {ACM} {SIGKDD} {International} {Conference} on {Knowledge} {Discovery} and {Data} {Mining}},
+  date       = {2017-08},
+  title      = {Interpretable {Predictions} of {Tree}-based {Ensembles} via {Actionable} {Feature} {Tweaking}},
+  doi        = {10.1145/3097983.3098039},
+  note       = {arXiv:1706.06691 [stat]},
+  pages      = {465--474},
+  url        = {http://arxiv.org/abs/1706.06691},
+  urldate    = {2023-06-21},
+  abstract   = {Machine-learned models are often described as "black boxes". In many real-world applications however, models may have to sacrifice predictive power in favour of human-interpretability. When this is the case, feature engineering becomes a crucial task, which requires significant and time-consuming human effort. Whilst some features are inherently static, representing properties that cannot be influenced (e.g., the age of an individual), others capture characteristics that could be adjusted (e.g., the daily amount of carbohydrates taken). Nonetheless, once a model is learned from the data, each prediction it makes on new instances is irreversible - assuming every instance to be a static point located in the chosen feature space. There are many circumstances however where it is important to understand (i) why a model outputs a certain prediction on a given instance, (ii) which adjustable features of that instance should be modified, and finally (iii) how to alter such a prediction when the mutated instance is input back to the model. In this paper, we present a technique that exploits the internals of a tree-based ensemble classifier to offer recommendations for transforming true negative instances into positively predicted ones. We demonstrate the validity of our approach using an online advertising application. First, we design a Random Forest classifier that effectively separates between two types of ads: low (negative) and high (positive) quality ads (instances). Then, we introduce an algorithm that provides recommendations that aim to transform a low quality ad (negative instance) into a high quality one (positive instance). Finally, we evaluate our approach on a subset of the active inventory of a large ad network, Yahoo Gemini.},
+  annotation = {Comment: 10 pages, KDD 2017},
+  file       = {arXiv Fulltext PDF:https\://arxiv.org/pdf/1706.06691.pdf:application/pdf},
+  keywords   = {Statistics - Machine Learning, 68T01, I.2.0, I.5.1},
+}
+
+@TechReport{dandl2023counterfactuals,
+  author      = {Dandl, Susanne and Hofheinz, Andreas and Binder, Martin and Bischl, Bernd and Casalicchio, Giuseppe},
+  date        = {2023-04},
+  institution = {arXiv},
+  title       = {counterfactuals: {An} {R} {Package} for {Counterfactual} {Explanation} {Methods}},
+  note        = {arXiv:2304.06569 [cs, stat] type: article},
+  url         = {http://arxiv.org/abs/2304.06569},
+  urldate     = {2023-06-21},
+  abstract    = {Counterfactual explanation methods provide information on how feature values of individual observations must be changed to obtain a desired prediction. Despite the increasing amount of proposed methods in research, only a few implementations exist whose interfaces and requirements vary widely. In this work, we introduce the counterfactuals R package, which provides a modular and unified R6-based interface for counterfactual explanation methods. We implemented three existing counterfactual explanation methods and propose some optional methodological extensions to generalize these methods to different scenarios and to make them more comparable. We explain the structure and workflow of the package using real use cases and show how to integrate additional counterfactual explanation methods into the package. In addition, we compared the implemented methods for a variety of models and datasets with regard to the quality of their counterfactual explanations and their runtime behavior.},
+  file        = {arXiv Fulltext PDF:https\://arxiv.org/pdf/2304.06569.pdf:application/pdf},
+  keywords    = {Statistics - Machine Learning, Computer Science - Machine Learning, Statistics - Computation},
+  shorttitle  = {counterfactuals},
+}
+
+@TechReport{laugel2017inversea,
+  author      = {Laugel, Thibault and Lesot, Marie-Jeanne and Marsala, Christophe and Renard, Xavier and Detyniecki, Marcin},
+  date        = {2017-12},
+  institution = {arXiv},
+  title       = {Inverse {Classification} for {Comparison}-based {Interpretability} in {Machine} {Learning}},
+  doi         = {10.48550/arXiv.1712.08443},
+  note        = {arXiv:1712.08443 [cs, stat] type: article},
+  url         = {http://arxiv.org/abs/1712.08443},
+  urldate     = {2023-06-21},
+  abstract    = {In the context of post-hoc interpretability, this paper addresses the task of explaining the prediction of a classifier, considering the case where no information is available, neither on the classifier itself, nor on the processed data (neither the training nor the test data). It proposes an instance-based approach whose principle consists in determining the minimal changes needed to alter a prediction: given a data point whose classification must be explained, the proposed method consists in identifying a close neighbour classified differently, where the closeness definition integrates a sparsity constraint. This principle is implemented using observation generation in the Growing Spheres algorithm. Experimental results on two datasets illustrate the relevance of the proposed approach that can be used to gain knowledge about the classifier.},
+  annotation  = {Comment: preprint},
+  file        = {arXiv Fulltext PDF:https\://arxiv.org/pdf/1712.08443.pdf:application/pdf},
+  keywords    = {Statistics - Machine Learning, Computer Science - Artificial Intelligence, Computer Science - Machine Learning},
+}
+
+@TechReport{delaney2021uncertainty,
+  author      = {Delaney, Eoin and Greene, Derek and Keane, Mark T.},
+  date        = {2021-07},
+  institution = {arXiv},
+  title       = {Uncertainty {Estimation} and {Out}-of-{Distribution} {Detection} for {Counterfactual} {Explanations}: {Pitfalls} and {Solutions}},
+  note        = {arXiv:2107.09734 [cs] type: article},
+  url         = {http://arxiv.org/abs/2107.09734},
+  urldate     = {2023-06-23},
+  abstract    = {Whilst an abundance of techniques have recently been proposed to generate counterfactual explanations for the predictions of opaque black-box systems, markedly less attention has been paid to exploring the uncertainty of these generated explanations. This becomes a critical issue in high-stakes scenarios, where uncertain and misleading explanations could have dire consequences (e.g., medical diagnosis and treatment planning). Moreover, it is often difficult to determine if the generated explanations are well grounded in the training data and sensitive to distributional shifts. This paper proposes several practical solutions that can be leveraged to solve these problems by establishing novel connections with other research works in explainability (e.g., trust scores) and uncertainty estimation (e.g., Monte Carlo Dropout). Two experiments demonstrate the utility of our proposed solutions.},
+  file        = {arXiv Fulltext PDF:https\://arxiv.org/pdf/2107.09734.pdf:application/pdf},
+  keywords    = {Computer Science - Machine Learning, Computer Science - Artificial Intelligence},
+  shorttitle  = {Uncertainty {Estimation} and {Out}-of-{Distribution} {Detection} for {Counterfactual} {Explanations}},
+}
+
+@InProceedings{casanueva2020efficient,
+  author    = {Casanueva, Iñigo and Temčinas, Tadas and Gerz, Daniela and Henderson, Matthew and Vulić, Ivan},
+  booktitle = {Proceedings of the 2nd {Workshop} on {Natural} {Language} {Processing} for {Conversational} {AI}},
+  date      = {2020-07},
+  title     = {Efficient {Intent} {Detection} with {Dual} {Sentence} {Encoders}},
+  doi       = {10.18653/v1/2020.nlp4convai-1.5},
+  location  = {Online},
+  pages     = {38--45},
+  publisher = {Association for Computational Linguistics},
+  url       = {https://aclanthology.org/2020.nlp4convai-1.5},
+  urldate   = {2023-06-27},
+  abstract  = {Building conversational systems in new domains and with added functionality requires resource-efficient models that work under low-data regimes (i.e., in few-shot setups). Motivated by these requirements, we introduce intent detection methods backed by pretrained dual sentence encoders such as USE and ConveRT. We demonstrate the usefulness and wide applicability of the proposed intent detectors, showing that: 1) they outperform intent detectors based on fine-tuning the full BERT-Large model or using BERT as a fixed black-box encoder on three diverse intent detection data sets; 2) the gains are especially pronounced in few-shot setups (i.e., with only 10 or 30 annotated examples per intent); 3) our intent detectors can be trained in a matter of minutes on a single CPU; and 4) they are stable across different hyperparameter settings. In hope of facilitating and democratizing research focused on intention detection, we release our code, as well as a new challenging single-domain intent detection dataset comprising 13,083 annotated examples over 77 intents.},
+  file      = {Full Text PDF:https\://aclanthology.org/2020.nlp4convai-1.5.pdf:application/pdf},
+}
+
+@TechReport{liu2019roberta,
+  author      = {Liu, Yinhan and Ott, Myle and Goyal, Naman and Du, Jingfei and Joshi, Mandar and Chen, Danqi and Levy, Omer and Lewis, Mike and Zettlemoyer, Luke and Stoyanov, Veselin},
+  date        = {2019-07},
+  institution = {arXiv},
+  title       = {{RoBERTa}: {A} {Robustly} {Optimized} {BERT} {Pretraining} {Approach}},
+  doi         = {10.48550/arXiv.1907.11692},
+  note        = {arXiv:1907.11692 [cs] type: article},
+  url         = {http://arxiv.org/abs/1907.11692},
+  urldate     = {2023-06-27},
+  abstract    = {Language model pretraining has led to significant performance gains but careful comparison between different approaches is challenging. Training is computationally expensive, often done on private datasets of different sizes, and, as we will show, hyperparameter choices have significant impact on the final results. We present a replication study of BERT pretraining (Devlin et al., 2019) that carefully measures the impact of many key hyperparameters and training data size. We find that BERT was significantly undertrained, and can match or exceed the performance of every model published after it. Our best model achieves state-of-the-art results on GLUE, RACE and SQuAD. These results highlight the importance of previously overlooked design choices, and raise questions about the source of recently reported improvements. We release our models and code.},
+  file        = {arXiv Fulltext PDF:https\://arxiv.org/pdf/1907.11692.pdf:application/pdf},
+  keywords    = {Computer Science - Computation and Language},
+  shorttitle  = {{RoBERTa}},
+}
+
+@TechReport{kunstner2020limitations,
+  author      = {Kunstner, Frederik and Balles, Lukas and Hennig, Philipp},
+  date        = {2020-06},
+  institution = {arXiv},
+  title       = {Limitations of the {Empirical} {Fisher} {Approximation} for {Natural} {Gradient} {Descent}},
+  doi         = {10.48550/arXiv.1905.12558},
+  note        = {arXiv:1905.12558 [cs, stat] type: article},
+  url         = {http://arxiv.org/abs/1905.12558},
+  urldate     = {2023-06-30},
+  abstract    = {Natural gradient descent, which preconditions a gradient descent update with the Fisher information matrix of the underlying statistical model, is a way to capture partial second-order information. Several highly visible works have advocated an approximation known as the empirical Fisher, drawing connections between approximate second-order methods and heuristics like Adam. We dispute this argument by showing that the empirical Fisher---unlike the Fisher---does not generally capture second-order information. We further argue that the conditions under which the empirical Fisher approaches the Fisher (and the Hessian) are unlikely to be met in practice, and that, even on simple optimization problems, the pathologies of the empirical Fisher can have undesirable effects.},
+  annotation  = {Comment: V3: Minor corrections (typographic errors)},
+  file        = {arXiv Fulltext PDF:https\://arxiv.org/pdf/1905.12558.pdf:application/pdf},
+  keywords    = {Computer Science - Machine Learning, Statistics - Machine Learning},
+}
+
+@TechReport{botev2017practical,
+  author      = {Botev, Aleksandar and Ritter, Hippolyt and Barber, David},
+  date        = {2017-06},
+  institution = {arXiv},
+  title       = {Practical {Gauss}-{Newton} {Optimisation} for {Deep} {Learning}},
+  doi         = {10.48550/arXiv.1706.03662},
+  note        = {arXiv:1706.03662 [stat] type: article},
+  url         = {http://arxiv.org/abs/1706.03662},
+  urldate     = {2023-06-30},
+  abstract    = {We present an efficient block-diagonal ap- proximation to the Gauss-Newton matrix for feedforward neural networks. Our result- ing algorithm is competitive against state- of-the-art first order optimisation methods, with sometimes significant improvement in optimisation performance. Unlike first-order methods, for which hyperparameter tuning of the optimisation parameters is often a labo- rious process, our approach can provide good performance even when used with default set- tings. A side result of our work is that for piecewise linear transfer functions, the net- work objective function can have no differ- entiable local maxima, which may partially explain why such transfer functions facilitate effective optimisation.},
+  annotation  = {Comment: ICML 2017},
+  file        = {arXiv Fulltext PDF:https\://arxiv.org/pdf/1706.03662.pdf:application/pdf},
+  keywords    = {Statistics - Machine Learning},
+}
+
+@TechReport{sharma2021sketching,
+  author      = {Sharma, Apoorva and Azizan, Navid and Pavone, Marco},
+  date        = {2021-02},
+  institution = {arXiv},
+  title       = {Sketching {Curvature} for {Efficient} {Out}-of-{Distribution} {Detection} for {Deep} {Neural} {Networks}},
+  doi         = {10.48550/arXiv.2102.12567},
+  note        = {arXiv:2102.12567 [cs] type: article},
+  url         = {http://arxiv.org/abs/2102.12567},
+  urldate     = {2023-06-30},
+  abstract    = {In order to safely deploy Deep Neural Networks (DNNs) within the perception pipelines of real-time decision making systems, there is a need for safeguards that can detect out-of-training-distribution (OoD) inputs both efficiently and accurately. Building on recent work leveraging the local curvature of DNNs to reason about epistemic uncertainty, we propose Sketching Curvature of OoD Detection (SCOD), an architecture-agnostic framework for equipping any trained DNN with a task-relevant epistemic uncertainty estimate. Offline, given a trained model and its training data, SCOD employs tools from matrix sketching to tractably compute a low-rank approximation of the Fisher information matrix, which characterizes which directions in the weight space are most influential on the predictions over the training data. Online, we estimate uncertainty by measuring how much perturbations orthogonal to these directions can alter predictions at a new test input. We apply SCOD to pre-trained networks of varying architectures on several tasks, ranging from regression to classification. We demonstrate that SCOD achieves comparable or better OoD detection performance with lower computational burden relative to existing baselines.},
+  file        = {arXiv Fulltext PDF:https\://arxiv.org/pdf/2102.12567.pdf:application/pdf},
+  keywords    = {Computer Science - Machine Learning},
+}
+
+@TechReport{amini2019spatial,
+  author      = {Amini, Alexander and Soleimany, Ava and Karaman, Sertac and Rus, Daniela},
+  date        = {2019-05},
+  institution = {arXiv},
+  title       = {Spatial {Uncertainty} {Sampling} for {End}-to-{End} {Control}},
+  doi         = {10.48550/arXiv.1805.04829},
+  note        = {arXiv:1805.04829 [cs] type: article},
+  url         = {http://arxiv.org/abs/1805.04829},
+  urldate     = {2023-06-30},
+  abstract    = {End-to-end trained neural networks (NNs) are a compelling approach to autonomous vehicle control because of their ability to learn complex tasks without manual engineering of rule-based decisions. However, challenging road conditions, ambiguous navigation situations, and safety considerations require reliable uncertainty estimation for the eventual adoption of full-scale autonomous vehicles. Bayesian deep learning approaches provide a way to estimate uncertainty by approximating the posterior distribution of weights given a set of training data. Dropout training in deep NNs approximates Bayesian inference in a deep Gaussian process and can thus be used to estimate model uncertainty. In this paper, we propose a Bayesian NN for end-to-end control that estimates uncertainty by exploiting feature map correlation during training. This approach achieves improved model fits, as well as tighter uncertainty estimates, than traditional element-wise dropout. We evaluate our algorithms on a challenging dataset collected over many different road types, times of day, and weather conditions, and demonstrate how uncertainties can be used in conjunction with a human controller in a parallel autonomous setting.},
+  annotation  = {Comment: Originally published in Neural Information Processing Systems (NIPS) Workshop on Bayesian Deep Learning 2017},
+  file        = {arXiv Fulltext PDF:https\://arxiv.org/pdf/1805.04829.pdf:application/pdf},
+  keywords    = {Computer Science - Artificial Intelligence, Computer Science - Machine Learning, Computer Science - Robotics},
+}
+
+@InProceedings{lecun1989optimal,
+  author    = {LeCun, Yann and Denker, John and Solla, Sara},
+  booktitle = {Advances in {Neural} {Information} {Processing} {Systems}},
+  date      = {1989},
+  title     = {Optimal {Brain} {Damage}},
+  publisher = {Morgan-Kaufmann},
+  url       = {https://proceedings.neurips.cc/paper/1989/hash/6c9882bbac1c7093bd25041881277658-Abstract.html},
+  urldate   = {2023-06-30},
+  volume    = {2},
+  abstract  = {We  have used  information-theoretic ideas  to derive  a class of prac(cid:173) tical  and  nearly  optimal schemes  for  adapting the size  of a  neural  network.  By  removing  unimportant  weights  from  a  network,  sev(cid:173) eral  improvements  can  be  expected:  better  generalization,  fewer  training examples required,  and improved speed  of learning and/or  classification.  The  basic  idea  is  to  use  second-derivative  informa(cid:173) tion to make a  tradeoff between  network  complexity  and  training  set error.  Experiments confirm  the usefulness  of the methods on a  real-world  application.},
+  file      = {Full Text PDF:https\://proceedings.neurips.cc/paper_files/paper/1989/file/6c9882bbac1c7093bd25041881277658-Paper.pdf:application/pdf},
+}
+
+@TechReport{martens2020optimizing,
+  author      = {Martens, James and Grosse, Roger},
+  date        = {2020-06},
+  institution = {arXiv},
+  title       = {Optimizing {Neural} {Networks} with {Kronecker}-factored {Approximate} {Curvature}},
+  doi         = {10.48550/arXiv.1503.05671},
+  note        = {arXiv:1503.05671 [cs, stat] type: article},
+  url         = {http://arxiv.org/abs/1503.05671},
+  urldate     = {2023-06-30},
+  abstract    = {We propose an efficient method for approximating natural gradient descent in neural networks which we call Kronecker-Factored Approximate Curvature (K-FAC). K-FAC is based on an efficiently invertible approximation of a neural network's Fisher information matrix which is neither diagonal nor low-rank, and in some cases is completely non-sparse. It is derived by approximating various large blocks of the Fisher (corresponding to entire layers) as being the Kronecker product of two much smaller matrices. While only several times more expensive to compute than the plain stochastic gradient, the updates produced by K-FAC make much more progress optimizing the objective, which results in an algorithm that can be much faster than stochastic gradient descent with momentum in practice. And unlike some previously proposed approximate natural-gradient/Newton methods which use high-quality non-diagonal curvature matrices (such as Hessian-free optimization), K-FAC works very well in highly stochastic optimization regimes. This is because the cost of storing and inverting K-FAC's approximation to the curvature matrix does not depend on the amount of data used to estimate it, which is a feature typically associated only with diagonal or low-rank approximations to the curvature matrix.},
+  annotation  = {Comment: Reduction ratio formula corrected. Removed incorrect claim about geodesics in footnote},
+  file        = {arXiv Fulltext PDF:https\://arxiv.org/pdf/1503.05671.pdf:application/pdf},
+  keywords    = {Computer Science - Machine Learning, Computer Science - Neural and Evolutionary Computing, Statistics - Machine Learning},
+}
+
+@TechReport{fong2021conformal,
+  author      = {Fong, Edwin and Holmes, Chris},
+  date        = {2021-06},
+  institution = {arXiv},
+  title       = {Conformal {Bayesian} {Computation}},
+  doi         = {10.48550/arXiv.2106.06137},
+  note        = {arXiv:2106.06137 [stat] type: article},
+  url         = {http://arxiv.org/abs/2106.06137},
+  urldate     = {2023-07-19},
+  abstract    = {We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, \$p(y {\textbackslash}mid x)\$, characterize subjective beliefs on outcomes of interest, \$y\$, conditional on predictors, \$x\$. Bayesian prediction is well-calibrated when the model is true, but the predictive intervals may exhibit poor empirical coverage when the model is misspecified, under the so called \$\{{\textbackslash}cal\{M\}\}\$-open perspective. In contrast, conformal inference provides finite sample frequentist guarantees on predictive confidence intervals without the requirement of model fidelity. Using 'add-one-in' importance sampling, we show that conformal Bayesian predictive intervals are efficiently obtained from re-weighted posterior samples of model parameters. Our approach contrasts with existing conformal methods that require expensive refitting of models or data-splitting to achieve computational efficiency. We demonstrate the utility on a range of examples including extensions to partially exchangeable settings such as hierarchical models.},
+  annotation  = {Comment: 19 pages, 4 figures, 12 tables; added references and fixed typos},
+  file        = {arXiv Fulltext PDF:https\://arxiv.org/pdf/2106.06137.pdf:application/pdf},
+  keywords    = {Statistics - Methodology, Statistics - Computation},
+}
+
+@Book{hyndman2018forecasting,
+  author     = {Hyndman, Rob J. and Athanasopoulos, George},
+  date       = {2018-05},
+  title      = {Forecasting: principles and practice},
+  isbn       = {9780987507112},
+  language   = {en},
+  note       = {Google-Books-ID: \_bBhDwAAQBAJ},
+  publisher  = {OTexts},
+  abstract   = {Forecasting is required in many situations. Stocking an inventory may require forecasts of demand months in advance. Telecommunication routing requires traffic forecasts a few minutes ahead. Whatever the circumstances or time horizons involved, forecasting is an important aid in effective and efficient planning.This textbook provides a comprehensive introduction to forecasting methods and presents enough information about each method for readers to use them sensibly.},
+  file       = {Google Books Link:https\://books.google.com/books?id=_bBhDwAAQBAJ:text/html},
+  keywords   = {Business \& Economics / Forecasting, Business \& Economics / Statistics, Computers / Databases / Data Mining, Computers / Mathematical \& Statistical Software},
+  shorttitle = {Forecasting},
+}
+
+@InProceedings{xu2021conformal,
+  author    = {Xu, Chen and Xie, Yao},
+  date      = {2021-07},
+  title     = {Conformal prediction interval for dynamic time-series},
+  language  = {en},
+  pages     = {11559--11569},
+  publisher = {PMLR},
+  url       = {https://proceedings.mlr.press/v139/xu21h.html},
+  urldate   = {2023-07-24},
+  abstract  = {We develop a method to construct distribution-free prediction intervals for dynamic time-series, called {\textbackslash}Verb{\textbar}EnbPI{\textbar} that wraps around any bootstrap ensemble estimator to construct sequential prediction intervals. {\textbackslash}Verb{\textbar}EnbPI{\textbar} is closely related to the conformal prediction (CP) framework but does not require data exchangeability. Theoretically, these intervals attain finite-sample, {\textbackslash}textit\{approximately valid\} marginal coverage for broad classes of regression functions and time-series with strongly mixing stochastic errors. Computationally, {\textbackslash}Verb{\textbar}EnbPI{\textbar} avoids overfitting and requires neither data-splitting nor training multiple ensemble estimators; it efficiently aggregates bootstrap estimators that have been trained. In general, {\textbackslash}Verb{\textbar}EnbPI{\textbar} is easy to implement, scalable to producing arbitrarily many prediction intervals sequentially, and well-suited to a wide range of regression functions. We perform extensive real-data analyses to demonstrate its effectiveness.},
+  file      = {Full Text PDF:http\://proceedings.mlr.press/v139/xu21h/xu21h.pdf:application/pdf},
+  issn      = {2640-3498},
+}
+
+@Book{howard2020deep,
+  author    = {Howard, Jeremy and Gugger, Sylvain},
+  date      = {2020-06},
+  title     = {Deep {Learning} for {Coders} with fastai and {PyTorch}},
+  isbn      = {9781492045496},
+  language  = {en},
+  note      = {Google-Books-ID: yATuDwAAQBAJ},
+  publisher = {"O'Reilly Media, Inc."},
+  abstract  = {Deep learning is often viewed as the exclusive domain of math PhDs and big tech companies. But as this hands-on guide demonstrates, programmers comfortable with Python can achieve impressive results in deep learning with little math background, small amounts of data, and minimal code. How? With fastai, the first library to provide a consistent interface to the most frequently used deep learning applications.Authors Jeremy Howard and Sylvain Gugger, the creators of fastai, show you how to train a model on a wide range of tasks using fastai and PyTorch. You’ll also dive progressively further into deep learning theory to gain a complete understanding of the algorithms behind the scenes.Train models in computer vision, natural language processing, tabular data, and collaborative filteringLearn the latest deep learning techniques that matter most in practiceImprove accuracy, speed, and reliability by understanding how deep learning models workDiscover how to turn your models into web applicationsImplement deep learning algorithms from scratchConsider the ethical implications of your workGain insight from the foreword by PyTorch cofounder, Soumith Chintala},
+  file      = {Google Books Link:https\://books.google.nl/books?id=yATuDwAAQBAJ:text/html},
+  keywords  = {Computers / Data Science / Machine Learning, Computers / Image Processing, Computers / Computer Science, Computers / Machine Theory, Computers / Data Science / Neural Networks, Computers / Programming / General, Computers / Languages / Python, Computers / Data Science / Data Visualization},
+}
+
+@Article{samoilescu2021model,
+  author  = {Samoilescu, Robert-Florian and Van Looveren, Arnaud and Klaise, Janis},
+  title   = {Model-agnostic and scalable counterfactual explanations via reinforcement learning},
+  journal = {arXiv preprint arXiv:2106.02597},
+  year    = {2021},
+}
+
+@Article{chen2021seven,
+  author  = {Chen, Jiahao and Storchan, Victor},
+  title   = {Seven challenges for harmonizing explainability requirements},
+  journal = {arXiv preprint arXiv:2108.05390},
+  year    = {2021},
+}
+
+@InProceedings{wang2003multiscale,
+  author       = {Wang, Zhou and Simoncelli, Eero P and Bovik, Alan C},
+  booktitle    = {The Thrity-Seventh Asilomar Conference on Signals, Systems \& Computers, 2003},
+  title        = {Multiscale structural similarity for image quality assessment},
+  organization = {Ieee},
+  pages        = {1398--1402},
+  volume       = {2},
+  year         = {2003},
+}
+
+@Article{dhurandhar2018explanations,
+  author  = {Dhurandhar, Amit and Chen, Pin-Yu and Luss, Ronny and Tu, Chun-Chen and Ting, Paishun and Shanmugam, Karthikeyan and Das, Payel},
+  title   = {Explanations based on the missing: Towards contrastive explanations with pertinent negatives},
+  volume  = {31},
+  journal = {Advances in neural information processing systems},
+  year    = {2018},
+}
+
+@InProceedings{liem2023treat,
+  author       = {Liem, Cynthia CS and Demetriou, Andrew M},
+  booktitle    = {2023 IEEE/ACM 45th International Conference on Software Engineering: Software Engineering in Society (ICSE-SEIS)},
+  title        = {Treat societally impactful scientific insights as open-source software artifacts},
+  organization = {IEEE},
+  pages        = {150--156},
+  year         = {2023},
+}
+
+@InProceedings{altmeyer2023explaining,
+  author    = {Altmeyer, Patrick and van Deursen, Arie and others},
+  booktitle = {Proceedings of the JuliaCon Conferences},
+  title     = {Explaining Black-Box Models through Counterfactuals},
+  number    = {1},
+  pages     = {130},
+  volume    = {1},
+  year      = {2023},
+}
+
+@Article{anand2022explainable,
+  author  = {Anand, Avishek and Lyu, Lijun and Idahl, Maximilian and Wang, Yumeng and Wallat, Jonas and Zhang, Zijian},
+  title   = {Explainable Information Retrieval: A Survey},
+  journal = {arXiv preprint arXiv:2211.02405},
+  year    = {2022},
+}
+
+@Article{leonhardt2023extractive,
+  author    = {Leonhardt, Jurek and Rudra, Koustav and Anand, Avishek},
+  title     = {Extractive explanations for interpretable text ranking},
+  number    = {4},
+  pages     = {1--31},
+  volume    = {41},
+  journal   = {ACM Transactions on Information Systems},
+  publisher = {ACM New York, NY, USA},
+  year      = {2023},
+}
+
+@Article{porsius2023private,
+  author = {Porsius Martins, C{\'e}lio},
+  title  = {Private cycle detection in financial transactions},
+  year   = {2023},
+}
+
+@Article{van2021one,
+  author = {van der Werf, Daan},
+  title  = {One Step Ahead: A weakly-supervised approach to training robust machine learning models for transaction monitoring},
+  year   = {2021},
+}
+
+@InProceedings{yang2018leveraging,
+  author    = {Yang, Jie and Drake, Thomas and Damianou, Andreas and Maarek, Yoelle},
+  booktitle = {Proceedings of the 2018 World Wide Web Conference},
+  title     = {Leveraging crowdsourcing data for deep active learning an application: Learning intents in alexa},
+  pages     = {23--32},
+  year      = {2018},
+}
+
+@Article{smirnova2022nessy,
+  author    = {Smirnova, Alisa and Yang, Jie and Yang, Dingqi and Cudre-Mauroux, Philippe},
+  title     = {Nessy: A Neuro-Symbolic System for Label Noise Reduction},
+  journal   = {IEEE Transactions on Knowledge and Data Engineering},
+  publisher = {IEEE},
+  year      = {2022},
+}
+
+@InProceedings{arous2021marta,
+  author    = {Arous, Ines and Dolamic, Ljiljana and Yang, Jie and Bhardwaj, Akansha and Cuccu, Giuseppe and Cudr{\'e}-Mauroux, Philippe},
+  booktitle = {Proceedings of the AAAI conference on artificial intelligence},
+  title     = {Marta: Leveraging human rationales for explainable text classification},
+  number    = {7},
+  pages     = {5868--5876},
+  volume    = {35},
+  year      = {2021},
+}
+
+@Article{agusti2021deep,
+  author = {Agust{\'\i}, Marc and Altmeyer, Patrick and Vidal-Quadras, Ignacio},
+  title  = {Deep vector autoregression for macroeconomic data},
+  year   = {2021},
+}
+
+@Article{altmeyer2023yield,
+  author = {Altmeyer, Patrick and Boneva, Lena and Kinston, Rafael and Saha, Shreyosi and Stoja, Evarist},
+  title  = {Yield curve sensitivity to investor positioning around economic shocks},
+  year   = {2023},
+}
+
+@Misc{DHPC2022,
+  author       = {{D}elft {H}igh {P}erformance {C}omputing {C}entre ({DHPC})},
+  title        = {{D}elft{B}lue {S}upercomputer ({P}hase 1)},
+  howpublished = {\url{https://www.tudelft.nl/dhpc/ark:/44463/DelftBluePhase1}},
+  note         = {Accessed: 2024-01-10},
+  year         = {2022},
+}
+
+@Article{lecun1998gradient,
+  author    = {LeCun, Yann and Bottou, L{\'e}on and Bengio, Yoshua and Haffner, Patrick},
+  title     = {Gradient-based learning applied to document recognition},
+  number    = {11},
+  pages     = {2278--2324},
+  volume    = {86},
+  journal   = {Proceedings of the IEEE},
+  publisher = {IEEE},
+  year      = {1998},
+}
+
+@Misc{alain2018understanding,
+  author        = {Guillaume Alain and Yoshua Bengio},
+  title         = {Understanding intermediate layers using linear classifier probes},
+  eprint        = {1610.01644},
+  archiveprefix = {arXiv},
+  primaryclass  = {stat.ML},
+  year          = {2018},
+}
+
+@Misc{belinkov2021probing,
+  author        = {Yonatan Belinkov},
+  title         = {Probing Classifiers: Promises, Shortcomings, and Advances},
+  eprint        = {2102.12452},
+  archiveprefix = {arXiv},
+  primaryclass  = {cs.CL},
+  year          = {2021},
+}
+
+@Misc{gurnee2023language,
+  author        = {Wes Gurnee and Max Tegmark},
+  title         = {Language Models Represent Space and Time},
+  eprint        = {2310.02207},
+  archiveprefix = {arXiv},
+  primaryclass  = {cs.LG},
+  year          = {2023},
+}
+
+@Misc{shah2023trillion,
+  author        = {Agam Shah and Suvan Paturi and Sudheer Chava},
+  title         = {Trillion Dollar Words: A New Financial Dataset, Task & Market Analysis},
+  eprint        = {2305.07972},
+  archiveprefix = {arXiv},
+  primaryclass  = {cs.CL},
+  year          = {2023},
+}
+
+@Misc{liu2019roberta,
+  author        = {Yinhan Liu and Myle Ott and Naman Goyal and Jingfei Du and Mandar Joshi and Danqi Chen and Omer Levy and Mike Lewis and Luke Zettlemoyer and Veselin Stoyanov},
+  title         = {RoBERTa: A Robustly Optimized BERT Pretraining Approach},
+  eprint        = {1907.11692},
+  archiveprefix = {arXiv},
+  primaryclass  = {cs.CL},
+  year          = {2019},
+}
+
+@Misc{altmeyer2023faithful,
+  author        = {Patrick Altmeyer and Mojtaba Farmanbar and Arie van Deursen and Cynthia C. S. Liem},
+  title         = {Faithful Model Explanations through Energy-Constrained Conformal Counterfactuals},
+  eprint        = {2312.10648},
+  archiveprefix = {arXiv},
+  primaryclass  = {cs.LG},
+  year          = {2023},
+}
+
+@Misc{touvron2023llama,
+  author        = {Hugo Touvron and Thibaut Lavril and Gautier Izacard and Xavier Martinet and Marie-Anne Lachaux and Timothée Lacroix and Baptiste Rozière and Naman Goyal and Eric Hambro and Faisal Azhar and Aurelien Rodriguez and Armand Joulin and Edouard Grave and Guillaume Lample},
+  title         = {{LLaMA: Open and Efficient Foundation Language Models}},
+  eprint        = {2302.13971},
+  archiveprefix = {arXiv},
+  primaryclass  = {cs.CL},
+  year          = {2023},
+}
+
+@Misc{dasgupta2013experiments,
+  author        = {Sanjoy Dasgupta},
+  title         = {{Experiments with Random Projection}},
+  eprint        = {1301.3849},
+  archiveprefix = {arXiv},
+  primaryclass  = {cs.LG},
+  year          = {2013},
+}
+
+@Misc{altmeyer2024position,
+  author        = {Patrick Altmeyer and Andrew M. Demetriou and Antony Bartlett and Cynthia C. S. Liem},
+  title         = {Position Paper: Against Spurious Sparks-Dovelating Inflated AI Claims},
+  eprint        = {2402.03962},
+  archiveprefix = {arXiv},
+  primaryclass  = {cs.AI},
+  year          = {2024},
+}
+
+@Article{he2023how,
+  author     = {He, Gaole and Buijsman, Stefan and Gadiraju, Ujwal},
+  title      = {How Stated Accuracy of an AI System and Analogies to Explain Accuracy Affect Human Reliance on the System},
+  doi        = {10.1145/3610067},
+  number     = {CSCW2},
+  url        = {https://doi.org/10.1145/3610067},
+  volume     = {7},
+  abstract   = {AI systems are increasingly being used to support human decision making. It is important that AI advice is followed appropriately. However, according to existing literature, users typically under-rely or over-rely on AI systems, and this leads to sub-optimal team performance. In this context, we investigate the role of stated system accuracy by contrasting the lack of system information with the presence of system accuracy in a loan prediction task. We explore how the degree to which humans understand system accuracy influences their reliance on the AI system, by investigating numeracy levels and with the aid of analogies to explain system accuracy in a first of its kind between-subjects study (N=281). We found that explaining the stated accuracy of a system using analogies failed to help users rely on the AI systemappropriately (i.e., the tendency of users to rely on the system when the system is correct, or on themselves otherwise). To eliminate the impact of subjective attitudes towards analogy domains, we conducted a within-subjects study (N=248) where each participant worked on tasks with analogy-based explanations from different domains. Results from this second study confirmed that explaining stated accuracy of the system with analogies was not sufficient to facilitate appropriate reliance on the AI system in the context of loan prediction tasks, irrespective of individual user differences. Based on our findings from the two studies, we reason that the under-reliance on the AI system may be a result of users' overestimation of their own ability to solve the given task. Thus, although familiar analogies can be effective in improving the intelligibility of stated accuracy of the system, an improved understanding of system accuracy does not necessarily lead to improved system reliance and team performance.},
+  address    = {New York, NY, USA},
+  articleno  = {276},
+  issue_date = {October 2023},
+  journal    = {Proc. ACM Hum.-Comput. Interact.},
+  keywords   = {analogy, human-subjects experiment, reliance, trust},
+  month      = {oct},
+  numpages   = {29},
+  publisher  = {Association for Computing Machinery},
+  year       = {2023},
+}
+
+@Article{london2019artificial,
+  author    = {London, Alex John},
+  title     = {Artificial intelligence and black-box medical decisions: accuracy versus explainability},
+  number    = {1},
+  pages     = {15--21},
+  volume    = {49},
+  journal   = {Hastings Center Report},
+  publisher = {Wiley Online Library},
+  year      = {2019},
+}
+
+@Article{robbins2019misdirected,
+  author    = {Robbins, Scott},
+  title     = {A misdirected principle with a catch: explicability for AI},
+  number    = {4},
+  pages     = {495--514},
+  volume    = {29},
+  journal   = {Minds and Machines},
+  publisher = {Springer},
+  year      = {2019},
+}
+
+@InProceedings{biswas2022chime,
+  author    = {Biswas, Shreyan and Corti, Lorenzo and Buijsman, Stefan and Yang, Jie},
+  booktitle = {Proceedings of the AAAI Conference on Human Computation and Crowdsourcing},
+  title     = {CHIME: Causal Human-in-the-Loop Model Explanations},
+  number    = {1},
+  pages     = {27--39},
+  volume    = {10},
+  year      = {2022},
+}
+
+@InProceedings{alufaisan2021does,
+  author    = {Alufaisan, Yasmeen and Marusich, Laura R and Bakdash, Jonathan Z and Zhou, Yan and Kantarcioglu, Murat},
+  booktitle = {Proceedings of the AAAI Conference on Artificial Intelligence},
+  title     = {Does explainable artificial intelligence improve human decision-making?},
+  number    = {8},
+  pages     = {6618--6626},
+  volume    = {35},
+  year      = {2021},
+}
+
+@InProceedings{altmeyer2024faithful,
+  author    = {Altmeyer, Patrick and Farmanbar, Mojtaba and van Deursen, Arie and Liem, Cynthia CS},
+  booktitle = {Proceedings of the AAAI Conference on Artificial Intelligence},
+  title     = {Faithful Model Explanations through Energy-Constrained Conformal Counterfactuals},
+  number    = {10},
+  pages     = {10829--10837},
+  volume    = {38},
+  year      = {2024},
+}
+
+@Misc{hengst2024conformal,
+  author        = {Floris den Hengst and Ralf Wolter and Patrick Altmeyer and Arda Kaygan},
+  title         = {Conformal Intent Classification and Clarification for Fast and Accurate Intent Recognition},
+  eprint        = {2403.18973},
+  archiveprefix = {arXiv},
+  primaryclass  = {cs.CL},
+  year          = {2024},
+}
+
+@Comment{jabref-meta: databaseType:biblatex;}
+
+@Comment{jabref-meta: keypatterndefault:[auth:lower][year][veryshorttitle:lower];}
+
+@Comment{jabref-meta: saveActions:disabled;
+all-text-fields[identity]
+date[normalize_date]
+month[normalize_month]
+pages[normalize_page_numbers]
+;}
diff --git a/profile/blog/posts/causal-recourse/index copy.qmd b/profile/blog/posts/causal-recourse/index copy.qmd
new file mode 100644
index 0000000..feef45f
--- /dev/null
+++ b/profile/blog/posts/causal-recourse/index copy.qmd	
@@ -0,0 +1,127 @@
+---
+title: "When Causal meets Recourse"
+subtitle: "Counterfactual Explanations through Structural Causal Models"
+bibliography: 
+date: '2024-09-03'
+description: |
+    This post introduces a new tool in CounterfactualExplanations.jl, enhancing the package with causal reasoning to generate counterfactual explanations. The functionality can be used to explain machine learning algorithms developed in Julia and other popular programming languages like Python and R. Unlike traditional counterfactual generators, this approach utilizes causal information to perturb features intelligently.
+author: 
+    - name: Jorge Luiz Franco 
+      url: https://www.linkedin.com/in/jorgelwyz/
+categories:
+  - counterfactuals
+  - explainable AI
+  - causality
+  - Julia
+image: www/intro.gif
+execute:
+  eval: false
+  echo: true
+draft: false
+---
+
+# Introduction
+
+In recent years, the need for interpretable and explainable AI has surged, particularly in high-stakes domains. Counterfactual explanations provide a means to understand how changes to input features could alter the outcomes of machine learning models. This blog post presents a new tool in the CounterfactualExplanations.jl package, developed during my JSoC (Julia Summer of Code) project, which incorporates causal reasoning into counterfactual generation.
+
+# Project Overview
+
+This project aimed to enhance the CounterfactualExplanations.jl package by infusing it with a robust mathematical foundation for minimal algorithmic recourse, based on the principles of causal reasoning [@karimi2021]. 
+
+## Key Contributions
+
+During the project, I contributed to two key repositories:
+
+1. **CounterfactualExplanations.jl**: Developed a new tool for generating counterfactual explanations using causal information. This allows users to create smarter perturbations rather than random adjustments, ultimately providing more meaningful insights.
+
+2. **CausalInference.jl**: Implemented a Structural Causal Model (SCM) structure that extracts information from data, laying the groundwork for the causal reasoning capabilities in CounterfactualExplanations.jl.
+
+This was an amazing experience, not just experience contribute to two repositories simultaneously, but also to work with the mantainers of these repos. I learned a lot about the Julia language and the Julia community. This was possible because of the mentorship of Patrick Altmeyer(CounterfactualExplanations) and Moritz Schauer (CausalInference), who guided me throughout the project and are amazing researchers.
+
+
+
+## The `MINTGenerator`
+
+In this project, we developed the MINTGenerator, a counterfactual generator based on the Recourse through Minimal
+Intervention (MINT) method proposed by @karimi2021.
+
+## Description
+
+The MINTGenerator incorporates causal reeasoning in algorithm recourse to achieve minimal interventions when generating a counterfactual explanation. In this sense, the main ideia is that just perturbating a black box model without taking into account the causal relations in the data can guide to misleading recommendations. Here we now shift to a perspective where every action/pertubation is an intervetion in the causal graph of the problem, thus the change is not made just in the intervened upon variable, but also in its childs in the causal structure. The generator utilizes a Structural Causal Model(SCM) to encode the variables in a way that causal effects are propagated and uses a generic gradient-based generator to create the search path, that is, any gradient-base generator (ECCo, REVISE, Watcher, ...) can be used with the MINT SCM encoder to generate counterfactual samples in latent space for minimal intervetions algorithm recourse.
+
+The MINT algorithm minimizes a loss function that combines the causal constraints of the SCM and the distance between the generated counterfactual and the original input. Since we want a gradient-based generator, we need to pass the constrained optimizaiton problem into an unconstrained one and we do this by using the Lagrangian. Initially, as defined in [@karimi2021], we aim to aim to find the minimal cost set of actions $A$ (in the form of structural interventions) that results in a counterfactual instance yielding the favorable output from $h$,
+
+
+\begin{aligned}
+
+A^* \in \arg\min_A \text{cost}(A; \mathbf{x}_F)\\
+\textrm{s.t.} \quad  h(\mathbf{x}_{SCF}) \neq h(\mathbf{x}_F) \; \; \text{,}\\
+
+\end{aligned} 
+
+where $\mathbf{x}_F$ is the original input, $\mathbf{x}_{SCF}$ is the counterfactual instance, and $h$ is the black-box model. We use the $\mathbf{x}_{SCF}$ terminology because the counterfactual is derived from the SCM,
+
+\begin{equation}
+
+x_{SCF_i} = 
+\begin{cases}
+x_{F_i} + \delta_i, & \text{if } i \in I \\
+x_{F_i} + f_i(\text{pa}_{SCF_i}) - f_i(\text{pa}_{F_i}), & \text{if } i \notin I  \; \; \text{,}
+\end{cases} 
+
+\end{equation}
+
+where $I$ is the set of intervened upon variables, $f_i$ is the function that generates the value of the variable $i$ given its parents, and $\text{pa}_{SCF_i}$ and $\text{pa}_{F_i}$ are the parents of the variable $i$ in the counterfactual and original instance, respectively. This closed formula for the decision variable $\mathbf{x}_{SCF}$ is what makes possible to use a gradient-based generator, since with it the lagrangian is differentiable,
+
+\begin{equation}
+\mathcal{L}(A ; \lambda) = \text{cost}(A; \mathbf{x}_F) + \lambda \left(h(\mathbf{x}_{SCF}) - h(\mathbf{x}_F) \right) \; \; \text{,}
+\end{equation}
+
+or in simple terms and more standard, since $\lambda$ is constant,
+
+\begin{equation}
+\mathcal{L_{\texttt{MINT}}}(\mathbf{x}_{SCF}) = \lambda \text{cost}(\mathbf{x}_{SCF}; \mathbf{x}_F) + \text{yloss}(\mathbf{x}_{SCF},y^*) \; \; \text{,}
+\end{equation}
+
+where $y^*$ is clearly $h(x_F)$ and $\text{yloss}$ is : 
+
+\begin{equation}  
+\text{yloss}(\mathbf{x}_{SCF}, y^*) = h \left(\left\{ x_{F_i} + \delta_i [i \in I] + \left(f_i(\text{pa}_{SCF_i}) - f_i(\text{pa}_{F_i}) \right) [i \notin I] \right\}_{i=1}^n \right) - y^* \; \; \text{.} 
+\end{equation}
+
+
+
+## Implementation
+
+In terms of implementation, we need to capture the causal relations from the data, that's where `CausalInference.jl` comes in. However, before the project, the package did not have a SCM structure, in the sense that the methods just captured the topological Directed Acyclic Graph (DAG) that generated the data, that is, no causal structural equations were provided,
+
+```{julia}
+using CausalInference
+using Plots, GraphRecipes
+using Random
+Random.seed!(1)
+
+N = 2000 # number of data points
+
+x = randn(N)
+v = x + randn(N)*0.25
+w = x + randn(N)*0.25
+z = v + w + randn(N)*0.25
+s = z + randn(N)*0.25
+
+df = (x=x, v=v, w=w, z=z, s=s)
+
+est_g, score = ges(df; penalty=1.0, parallel=true)
+
+graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)])
+```
+
+So, our goal was given the DAG provided by the `ges` method in the causal discovery [@ges2003], generate equations that rules each of these causal relations, represented in the DAG as directed edges. The SCM is the union of the DAG and these causal equations, that is, the SCM is a tuple $(G, \mathbf{f})$, where $G$ is the DAG and $\mathbf{f}$ is the set of functions that generates the value of each variable given its parents. 
+
+Our solution for constructing the structural causal equations was to assume that the data was generated by a linear model, ie, the causal relations were linear. For the data provided in the code example we have   $ v = \mathcal{b}_v $ , $` x = v + \mathcal{b}_v `$, $` w = \epsilon_w + x `$, $` z = \epsilon_z + v + w `$, $s = \epsilon_s + z$, where $\epsilon_i$ is the noise term.
+
+# Conclusion
+
+
+
+# References
diff --git a/profile/blog/posts/causal-recourse/index.html b/profile/blog/posts/causal-recourse/index.html
index 2e37acc..1597120 100644
--- a/profile/blog/posts/causal-recourse/index.html
+++ b/profile/blog/posts/causal-recourse/index.html
@@ -6,6 +6,7 @@
 
 
 
+
 
 
 
@@ -56,7 +57,27 @@
 @media screen {
 pre > code.sourceCode > span > a:first-child::before { text-decoration: underline; }
 }
-
+/* CSS for citations */
+div.csl-bib-body { }
+div.csl-entry {
+  clear: both;
+  margin-bottom: 0em;
+}
+.hanging-indent div.csl-entry {
+  margin-left:2em;
+  text-indent:-2em;
+}
+div.csl-left-margin {
+  min-width:2em;
+  float:left;
+}
+div.csl-right-inline {
+  margin-left:2em;
+  padding-left:1em;
+}
+div.csl-indent {
+  margin-left: 2em;
+}
 
 
 
@@ -129,6 +150,12 @@ 
    When Causal meets Recourse
    
 
 
    
 
+    
    
+    
    Author
    
+    
    
+             
    Jorge Luiz Franco 
    
+          
    
+  
    
     
     
    
     
    Published
    
@@ -151,7 +178,7 @@ 
    Introduction
    
 
    
 
    
 
    Project Overview
    
-
    This project aimed to enhance the CounterfactualExplanations.jl package by infusing it with a robust mathematical foundation for minimal algorithmic recourse, based on the principles of causal reasoning @karimi2021.
    
+
    This project aimed to enhance the CounterfactualExplanations.jl package by infusing it with a robust mathematical foundation for minimal algorithmic recourse, based on the principles of causal reasoning (Karimi, Schölkopf, and Valera 2021).
    
 
    
 
    Key Contributions
    
 
    During the project, I contributed to two key repositories:
    
@@ -163,12 +190,12 @@ 
    Key Contributions
    
 
    
 
    
 
    The MINTGenerator
    
-
    In this project, we developed the MINTGenerator, a counterfactual generator based on the Recourse through Minimal Intervention (MINT) method proposed by @karimi2021.
    
+
    In this project, we developed the MINTGenerator, a counterfactual generator based on the Recourse through Minimal Intervention (MINT) method proposed by Karimi, Schölkopf, and Valera (2021).
    
 
    
 
    
 
    Description
    
 
    The MINTGenerator incorporates causal reeasoning in algorithm recourse to achieve minimal interventions when generating a counterfactual explanation. In this sense, the main ideia is that just perturbating a black box model without taking into account the causal relations in the data can guide to misleading recommendations. Here we now shift to a perspective where every action/pertubation is an intervetion in the causal graph of the problem, thus the change is not made just in the intervened upon variable, but also in its childs in the causal structure. The generator utilizes a Structural Causal Model(SCM) to encode the variables in a way that causal effects are propagated and uses a generic gradient-based generator to create the search path, that is, any gradient-base generator (ECCo, REVISE, Watcher, …) can be used with the MINT SCM encoder to generate counterfactual samples in latent space for minimal intervetions algorithm recourse.
    
-
    The MINT algorithm minimizes a loss function that combines the causal constraints of the SCM and the distance between the generated counterfactual and the original input. Since we want a gradient-based generator, we need to pass the constrained optimizaiton problem into an unconstrained one and we do this by using the Lagrangian. Initially, as defined in [@karimi2021], we aim to aim to find the minimal cost set of actions \(A\) (in the form of structural interventions) that results in a counterfactual instance yielding the favorable output from \(h\),
    
+
    The MINT algorithm minimizes a loss function that combines the causal constraints of the SCM and the distance between the generated counterfactual and the original input. Since we want a gradient-based generator, we need to pass the constrained optimizaiton problem into an unconstrained one and we do this by using the Lagrangian. Initially, as defined in (Karimi, Schölkopf, and Valera 2021), we aim to aim to find the minimal cost set of actions \(A\) (in the form of structural interventions) that results in a counterfactual instance yielding the favorable output from \(h\),
    
 \[\begin{aligned}
 
 A^* \in \arg\min_A \text{cost}(A; \mathbf{x}_F)\\
@@ -200,8 +227,10 @@ 
    Description
    
 
    
 
    
 
    Implementation
    
-
    In terms of implementation, we need to capture the causal relations from the data, that’s where CausalInference.jl comes in. However, before the project, the package did not have a SCM structure, in the sense that the methods just captured the topological Directed Acyclic Graph (DAG) that generated the data, that is, no causal structural equations were provided,
    
-
    
+
    
+
    CausalInference.jl
    
+
    In terms of implementation, we need to capture the causal relations from the data, that’s where CausalInference.jl comes in. However, before the project, the package did not have a SCM structure, in the sense that the methods just captured the topological Directed Acyclic Graph (DAG) that showed the causality ruling the data, that is, no causal structural equations were provided,
    
+
    
 
    using CausalInference
 using Plots, GraphRecipes
 using Random
@@ -219,19 +248,107 @@ 
    Implementation
    
 
 est_g, score = ges(df; penalty=1.0, parallel=true)
 
-graphplot(est_g, names= [String(k) for k in keys(df)])
    
+graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)])
    
 
    
+
    So, our goal was given the DAG provided by the ges method in the causal discovery (Chickering 2003), generate equations that rules each of these causal relations, represented in the DAG as directed edges. The SCM is the union of the DAG and these causal equations, that is, the SCM is a tuple \((G, \mathbf{f})\), where \(G\) is the DAG and \(\mathbf{f}\) is the set of functions that generates the value of each variable given its parents.
    
+
    Our solution for constructing the structural causal equations was to assume that the data was generated by a linear model, ie, the causal relations were linear. For the DAG provided in the code example we derive
    
+
    \[ v = \mathcal{b}_v \]
    
+
    \[ x = \mathcal{a}_{v \to x} v + \mathcal{b}_x \]
    
+
    \[ w = \mathcal{a}_{x \to w} x + \mathcal{b}_w \]
    
+
    \[ z = \mathcal{a}_{v \to z} v+ \mathcal{a}_{w \to z} w + \mathcal{b}_z \]
    
+
    \[ s = \mathcal{a}_{z \to s} z + \mathcal{b}_s \]
    
+
    and that’s the tricky thing, as we can see these causal equations are different than the ones that generated the data, but they are the ones that respect the causal system obtained from the obtained DAG. Here \(\mathcal{b}_i\) and \(\mathcal{a}_{i \to j}\) are the intercept term and the coefficient obtained from the linear regression, respectively. To correctly solve the linear regression respecting the dependencies of the causal graph, we use topological_sort_by_dfs from Graphs.jl.
    
+
    Now, with the SCM structure in hand, we see that the representation could be a struct containing the DAG and the coefficients/intercepts of the causal equations, this maps exactly the tuple \((G, \mathbf{f})\) that we defined. However, since we need these equations to be differentiable, we need to define a function that takes the SCM and returns the value of the variable given its parents and using just the coefficients and the DAG, lead to errors, because AutoDiff does not deal well with functions that are conditioned (if statements). So, we need to define a way to retrieve the system of causal equations in a smooth way and that’s where the causal_effects matrix comes to the rescue.
    
+
    Let the factual vector of features be denoted as:
    
+
    \[
+\mathbf{x}_F =
+\begin{bmatrix}
+x_{F_1} \\
+x_{F_2} \\
+x_{F_3} \\
+\vdots \\
+x_{F_n}
+\end{bmatrix}
+\]
    
+
    Let the causal_effects matrix be:
    
+
    \[
+\mathbf{C} =
+\begin{bmatrix}
+a_{11} & a_{12} & \cdots & a_{1n} & b_1 \\
+a_{21} & a_{22} & \cdots & a_{2n} & b_2 \\
+a_{31} & a_{32} & \cdots & a_{3n} & b_3 \\
+\vdots & \vdots & \ddots & \vdots & \vdots \\
+a_{n1} & a_{n2} & \cdots & a_{nn} & b_n \\
+\end{bmatrix}
+\]
    
+
    Here, \(a_{ij}\) represents the coefficient from the causal effect of \(x_{F_j}\) on \(x_{F_i}\), and \(b_i\) represents the intercept term for the variable \(x_{F_i}\).
    
+
    The matrix multiplication of the causal_effects matrix with the factual vector (excluding the bias term) is given by:
    
+
    \[
+\mathbf{C}_{:, 1:n} \cdot \mathbf{x}_F =
+\begin{bmatrix}
+a_{11} & a_{12} & \cdots & a_{1n} \\
+a_{21} & a_{22} & \cdots & a_{2n} \\
+a_{31} & a_{32} & \cdots & a_{3n} \\
+\vdots & \vdots & \ddots & \vdots \\
+a_{n1} & a_{n2} & \cdots & a_{nn}
+\end{bmatrix}
+\begin{bmatrix}
+x_{F_1} \\
+x_{F_2} \\
+x_{F_3} \\
+\vdots \\
+x_{F_n}
+\end{bmatrix}
+\]
    
+
    Finally, we add the bias term:
    
+
    \[
+\mathbf{x}_{SCF} = \mathbf{C}_{:, 1:n} \cdot \mathbf{x}_F +
+\begin{bmatrix}
+b_1 \\
+b_2 \\
+b_3 \\
+\vdots \\
+b_n
+\end{bmatrix}
+\]
    
+
    In expanded form:
    
+
    \[
+\mathbf{x}_{SCF_i} = a_{i1} x_{F_1} + a_{i2} x_{F_2} + \cdots + a_{in} x_{F_n} + b_i, \quad \forall i = 1, 2, \dots, n
+\]
    
+
    This equation shows how each counterfactual variable \(x_{SCF_i}\) is generated as a linear combination of the factual inputs \(x_{F_j}\) based on the causal effects matrix, with an intercept term \(b_i\) added for each variable.
    
+
    One can note that the orphan nodes, that is, the nodes that do not have parents in the DAG, are going to be equal to the intercept term \(\mathcal{b}_\hat{o}\). The intuition behind this is that when we do the linear regression, variables that have no causal parents are just equal to the unconditional mean of the variable, i.e, we get \(x_{SCF_\hat{o}} = \mathbb{E}(x_\hat{o})\). Because of this, in some cases a better understanding of the regression is needed, so the residuals are also part of the SCM structure,
    
+
    
+
    struct SCM
+    variables::Vector{String}
+    coefficients::Vector{Vector{Float64}}
+    residuals::Vector{Vector{Float64}}
+    dag::DiGraph
+    causal_effects::Matrix{Float64}
+end
    
+
    
+
    +
    +

    CounterfactualExplanations.jl

    +

    Conclusion

    -

    In conclusion, this project has successfully integrated causal reasoning into the CounterfactualExplanations.jl package, providing a valuable tool for generating counterfactual explanations that are not only interpretable but also actionable.

    +
    -
    -

    References

    +
    + +
    - +

    References

    +
    +Chickering, David Maxwell. 2003. “Optimal Structure Identification with Greedy Search.” J. Mach. Learn. Res. 3 (null): 507–54. https://doi.org/10.1162/153244303321897717. +
    +
    +Karimi, Amir-Hossein, Bernhard Schölkopf, and Isabel Valera. 2021. “Algorithmic Recourse: From Counterfactual Explanations to Interventions.” In Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency, 353–62. FAccT ’21. New York, NY, USA: Association for Computing Machinery. https://doi.org/10.1145/3442188.3445899. +
    +
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992px){.navbar-expand-lg{flex-wrap:nowrap;-webkit-flex-wrap:nowrap;justify-content:flex-start;-webkit-justify-content:flex-start}.navbar-expand-lg .navbar-nav{flex-direction:row;-webkit-flex-direction:row}.navbar-expand-lg .navbar-nav .dropdown-menu{position:absolute}.navbar-expand-lg .navbar-nav .nav-link{padding-right:var(--bs-navbar-nav-link-padding-x);padding-left:var(--bs-navbar-nav-link-padding-x)}.navbar-expand-lg .navbar-nav-scroll{overflow:visible}.navbar-expand-lg .navbar-collapse{display:flex !important;display:-webkit-flex !important;flex-basis:auto;-webkit-flex-basis:auto}.navbar-expand-lg .navbar-toggler{display:none}.navbar-expand-lg .offcanvas{position:static;z-index:auto;flex-grow:1;-webkit-flex-grow:1;width:auto !important;height:auto !important;visibility:visible !important;background-color:rgba(0,0,0,0) !important;border:0 !important;transform:none !important;transition:none}.navbar-expand-lg .offcanvas .offcanvas-header{display:none}.navbar-expand-lg .offcanvas 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.offcanvas{position:static;z-index:auto;flex-grow:1;-webkit-flex-grow:1;width:auto !important;height:auto !important;visibility:visible !important;background-color:rgba(0,0,0,0) !important;border:0 !important;transform:none !important;transition:none}.navbar-expand-xxl .offcanvas .offcanvas-header{display:none}.navbar-expand-xxl .offcanvas .offcanvas-body{display:flex;display:-webkit-flex;flex-grow:0;-webkit-flex-grow:0;padding:0;overflow-y:visible}}.navbar-expand{flex-wrap:nowrap;-webkit-flex-wrap:nowrap;justify-content:flex-start;-webkit-justify-content:flex-start}.navbar-expand .navbar-nav{flex-direction:row;-webkit-flex-direction:row}.navbar-expand .navbar-nav .dropdown-menu{position:absolute}.navbar-expand .navbar-nav .nav-link{padding-right:var(--bs-navbar-nav-link-padding-x);padding-left:var(--bs-navbar-nav-link-padding-x)}.navbar-expand .navbar-nav-scroll{overflow:visible}.navbar-expand .navbar-collapse{display:flex !important;display:-webkit-flex 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var(--bs-card-spacer-x);color:var(--bs-card-color)}.card-title{margin-bottom:var(--bs-card-title-spacer-y);color:var(--bs-card-title-color)}.card-subtitle{margin-top:calc(-0.5*var(--bs-card-title-spacer-y));margin-bottom:0;color:var(--bs-card-subtitle-color)}.card-text:last-child{margin-bottom:0}.card-link+.card-link{margin-left:var(--bs-card-spacer-x)}.card-header{padding:var(--bs-card-cap-padding-y) var(--bs-card-cap-padding-x);margin-bottom:0;color:var(--bs-card-cap-color);background-color:var(--bs-card-cap-bg);border-bottom:var(--bs-card-border-width) solid var(--bs-card-border-color)}.card-header:first-child{border-radius:var(--bs-card-inner-border-radius) var(--bs-card-inner-border-radius) 0 0}.card-footer{padding:var(--bs-card-cap-padding-y) var(--bs-card-cap-padding-x);color:var(--bs-card-cap-color);background-color:var(--bs-card-cap-bg);border-top:var(--bs-card-border-width) solid var(--bs-card-border-color)}.card-footer:last-child{border-radius:0 0 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.nav-link.active{background-color:var(--bs-card-bg);border-bottom-color:var(--bs-card-bg)}.card-header-pills{margin-right:calc(-0.5*var(--bs-card-cap-padding-x));margin-left:calc(-0.5*var(--bs-card-cap-padding-x))}.card-img-overlay{position:absolute;top:0;right:0;bottom:0;left:0;padding:var(--bs-card-img-overlay-padding);border-radius:var(--bs-card-inner-border-radius)}.card-img,.card-img-top,.card-img-bottom{width:100%}.card-img,.card-img-top{border-top-left-radius:var(--bs-card-inner-border-radius);border-top-right-radius:var(--bs-card-inner-border-radius)}.card-img,.card-img-bottom{border-bottom-right-radius:var(--bs-card-inner-border-radius);border-bottom-left-radius:var(--bs-card-inner-border-radius)}.card-group>.card{margin-bottom:var(--bs-card-group-margin)}@media(min-width: 576px){.card-group{display:flex;display:-webkit-flex;flex-flow:row wrap;-webkit-flex-flow:row wrap}.card-group>.card{flex:1 0 0%;-webkit-flex:1 0 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var(--bs-accordion-border-color)}.accordion-button:not(.collapsed)::after{background-image:var(--bs-accordion-btn-active-icon);transform:var(--bs-accordion-btn-icon-transform)}.accordion-button::after{flex-shrink:0;-webkit-flex-shrink:0;width:var(--bs-accordion-btn-icon-width);height:var(--bs-accordion-btn-icon-width);margin-left:auto;content:"";background-image:var(--bs-accordion-btn-icon);background-repeat:no-repeat;background-size:var(--bs-accordion-btn-icon-width);transition:var(--bs-accordion-btn-icon-transition)}@media(prefers-reduced-motion: reduce){.accordion-button::after{transition:none}}.accordion-button:hover{z-index:2}.accordion-button:focus{z-index:3;border-color:var(--bs-accordion-btn-focus-border-color);outline:0;box-shadow:var(--bs-accordion-btn-focus-box-shadow)}.accordion-header{margin-bottom:0}.accordion-item{color:var(--bs-accordion-color);background-color:var(--bs-accordion-bg);border:var(--bs-accordion-border-width) solid var(--bs-accordion-border-color)}.accordion-item:first-of-type{border-top-left-radius:var(--bs-accordion-border-radius);border-top-right-radius:var(--bs-accordion-border-radius)}.accordion-item:first-of-type .accordion-button{border-top-left-radius:var(--bs-accordion-inner-border-radius);border-top-right-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:not(:first-of-type){border-top:0}.accordion-item:last-of-type{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-item:last-of-type .accordion-button.collapsed{border-bottom-right-radius:var(--bs-accordion-inner-border-radius);border-bottom-left-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:last-of-type .accordion-collapse{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-body{padding:var(--bs-accordion-body-padding-y) var(--bs-accordion-body-padding-x)}.accordion-flush .accordion-collapse{border-width:0}.accordion-flush .accordion-item{border-right:0;border-left:0;border-radius:0}.accordion-flush .accordion-item:first-child{border-top:0}.accordion-flush .accordion-item:last-child{border-bottom:0}.accordion-flush .accordion-item .accordion-button,.accordion-flush .accordion-item .accordion-button.collapsed{border-radius:0}[data-bs-theme=dark] .accordion-button::after{--bs-accordion-btn-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%236ea8fe'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-active-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%236ea8fe'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e")}.breadcrumb{--bs-breadcrumb-padding-x: 0;--bs-breadcrumb-padding-y: 0;--bs-breadcrumb-margin-bottom: 1rem;--bs-breadcrumb-bg: ;--bs-breadcrumb-border-radius: ;--bs-breadcrumb-divider-color: rgba(33, 37, 41, 0.75);--bs-breadcrumb-item-padding-x: 0.5rem;--bs-breadcrumb-item-active-color: rgba(33, 37, 41, 0.75);display:flex;display:-webkit-flex;flex-wrap:wrap;-webkit-flex-wrap:wrap;padding:var(--bs-breadcrumb-padding-y) var(--bs-breadcrumb-padding-x);margin-bottom:var(--bs-breadcrumb-margin-bottom);font-size:var(--bs-breadcrumb-font-size);list-style:none;background-color:var(--bs-breadcrumb-bg);border-radius:var(--bs-breadcrumb-border-radius)}.breadcrumb-item+.breadcrumb-item{padding-left:var(--bs-breadcrumb-item-padding-x)}.breadcrumb-item+.breadcrumb-item::before{float:left;padding-right:var(--bs-breadcrumb-item-padding-x);color:var(--bs-breadcrumb-divider-color);content:var(--bs-breadcrumb-divider, ">") /* rtl: var(--bs-breadcrumb-divider, ">") */}.breadcrumb-item.active{color:var(--bs-breadcrumb-item-active-color)}.pagination{--bs-pagination-padding-x: 0.75rem;--bs-pagination-padding-y: 0.375rem;--bs-pagination-font-size:1rem;--bs-pagination-color: #0d6efd;--bs-pagination-bg: #ffffff;--bs-pagination-border-width: 1px;--bs-pagination-border-color: #dee2e6;--bs-pagination-border-radius: 0.375rem;--bs-pagination-hover-color: #0a58ca;--bs-pagination-hover-bg: #f8f9fa;--bs-pagination-hover-border-color: #dee2e6;--bs-pagination-focus-color: #0a58ca;--bs-pagination-focus-bg: #e9ecef;--bs-pagination-focus-box-shadow: 0 0 0 0.25rem rgba(13, 110, 253, 0.25);--bs-pagination-active-color: #ffffff;--bs-pagination-active-bg: #0d6efd;--bs-pagination-active-border-color: #0d6efd;--bs-pagination-disabled-color: rgba(33, 37, 41, 0.75);--bs-pagination-disabled-bg: #e9ecef;--bs-pagination-disabled-border-color: #dee2e6;display:flex;display:-webkit-flex;padding-left:0;list-style:none}.page-link{position:relative;display:block;padding:var(--bs-pagination-padding-y) var(--bs-pagination-padding-x);font-size:var(--bs-pagination-font-size);color:var(--bs-pagination-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-pagination-bg);border:var(--bs-pagination-border-width) solid var(--bs-pagination-border-color);transition:color .15s ease-in-out,background-color .15s ease-in-out,border-color .15s ease-in-out,box-shadow .15s ease-in-out}@media(prefers-reduced-motion: reduce){.page-link{transition:none}}.page-link:hover{z-index:2;color:var(--bs-pagination-hover-color);background-color:var(--bs-pagination-hover-bg);border-color:var(--bs-pagination-hover-border-color)}.page-link:focus{z-index:3;color:var(--bs-pagination-focus-color);background-color:var(--bs-pagination-focus-bg);outline:0;box-shadow:var(--bs-pagination-focus-box-shadow)}.page-link.active,.active>.page-link{z-index:3;color:var(--bs-pagination-active-color);background-color:var(--bs-pagination-active-bg);border-color:var(--bs-pagination-active-border-color)}.page-link.disabled,.disabled>.page-link{color:var(--bs-pagination-disabled-color);pointer-events:none;background-color:var(--bs-pagination-disabled-bg);border-color:var(--bs-pagination-disabled-border-color)}.page-item:not(:first-child) .page-link{margin-left:calc(1px*-1)}.page-item:first-child .page-link{border-top-left-radius:var(--bs-pagination-border-radius);border-bottom-left-radius:var(--bs-pagination-border-radius)}.page-item:last-child .page-link{border-top-right-radius:var(--bs-pagination-border-radius);border-bottom-right-radius:var(--bs-pagination-border-radius)}.pagination-lg{--bs-pagination-padding-x: 1.5rem;--bs-pagination-padding-y: 0.75rem;--bs-pagination-font-size:1.25rem;--bs-pagination-border-radius: 0.5rem}.pagination-sm{--bs-pagination-padding-x: 0.5rem;--bs-pagination-padding-y: 0.25rem;--bs-pagination-font-size:0.875rem;--bs-pagination-border-radius: 0.25rem}.badge{--bs-badge-padding-x: 0.65em;--bs-badge-padding-y: 0.35em;--bs-badge-font-size:0.75em;--bs-badge-font-weight: 700;--bs-badge-color: #ffffff;--bs-badge-border-radius: 0.375rem;display:inline-block;padding:var(--bs-badge-padding-y) var(--bs-badge-padding-x);font-size:var(--bs-badge-font-size);font-weight:var(--bs-badge-font-weight);line-height:1;color:var(--bs-badge-color);text-align:center;white-space:nowrap;vertical-align:baseline;border-radius:var(--bs-badge-border-radius)}.badge:empty{display:none}.btn .badge{position:relative;top:-1px}.alert{--bs-alert-bg: transparent;--bs-alert-padding-x: 1rem;--bs-alert-padding-y: 1rem;--bs-alert-margin-bottom: 1rem;--bs-alert-color: inherit;--bs-alert-border-color: transparent;--bs-alert-border: 1px solid var(--bs-alert-border-color);--bs-alert-border-radius: 0.375rem;--bs-alert-link-color: inherit;position:relative;padding:var(--bs-alert-padding-y) var(--bs-alert-padding-x);margin-bottom:var(--bs-alert-margin-bottom);color:var(--bs-alert-color);background-color:var(--bs-alert-bg);border:var(--bs-alert-border);border-radius:var(--bs-alert-border-radius)}.alert-heading{color:inherit}.alert-link{font-weight:700;color:var(--bs-alert-link-color)}.alert-dismissible{padding-right:3rem}.alert-dismissible .btn-close{position:absolute;top:0;right:0;z-index:2;padding:1.25rem 1rem}.alert-default{--bs-alert-color: var(--bs-default-text-emphasis);--bs-alert-bg: var(--bs-default-bg-subtle);--bs-alert-border-color: var(--bs-default-border-subtle);--bs-alert-link-color: var(--bs-default-text-emphasis)}.alert-primary{--bs-alert-color: var(--bs-primary-text-emphasis);--bs-alert-bg: var(--bs-primary-bg-subtle);--bs-alert-border-color: var(--bs-primary-border-subtle);--bs-alert-link-color: var(--bs-primary-text-emphasis)}.alert-secondary{--bs-alert-color: var(--bs-secondary-text-emphasis);--bs-alert-bg: var(--bs-secondary-bg-subtle);--bs-alert-border-color: var(--bs-secondary-border-subtle);--bs-alert-link-color: var(--bs-secondary-text-emphasis)}.alert-success{--bs-alert-color: var(--bs-success-text-emphasis);--bs-alert-bg: var(--bs-success-bg-subtle);--bs-alert-border-color: var(--bs-success-border-subtle);--bs-alert-link-color: var(--bs-success-text-emphasis)}.alert-info{--bs-alert-color: var(--bs-info-text-emphasis);--bs-alert-bg: var(--bs-info-bg-subtle);--bs-alert-border-color: var(--bs-info-border-subtle);--bs-alert-link-color: var(--bs-info-text-emphasis)}.alert-warning{--bs-alert-color: var(--bs-warning-text-emphasis);--bs-alert-bg: var(--bs-warning-bg-subtle);--bs-alert-border-color: var(--bs-warning-border-subtle);--bs-alert-link-color: var(--bs-warning-text-emphasis)}.alert-danger{--bs-alert-color: var(--bs-danger-text-emphasis);--bs-alert-bg: var(--bs-danger-bg-subtle);--bs-alert-border-color: var(--bs-danger-border-subtle);--bs-alert-link-color: var(--bs-danger-text-emphasis)}.alert-light{--bs-alert-color: var(--bs-light-text-emphasis);--bs-alert-bg: var(--bs-light-bg-subtle);--bs-alert-border-color: var(--bs-light-border-subtle);--bs-alert-link-color: var(--bs-light-text-emphasis)}.alert-dark{--bs-alert-color: var(--bs-dark-text-emphasis);--bs-alert-bg: var(--bs-dark-bg-subtle);--bs-alert-border-color: var(--bs-dark-border-subtle);--bs-alert-link-color: var(--bs-dark-text-emphasis)}@keyframes progress-bar-stripes{0%{background-position-x:1rem}}.progress,.progress-stacked{--bs-progress-height: 1rem;--bs-progress-font-size:0.75rem;--bs-progress-bg: #e9ecef;--bs-progress-border-radius: 0.375rem;--bs-progress-box-shadow: inset 0 1px 2px rgba(0, 0, 0, 0.075);--bs-progress-bar-color: #ffffff;--bs-progress-bar-bg: #0d6efd;--bs-progress-bar-transition: width 0.6s ease;display:flex;display:-webkit-flex;height:var(--bs-progress-height);overflow:hidden;font-size:var(--bs-progress-font-size);background-color:var(--bs-progress-bg);border-radius:var(--bs-progress-border-radius)}.progress-bar{display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;justify-content:center;-webkit-justify-content:center;overflow:hidden;color:var(--bs-progress-bar-color);text-align:center;white-space:nowrap;background-color:var(--bs-progress-bar-bg);transition:var(--bs-progress-bar-transition)}@media(prefers-reduced-motion: reduce){.progress-bar{transition:none}}.progress-bar-striped{background-image:linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);background-size:var(--bs-progress-height) var(--bs-progress-height)}.progress-stacked>.progress{overflow:visible}.progress-stacked>.progress>.progress-bar{width:100%}.progress-bar-animated{animation:1s linear infinite progress-bar-stripes}@media(prefers-reduced-motion: reduce){.progress-bar-animated{animation:none}}.list-group{--bs-list-group-color: #212529;--bs-list-group-bg: #ffffff;--bs-list-group-border-color: #dee2e6;--bs-list-group-border-width: 1px;--bs-list-group-border-radius: 0.375rem;--bs-list-group-item-padding-x: 1rem;--bs-list-group-item-padding-y: 0.5rem;--bs-list-group-action-color: rgba(33, 37, 41, 0.75);--bs-list-group-action-hover-color: #000;--bs-list-group-action-hover-bg: #f8f9fa;--bs-list-group-action-active-color: #212529;--bs-list-group-action-active-bg: #e9ecef;--bs-list-group-disabled-color: rgba(33, 37, 41, 0.75);--bs-list-group-disabled-bg: #ffffff;--bs-list-group-active-color: #ffffff;--bs-list-group-active-bg: #0d6efd;--bs-list-group-active-border-color: #0d6efd;display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;padding-left:0;margin-bottom:0;border-radius:var(--bs-list-group-border-radius)}.list-group-numbered{list-style-type:none;counter-reset:section}.list-group-numbered>.list-group-item::before{content:counters(section, ".") ". ";counter-increment:section}.list-group-item-action{width:100%;color:var(--bs-list-group-action-color);text-align:inherit}.list-group-item-action:hover,.list-group-item-action:focus{z-index:1;color:var(--bs-list-group-action-hover-color);text-decoration:none;background-color:var(--bs-list-group-action-hover-bg)}.list-group-item-action:active{color:var(--bs-list-group-action-active-color);background-color:var(--bs-list-group-action-active-bg)}.list-group-item{position:relative;display:block;padding:var(--bs-list-group-item-padding-y) var(--bs-list-group-item-padding-x);color:var(--bs-list-group-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-list-group-bg);border:var(--bs-list-group-border-width) solid var(--bs-list-group-border-color)}.list-group-item:first-child{border-top-left-radius:inherit;border-top-right-radius:inherit}.list-group-item:last-child{border-bottom-right-radius:inherit;border-bottom-left-radius:inherit}.list-group-item.disabled,.list-group-item:disabled{color:var(--bs-list-group-disabled-color);pointer-events:none;background-color:var(--bs-list-group-disabled-bg)}.list-group-item.active{z-index:2;color:var(--bs-list-group-active-color);background-color:var(--bs-list-group-active-bg);border-color:var(--bs-list-group-active-border-color)}.list-group-item+.list-group-item{border-top-width:0}.list-group-item+.list-group-item.active{margin-top:calc(-1*var(--bs-list-group-border-width));border-top-width:var(--bs-list-group-border-width)}.list-group-horizontal{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal>.list-group-item.active{margin-top:0}.list-group-horizontal>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}@media(min-width: 576px){.list-group-horizontal-sm{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-sm>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-sm>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-sm>.list-group-item.active{margin-top:0}.list-group-horizontal-sm>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-sm>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 768px){.list-group-horizontal-md{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-md>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-md>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-md>.list-group-item.active{margin-top:0}.list-group-horizontal-md>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-md>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 992px){.list-group-horizontal-lg{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-lg>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-lg>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-lg>.list-group-item.active{margin-top:0}.list-group-horizontal-lg>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-lg>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 1200px){.list-group-horizontal-xl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xl>.list-group-item.active{margin-top:0}.list-group-horizontal-xl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xl>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 1400px){.list-group-horizontal-xxl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xxl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xxl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xxl>.list-group-item.active{margin-top:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}.list-group-flush{border-radius:0}.list-group-flush>.list-group-item{border-width:0 0 var(--bs-list-group-border-width)}.list-group-flush>.list-group-item:last-child{border-bottom-width:0}.list-group-item-default{--bs-list-group-color: var(--bs-default-text-emphasis);--bs-list-group-bg: var(--bs-default-bg-subtle);--bs-list-group-border-color: var(--bs-default-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-default-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-default-border-subtle);--bs-list-group-active-color: var(--bs-default-bg-subtle);--bs-list-group-active-bg: var(--bs-default-text-emphasis);--bs-list-group-active-border-color: var(--bs-default-text-emphasis)}.list-group-item-primary{--bs-list-group-color: var(--bs-primary-text-emphasis);--bs-list-group-bg: var(--bs-primary-bg-subtle);--bs-list-group-border-color: var(--bs-primary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-primary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-primary-border-subtle);--bs-list-group-active-color: var(--bs-primary-bg-subtle);--bs-list-group-active-bg: var(--bs-primary-text-emphasis);--bs-list-group-active-border-color: var(--bs-primary-text-emphasis)}.list-group-item-secondary{--bs-list-group-color: var(--bs-secondary-text-emphasis);--bs-list-group-bg: var(--bs-secondary-bg-subtle);--bs-list-group-border-color: var(--bs-secondary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-secondary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-secondary-border-subtle);--bs-list-group-active-color: var(--bs-secondary-bg-subtle);--bs-list-group-active-bg: var(--bs-secondary-text-emphasis);--bs-list-group-active-border-color: var(--bs-secondary-text-emphasis)}.list-group-item-success{--bs-list-group-color: var(--bs-success-text-emphasis);--bs-list-group-bg: var(--bs-success-bg-subtle);--bs-list-group-border-color: var(--bs-success-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-success-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-success-border-subtle);--bs-list-group-active-color: var(--bs-success-bg-subtle);--bs-list-group-active-bg: var(--bs-success-text-emphasis);--bs-list-group-active-border-color: var(--bs-success-text-emphasis)}.list-group-item-info{--bs-list-group-color: var(--bs-info-text-emphasis);--bs-list-group-bg: var(--bs-info-bg-subtle);--bs-list-group-border-color: var(--bs-info-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-info-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-info-border-subtle);--bs-list-group-active-color: var(--bs-info-bg-subtle);--bs-list-group-active-bg: var(--bs-info-text-emphasis);--bs-list-group-active-border-color: var(--bs-info-text-emphasis)}.list-group-item-warning{--bs-list-group-color: var(--bs-warning-text-emphasis);--bs-list-group-bg: var(--bs-warning-bg-subtle);--bs-list-group-border-color: var(--bs-warning-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-warning-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-warning-border-subtle);--bs-list-group-active-color: var(--bs-warning-bg-subtle);--bs-list-group-active-bg: var(--bs-warning-text-emphasis);--bs-list-group-active-border-color: var(--bs-warning-text-emphasis)}.list-group-item-danger{--bs-list-group-color: var(--bs-danger-text-emphasis);--bs-list-group-bg: var(--bs-danger-bg-subtle);--bs-list-group-border-color: var(--bs-danger-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-danger-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-danger-border-subtle);--bs-list-group-active-color: var(--bs-danger-bg-subtle);--bs-list-group-active-bg: var(--bs-danger-text-emphasis);--bs-list-group-active-border-color: var(--bs-danger-text-emphasis)}.list-group-item-light{--bs-list-group-color: var(--bs-light-text-emphasis);--bs-list-group-bg: var(--bs-light-bg-subtle);--bs-list-group-border-color: var(--bs-light-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-light-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-light-border-subtle);--bs-list-group-active-color: var(--bs-light-bg-subtle);--bs-list-group-active-bg: var(--bs-light-text-emphasis);--bs-list-group-active-border-color: var(--bs-light-text-emphasis)}.list-group-item-dark{--bs-list-group-color: var(--bs-dark-text-emphasis);--bs-list-group-bg: var(--bs-dark-bg-subtle);--bs-list-group-border-color: var(--bs-dark-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-dark-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-dark-border-subtle);--bs-list-group-active-color: var(--bs-dark-bg-subtle);--bs-list-group-active-bg: var(--bs-dark-text-emphasis);--bs-list-group-active-border-color: var(--bs-dark-text-emphasis)}.btn-close{--bs-btn-close-color: #000;--bs-btn-close-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%23000'%3e%3cpath d='M.293.293a1 1 0 0 1 1.414 0L8 6.586 14.293.293a1 1 0 1 1 1.414 1.414L9.414 8l6.293 6.293a1 1 0 0 1-1.414 1.414L8 9.414l-6.293 6.293a1 1 0 0 1-1.414-1.414L6.586 8 .293 1.707a1 1 0 0 1 0-1.414z'/%3e%3c/svg%3e");--bs-btn-close-opacity: 0.5;--bs-btn-close-hover-opacity: 0.75;--bs-btn-close-focus-shadow: 0 0 0 0.25rem rgba(13, 110, 253, 0.25);--bs-btn-close-focus-opacity: 1;--bs-btn-close-disabled-opacity: 0.25;--bs-btn-close-white-filter: invert(1) grayscale(100%) brightness(200%);box-sizing:content-box;width:1em;height:1em;padding:.25em .25em;color:var(--bs-btn-close-color);background:rgba(0,0,0,0) var(--bs-btn-close-bg) center/1em auto 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e=/input|textarea/i.test(t.target.tagName),i="Escape"===t.key,n=[Ei,Ti].includes(t.key);if(!n&&!i)return;if(e&&!i)return;t.preventDefault();const s=this.matches(Ii)?this:z.prev(this,Ii)[0]||z.next(this,Ii)[0]||z.findOne(Ii,t.delegateTarget.parentNode),o=qi.getOrCreateInstance(s);if(n)return t.stopPropagation(),o.show(),void o._selectMenuItem(t);o._isShown()&&(t.stopPropagation(),o.hide(),s.focus())}}N.on(document,Si,Ii,qi.dataApiKeydownHandler),N.on(document,Si,Pi,qi.dataApiKeydownHandler),N.on(document,Li,qi.clearMenus),N.on(document,Di,qi.clearMenus),N.on(document,Li,Ii,(function(t){t.preventDefault(),qi.getOrCreateInstance(this).toggle()})),m(qi);const Vi="backdrop",Ki="show",Qi=`mousedown.bs.${Vi}`,Xi={className:"modal-backdrop",clickCallback:null,isAnimated:!1,isVisible:!0,rootElement:"body"},Yi={className:"string",clickCallback:"(function|null)",isAnimated:"boolean",isVisible:"boolean",rootElement:"(element|string)"};class Ui extends H{constructor(t){super(),this._config=this._getConfig(t),this._isAppended=!1,this._element=null}static get Default(){return Xi}static get DefaultType(){return Yi}static get NAME(){return Vi}show(t){if(!this._config.isVisible)return void g(t);this._append();const e=this._getElement();this._config.isAnimated&&d(e),e.classList.add(Ki),this._emulateAnimation((()=>{g(t)}))}hide(t){this._config.isVisible?(this._getElement().classList.remove(Ki),this._emulateAnimation((()=>{this.dispose(),g(t)}))):g(t)}dispose(){this._isAppended&&(N.off(this._element,Qi),this._element.remove(),this._isAppended=!1)}_getElement(){if(!this._element){const t=document.createElement("div");t.className=this._config.className,this._config.isAnimated&&t.classList.add("fade"),this._element=t}return this._element}_configAfterMerge(t){return t.rootElement=r(t.rootElement),t}_append(){if(this._isAppended)return;const t=this._getElement();this._config.rootElement.append(t),N.on(t,Qi,(()=>{g(this._config.clickCallback)})),this._isAppended=!0}_emulateAnimation(t){_(t,this._getElement(),this._config.isAnimated)}}const Gi=".bs.focustrap",Ji=`focusin${Gi}`,Zi=`keydown.tab${Gi}`,tn="backward",en={autofocus:!0,trapElement:null},nn={autofocus:"boolean",trapElement:"element"};class sn extends H{constructor(t){super(),this._config=this._getConfig(t),this._isActive=!1,this._lastTabNavDirection=null}static get Default(){return en}static get DefaultType(){return nn}static get NAME(){return"focustrap"}activate(){this._isActive||(this._config.autofocus&&this._config.trapElement.focus(),N.off(document,Gi),N.on(document,Ji,(t=>this._handleFocusin(t))),N.on(document,Zi,(t=>this._handleKeydown(t))),this._isActive=!0)}deactivate(){this._isActive&&(this._isActive=!1,N.off(document,Gi))}_handleFocusin(t){const{trapElement:e}=this._config;if(t.target===document||t.target===e||e.contains(t.target))return;const i=z.focusableChildren(e);0===i.length?e.focus():this._lastTabNavDirection===tn?i[i.length-1].focus():i[0].focus()}_handleKeydown(t){"Tab"===t.key&&(this._lastTabNavDirection=t.shiftKey?tn:"forward")}}const on=".fixed-top, .fixed-bottom, .is-fixed, .sticky-top",rn=".sticky-top",an="padding-right",ln="margin-right";class cn{constructor(){this._element=document.body}getWidth(){const t=document.documentElement.clientWidth;return Math.abs(window.innerWidth-t)}hide(){const t=this.getWidth();this._disableOverFlow(),this._setElementAttributes(this._element,an,(e=>e+t)),this._setElementAttributes(on,an,(e=>e+t)),this._setElementAttributes(rn,ln,(e=>e-t))}reset(){this._resetElementAttributes(this._element,"overflow"),this._resetElementAttributes(this._element,an),this._resetElementAttributes(on,an),this._resetElementAttributes(rn,ln)}isOverflowing(){return this.getWidth()>0}_disableOverFlow(){this._saveInitialAttribute(this._element,"overflow"),this._element.style.overflow="hidden"}_setElementAttributes(t,e,i){const n=this.getWidth();this._applyManipulationCallback(t,(t=>{if(t!==this._element&&window.innerWidth>t.clientWidth+n)return;this._saveInitialAttribute(t,e);const s=window.getComputedStyle(t).getPropertyValue(e);t.style.setProperty(e,`${i(Number.parseFloat(s))}px`)}))}_saveInitialAttribute(t,e){const i=t.style.getPropertyValue(e);i&&F.setDataAttribute(t,e,i)}_resetElementAttributes(t,e){this._applyManipulationCallback(t,(t=>{const i=F.getDataAttribute(t,e);null!==i?(F.removeDataAttribute(t,e),t.style.setProperty(e,i)):t.style.removeProperty(e)}))}_applyManipulationCallback(t,e){if(o(t))e(t);else for(const i of z.find(t,this._element))e(i)}}const hn=".bs.modal",dn=`hide${hn}`,un=`hidePrevented${hn}`,fn=`hidden${hn}`,pn=`show${hn}`,mn=`shown${hn}`,gn=`resize${hn}`,_n=`click.dismiss${hn}`,bn=`mousedown.dismiss${hn}`,vn=`keydown.dismiss${hn}`,yn=`click${hn}.data-api`,wn="modal-open",An="show",En="modal-static",Tn={backdrop:!0,focus:!0,keyboard:!0},Cn={backdrop:"(boolean|string)",focus:"boolean",keyboard:"boolean"};class On extends W{constructor(t,e){super(t,e),this._dialog=z.findOne(".modal-dialog",this._element),this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._isShown=!1,this._isTransitioning=!1,this._scrollBar=new cn,this._addEventListeners()}static get Default(){return Tn}static get DefaultType(){return Cn}static get NAME(){return"modal"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||this._isTransitioning||N.trigger(this._element,pn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._isTransitioning=!0,this._scrollBar.hide(),document.body.classList.add(wn),this._adjustDialog(),this._backdrop.show((()=>this._showElement(t))))}hide(){this._isShown&&!this._isTransitioning&&(N.trigger(this._element,dn).defaultPrevented||(this._isShown=!1,this._isTransitioning=!0,this._focustrap.deactivate(),this._element.classList.remove(An),this._queueCallback((()=>this._hideModal()),this._element,this._isAnimated())))}dispose(){N.off(window,hn),N.off(this._dialog,hn),this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}handleUpdate(){this._adjustDialog()}_initializeBackDrop(){return new Ui({isVisible:Boolean(this._config.backdrop),isAnimated:this._isAnimated()})}_initializeFocusTrap(){return new sn({trapElement:this._element})}_showElement(t){document.body.contains(this._element)||document.body.append(this._element),this._element.style.display="block",this._element.removeAttribute("aria-hidden"),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.scrollTop=0;const e=z.findOne(".modal-body",this._dialog);e&&(e.scrollTop=0),d(this._element),this._element.classList.add(An),this._queueCallback((()=>{this._config.focus&&this._focustrap.activate(),this._isTransitioning=!1,N.trigger(this._element,mn,{relatedTarget:t})}),this._dialog,this._isAnimated())}_addEventListeners(){N.on(this._element,vn,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():this._triggerBackdropTransition())})),N.on(window,gn,(()=>{this._isShown&&!this._isTransitioning&&this._adjustDialog()})),N.on(this._element,bn,(t=>{N.one(this._element,_n,(e=>{this._element===t.target&&this._element===e.target&&("static"!==this._config.backdrop?this._config.backdrop&&this.hide():this._triggerBackdropTransition())}))}))}_hideModal(){this._element.style.display="none",this._element.setAttribute("aria-hidden",!0),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._isTransitioning=!1,this._backdrop.hide((()=>{document.body.classList.remove(wn),this._resetAdjustments(),this._scrollBar.reset(),N.trigger(this._element,fn)}))}_isAnimated(){return this._element.classList.contains("fade")}_triggerBackdropTransition(){if(N.trigger(this._element,un).defaultPrevented)return;const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._element.style.overflowY;"hidden"===e||this._element.classList.contains(En)||(t||(this._element.style.overflowY="hidden"),this._element.classList.add(En),this._queueCallback((()=>{this._element.classList.remove(En),this._queueCallback((()=>{this._element.style.overflowY=e}),this._dialog)}),this._dialog),this._element.focus())}_adjustDialog(){const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._scrollBar.getWidth(),i=e>0;if(i&&!t){const t=p()?"paddingLeft":"paddingRight";this._element.style[t]=`${e}px`}if(!i&&t){const t=p()?"paddingRight":"paddingLeft";this._element.style[t]=`${e}px`}}_resetAdjustments(){this._element.style.paddingLeft="",this._element.style.paddingRight=""}static jQueryInterface(t,e){return this.each((function(){const i=On.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===i[t])throw new TypeError(`No method named "${t}"`);i[t](e)}}))}}N.on(document,yn,'[data-bs-toggle="modal"]',(function(t){const e=z.getElementFromSelector(this);["A","AREA"].includes(this.tagName)&&t.preventDefault(),N.one(e,pn,(t=>{t.defaultPrevented||N.one(e,fn,(()=>{a(this)&&this.focus()}))}));const i=z.findOne(".modal.show");i&&On.getInstance(i).hide(),On.getOrCreateInstance(e).toggle(this)})),R(On),m(On);const xn=".bs.offcanvas",kn=".data-api",Ln=`load${xn}${kn}`,Sn="show",Dn="showing",$n="hiding",In=".offcanvas.show",Nn=`show${xn}`,Pn=`shown${xn}`,Mn=`hide${xn}`,jn=`hidePrevented${xn}`,Fn=`hidden${xn}`,Hn=`resize${xn}`,Wn=`click${xn}${kn}`,Bn=`keydown.dismiss${xn}`,zn={backdrop:!0,keyboard:!0,scroll:!1},Rn={backdrop:"(boolean|string)",keyboard:"boolean",scroll:"boolean"};class qn extends W{constructor(t,e){super(t,e),this._isShown=!1,this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._addEventListeners()}static get Default(){return zn}static get DefaultType(){return Rn}static get NAME(){return"offcanvas"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||N.trigger(this._element,Nn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._backdrop.show(),this._config.scroll||(new cn).hide(),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.classList.add(Dn),this._queueCallback((()=>{this._config.scroll&&!this._config.backdrop||this._focustrap.activate(),this._element.classList.add(Sn),this._element.classList.remove(Dn),N.trigger(this._element,Pn,{relatedTarget:t})}),this._element,!0))}hide(){this._isShown&&(N.trigger(this._element,Mn).defaultPrevented||(this._focustrap.deactivate(),this._element.blur(),this._isShown=!1,this._element.classList.add($n),this._backdrop.hide(),this._queueCallback((()=>{this._element.classList.remove(Sn,$n),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._config.scroll||(new cn).reset(),N.trigger(this._element,Fn)}),this._element,!0)))}dispose(){this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}_initializeBackDrop(){const t=Boolean(this._config.backdrop);return new Ui({className:"offcanvas-backdrop",isVisible:t,isAnimated:!0,rootElement:this._element.parentNode,clickCallback:t?()=>{"static"!==this._config.backdrop?this.hide():N.trigger(this._element,jn)}:null})}_initializeFocusTrap(){return new sn({trapElement:this._element})}_addEventListeners(){N.on(this._element,Bn,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():N.trigger(this._element,jn))}))}static jQueryInterface(t){return this.each((function(){const e=qn.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t]||t.startsWith("_")||"constructor"===t)throw new TypeError(`No method named "${t}"`);e[t](this)}}))}}N.on(document,Wn,'[data-bs-toggle="offcanvas"]',(function(t){const e=z.getElementFromSelector(this);if(["A","AREA"].includes(this.tagName)&&t.preventDefault(),l(this))return;N.one(e,Fn,(()=>{a(this)&&this.focus()}));const i=z.findOne(In);i&&i!==e&&qn.getInstance(i).hide(),qn.getOrCreateInstance(e).toggle(this)})),N.on(window,Ln,(()=>{for(const t of z.find(In))qn.getOrCreateInstance(t).show()})),N.on(window,Hn,(()=>{for(const t of z.find("[aria-modal][class*=show][class*=offcanvas-]"))"fixed"!==getComputedStyle(t).position&&qn.getOrCreateInstance(t).hide()})),R(qn),m(qn);const Vn={"*":["class","dir","id","lang","role",/^aria-[\w-]*$/i],a:["target","href","title","rel"],area:[],b:[],br:[],col:[],code:[],div:[],em:[],hr:[],h1:[],h2:[],h3:[],h4:[],h5:[],h6:[],i:[],img:["src","srcset","alt","title","width","height"],li:[],ol:[],p:[],pre:[],s:[],small:[],span:[],sub:[],sup:[],strong:[],u:[],ul:[]},Kn=new Set(["background","cite","href","itemtype","longdesc","poster","src","xlink:href"]),Qn=/^(?!javascript:)(?:[a-z0-9+.-]+:|[^&:/?#]*(?:[/?#]|$))/i,Xn=(t,e)=>{const i=t.nodeName.toLowerCase();return e.includes(i)?!Kn.has(i)||Boolean(Qn.test(t.nodeValue)):e.filter((t=>t instanceof RegExp)).some((t=>t.test(i)))},Yn={allowList:Vn,content:{},extraClass:"",html:!1,sanitize:!0,sanitizeFn:null,template:"

    "},Un={allowList:"object",content:"object",extraClass:"(string|function)",html:"boolean",sanitize:"boolean",sanitizeFn:"(null|function)",template:"string"},Gn={entry:"(string|element|function|null)",selector:"(string|element)"};class Jn extends H{constructor(t){super(),this._config=this._getConfig(t)}static get Default(){return Yn}static get DefaultType(){return Un}static get NAME(){return"TemplateFactory"}getContent(){return Object.values(this._config.content).map((t=>this._resolvePossibleFunction(t))).filter(Boolean)}hasContent(){return this.getContent().length>0}changeContent(t){return this._checkContent(t),this._config.content={...this._config.content,...t},this}toHtml(){const t=document.createElement("div");t.innerHTML=this._maybeSanitize(this._config.template);for(const[e,i]of Object.entries(this._config.content))this._setContent(t,i,e);const e=t.children[0],i=this._resolvePossibleFunction(this._config.extraClass);return i&&e.classList.add(...i.split(" ")),e}_typeCheckConfig(t){super._typeCheckConfig(t),this._checkContent(t.content)}_checkContent(t){for(const[e,i]of Object.entries(t))super._typeCheckConfig({selector:e,entry:i},Gn)}_setContent(t,e,i){const n=z.findOne(i,t);n&&((e=this._resolvePossibleFunction(e))?o(e)?this._putElementInTemplate(r(e),n):this._config.html?n.innerHTML=this._maybeSanitize(e):n.textContent=e:n.remove())}_maybeSanitize(t){return this._config.sanitize?function(t,e,i){if(!t.length)return t;if(i&&"function"==typeof i)return i(t);const n=(new window.DOMParser).parseFromString(t,"text/html"),s=[].concat(...n.body.querySelectorAll("*"));for(const t of s){const i=t.nodeName.toLowerCase();if(!Object.keys(e).includes(i)){t.remove();continue}const n=[].concat(...t.attributes),s=[].concat(e["*"]||[],e[i]||[]);for(const e of n)Xn(e,s)||t.removeAttribute(e.nodeName)}return n.body.innerHTML}(t,this._config.allowList,this._config.sanitizeFn):t}_resolvePossibleFunction(t){return g(t,[this])}_putElementInTemplate(t,e){if(this._config.html)return e.innerHTML="",void e.append(t);e.textContent=t.textContent}}const Zn=new Set(["sanitize","allowList","sanitizeFn"]),ts="fade",es="show",is=".modal",ns="hide.bs.modal",ss="hover",os="focus",rs={AUTO:"auto",TOP:"top",RIGHT:p()?"left":"right",BOTTOM:"bottom",LEFT:p()?"right":"left"},as={allowList:Vn,animation:!0,boundary:"clippingParents",container:!1,customClass:"",delay:0,fallbackPlacements:["top","right","bottom","left"],html:!1,offset:[0,6],placement:"top",popperConfig:null,sanitize:!0,sanitizeFn:null,selector:!1,template:'',title:"",trigger:"hover focus"},ls={allowList:"object",animation:"boolean",boundary:"(string|element)",container:"(string|element|boolean)",customClass:"(string|function)",delay:"(number|object)",fallbackPlacements:"array",html:"boolean",offset:"(array|string|function)",placement:"(string|function)",popperConfig:"(null|object|function)",sanitize:"boolean",sanitizeFn:"(null|function)",selector:"(string|boolean)",template:"string",title:"(string|element|function)",trigger:"string"};class cs extends W{constructor(t,e){if(void 0===vi)throw new TypeError("Bootstrap's tooltips require Popper (https://popper.js.org)");super(t,e),this._isEnabled=!0,this._timeout=0,this._isHovered=null,this._activeTrigger={},this._popper=null,this._templateFactory=null,this._newContent=null,this.tip=null,this._setListeners(),this._config.selector||this._fixTitle()}static get Default(){return as}static get DefaultType(){return ls}static get NAME(){return"tooltip"}enable(){this._isEnabled=!0}disable(){this._isEnabled=!1}toggleEnabled(){this._isEnabled=!this._isEnabled}toggle(){this._isEnabled&&(this._activeTrigger.click=!this._activeTrigger.click,this._isShown()?this._leave():this._enter())}dispose(){clearTimeout(this._timeout),N.off(this._element.closest(is),ns,this._hideModalHandler),this._element.getAttribute("data-bs-original-title")&&this._element.setAttribute("title",this._element.getAttribute("data-bs-original-title")),this._disposePopper(),super.dispose()}show(){if("none"===this._element.style.display)throw new Error("Please use show on visible elements");if(!this._isWithContent()||!this._isEnabled)return;const t=N.trigger(this._element,this.constructor.eventName("show")),e=(c(this._element)||this._element.ownerDocument.documentElement).contains(this._element);if(t.defaultPrevented||!e)return;this._disposePopper();const i=this._getTipElement();this._element.setAttribute("aria-describedby",i.getAttribute("id"));const{container:n}=this._config;if(this._element.ownerDocument.documentElement.contains(this.tip)||(n.append(i),N.trigger(this._element,this.constructor.eventName("inserted"))),this._popper=this._createPopper(i),i.classList.add(es),"ontouchstart"in document.documentElement)for(const t of[].concat(...document.body.children))N.on(t,"mouseover",h);this._queueCallback((()=>{N.trigger(this._element,this.constructor.eventName("shown")),!1===this._isHovered&&this._leave(),this._isHovered=!1}),this.tip,this._isAnimated())}hide(){if(this._isShown()&&!N.trigger(this._element,this.constructor.eventName("hide")).defaultPrevented){if(this._getTipElement().classList.remove(es),"ontouchstart"in document.documentElement)for(const t of[].concat(...document.body.children))N.off(t,"mouseover",h);this._activeTrigger.click=!1,this._activeTrigger[os]=!1,this._activeTrigger[ss]=!1,this._isHovered=null,this._queueCallback((()=>{this._isWithActiveTrigger()||(this._isHovered||this._disposePopper(),this._element.removeAttribute("aria-describedby"),N.trigger(this._element,this.constructor.eventName("hidden")))}),this.tip,this._isAnimated())}}update(){this._popper&&this._popper.update()}_isWithContent(){return Boolean(this._getTitle())}_getTipElement(){return this.tip||(this.tip=this._createTipElement(this._newContent||this._getContentForTemplate())),this.tip}_createTipElement(t){const e=this._getTemplateFactory(t).toHtml();if(!e)return null;e.classList.remove(ts,es),e.classList.add(`bs-${this.constructor.NAME}-auto`);const i=(t=>{do{t+=Math.floor(1e6*Math.random())}while(document.getElementById(t));return t})(this.constructor.NAME).toString();return e.setAttribute("id",i),this._isAnimated()&&e.classList.add(ts),e}setContent(t){this._newContent=t,this._isShown()&&(this._disposePopper(),this.show())}_getTemplateFactory(t){return this._templateFactory?this._templateFactory.changeContent(t):this._templateFactory=new Jn({...this._config,content:t,extraClass:this._resolvePossibleFunction(this._config.customClass)}),this._templateFactory}_getContentForTemplate(){return{".tooltip-inner":this._getTitle()}}_getTitle(){return this._resolvePossibleFunction(this._config.title)||this._element.getAttribute("data-bs-original-title")}_initializeOnDelegatedTarget(t){return this.constructor.getOrCreateInstance(t.delegateTarget,this._getDelegateConfig())}_isAnimated(){return this._config.animation||this.tip&&this.tip.classList.contains(ts)}_isShown(){return this.tip&&this.tip.classList.contains(es)}_createPopper(t){const e=g(this._config.placement,[this,t,this._element]),i=rs[e.toUpperCase()];return 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font-style: inherit; +} + +code span.fl { + color: #AD0000; + font-style: inherit; +} + +code span.co { + color: #5E5E5E; + font-style: inherit; +} + +code span.cv { + color: #5E5E5E; + font-style: italic; +} + +code span.cn { + color: #8f5902; + font-style: inherit; +} + +code span.sc { + color: #5E5E5E; + font-style: inherit; +} + +code span.dv { + color: #AD0000; + font-style: inherit; +} + +code span.kw { + color: #003B4F; + font-weight: bold; + font-style: inherit; +} + +.prevent-inlining { + content: " { + // Find any conflicting margin elements and add margins to the + // top to prevent overlap + const marginChildren = window.document.querySelectorAll( + ".column-margin.column-container > *, .margin-caption, .aside" + ); + + let lastBottom = 0; + for (const marginChild of marginChildren) { + if (marginChild.offsetParent !== null) { + // clear the top margin so we recompute it + marginChild.style.marginTop = null; + const top = marginChild.getBoundingClientRect().top + window.scrollY; + if (top < lastBottom) { + const marginChildStyle = window.getComputedStyle(marginChild); + const marginBottom = parseFloat(marginChildStyle["marginBottom"]); + const margin = lastBottom - top + marginBottom; + marginChild.style.marginTop = `${margin}px`; + } + const styles = window.getComputedStyle(marginChild); + const marginTop = parseFloat(styles["marginTop"]); + lastBottom = top + marginChild.getBoundingClientRect().height + marginTop; + } + } +}; + +window.document.addEventListener("DOMContentLoaded", function (_event) { + // Recompute the position of margin elements anytime the body size changes + if (window.ResizeObserver) { + const resizeObserver = new window.ResizeObserver( + throttle(() => { + layoutMarginEls(); + if ( + window.document.body.getBoundingClientRect().width < 990 && + isReaderMode() + ) { + quartoToggleReader(); + } + }, 50) + ); + resizeObserver.observe(window.document.body); + } + + const tocEl = window.document.querySelector('nav.toc-active[role="doc-toc"]'); + const sidebarEl = window.document.getElementById("quarto-sidebar"); + const leftTocEl = window.document.getElementById("quarto-sidebar-toc-left"); + const marginSidebarEl = window.document.getElementById( + "quarto-margin-sidebar" + ); + // function to determine whether the element has a previous sibling that is active + const prevSiblingIsActiveLink = (el) => { + const sibling = el.previousElementSibling; + if (sibling && sibling.tagName === "A") { + return sibling.classList.contains("active"); + } else { + return false; + } + }; + + // fire slideEnter for bootstrap tab activations (for htmlwidget resize behavior) + function fireSlideEnter(e) { + const event = window.document.createEvent("Event"); + event.initEvent("slideenter", true, true); + window.document.dispatchEvent(event); + } + const tabs = window.document.querySelectorAll('a[data-bs-toggle="tab"]'); + tabs.forEach((tab) => { + tab.addEventListener("shown.bs.tab", fireSlideEnter); + }); + + // fire slideEnter for tabby tab activations (for htmlwidget resize behavior) + document.addEventListener("tabby", fireSlideEnter, false); + + // Track scrolling and mark TOC links as active + // get table of contents and sidebar (bail if we don't have at least one) + const tocLinks = tocEl + ? [...tocEl.querySelectorAll("a[data-scroll-target]")] + : []; + const makeActive = (link) => tocLinks[link].classList.add("active"); + const removeActive = (link) => tocLinks[link].classList.remove("active"); + const removeAllActive = () => + [...Array(tocLinks.length).keys()].forEach((link) => removeActive(link)); + + // activate the anchor for a section associated with this TOC entry + tocLinks.forEach((link) => { + link.addEventListener("click", () => { + if (link.href.indexOf("#") !== -1) { + const anchor = link.href.split("#")[1]; + const heading = window.document.querySelector( + `[data-anchor-id="${anchor}"]` + ); + if (heading) { + // Add the class + heading.classList.add("reveal-anchorjs-link"); + + // function to show the anchor + const handleMouseout = () => { + heading.classList.remove("reveal-anchorjs-link"); + heading.removeEventListener("mouseout", handleMouseout); + }; + + // add a function to clear the anchor when the user mouses out of it + heading.addEventListener("mouseout", handleMouseout); + } + } + }); + }); + + const sections = tocLinks.map((link) => { + const target = link.getAttribute("data-scroll-target"); + if (target.startsWith("#")) { + return window.document.getElementById(decodeURI(`${target.slice(1)}`)); + } else { + return window.document.querySelector(decodeURI(`${target}`)); + } + }); + + const sectionMargin = 200; + let currentActive = 0; + // track whether we've initialized state the first time + let init = false; + + const updateActiveLink = () => { + // The index from bottom to top (e.g. reversed list) + let sectionIndex = -1; + if ( + window.innerHeight + window.pageYOffset >= + window.document.body.offsetHeight + ) { + // This is the no-scroll case where last section should be the active one + sectionIndex = 0; + } else { + // This finds the last section visible on screen that should be made active + sectionIndex = [...sections].reverse().findIndex((section) => { + if (section) { + return window.pageYOffset >= section.offsetTop - sectionMargin; + } else { + return false; + } + }); + } + if (sectionIndex > -1) { + const current = sections.length - sectionIndex - 1; + if (current !== currentActive) { + removeAllActive(); + currentActive = current; + makeActive(current); + if (init) { + window.dispatchEvent(sectionChanged); + } + init = true; + } + } + }; + + const inHiddenRegion = (top, bottom, hiddenRegions) => { + for (const region of hiddenRegions) { + if (top <= region.bottom && bottom >= region.top) { + return true; + } + } + return false; + }; + + const categorySelector = "header.quarto-title-block .quarto-category"; + const activateCategories = (href) => { + // Find any categories + // Surround them with a link pointing back to: + // #category=Authoring + try { + const categoryEls = window.document.querySelectorAll(categorySelector); + for (const categoryEl of categoryEls) { + const categoryText = categoryEl.textContent; + if (categoryText) { + const link = `${href}#category=${encodeURIComponent(categoryText)}`; + const linkEl = window.document.createElement("a"); + linkEl.setAttribute("href", link); + for (const child of categoryEl.childNodes) { + linkEl.append(child); + } + categoryEl.appendChild(linkEl); + } + } + } catch { + // Ignore errors + } + }; + function hasTitleCategories() { + return window.document.querySelector(categorySelector) !== null; + } + + function offsetRelativeUrl(url) { + const offset = getMeta("quarto:offset"); + return offset ? offset + url : url; + } + + function offsetAbsoluteUrl(url) { + const offset = getMeta("quarto:offset"); + const baseUrl = new URL(offset, window.location); + + const projRelativeUrl = url.replace(baseUrl, ""); + if (projRelativeUrl.startsWith("/")) { + return projRelativeUrl; + } else { + return "/" + projRelativeUrl; + } + } + + // read a meta tag value + function getMeta(metaName) { + const metas = window.document.getElementsByTagName("meta"); + for (let i = 0; i < metas.length; i++) { + if (metas[i].getAttribute("name") === metaName) { + return metas[i].getAttribute("content"); + } + } + return ""; + } + + async function findAndActivateCategories() { + const currentPagePath = offsetAbsoluteUrl(window.location.href); + const response = await fetch(offsetRelativeUrl("listings.json")); + if (response.status == 200) { + return response.json().then(function (listingPaths) { + const listingHrefs = []; + for (const listingPath of listingPaths) { + const pathWithoutLeadingSlash = listingPath.listing.substring(1); + for (const item of listingPath.items) { + if ( + item === currentPagePath || + item === currentPagePath + "index.html" + ) { + // Resolve this path against the offset to be sure + // we already are using the correct path to the listing + // (this adjusts the listing urls to be rooted against + // whatever root the page is actually running against) + const relative = offsetRelativeUrl(pathWithoutLeadingSlash); + const baseUrl = window.location; + const resolvedPath = new URL(relative, baseUrl); + listingHrefs.push(resolvedPath.pathname); + break; + } + } + } + + // Look up the tree for a nearby linting and use that if we find one + const nearestListing = findNearestParentListing( + offsetAbsoluteUrl(window.location.pathname), + listingHrefs + ); + if (nearestListing) { + activateCategories(nearestListing); + } else { + // See if the referrer is a listing page for this item + const referredRelativePath = offsetAbsoluteUrl(document.referrer); + const referrerListing = listingHrefs.find((listingHref) => { + const isListingReferrer = + listingHref === referredRelativePath || + listingHref === referredRelativePath + "index.html"; + return isListingReferrer; + }); + + if (referrerListing) { + // Try to use the referrer if possible + activateCategories(referrerListing); + } else if (listingHrefs.length > 0) { + // Otherwise, just fall back to the first listing + activateCategories(listingHrefs[0]); + } + } + }); + } + } + if (hasTitleCategories()) { + findAndActivateCategories(); + } + + const findNearestParentListing = (href, listingHrefs) => { + if (!href || !listingHrefs) { + return undefined; + } + // Look up the tree for a nearby linting and use that if we find one + const relativeParts = href.substring(1).split("/"); + while (relativeParts.length > 0) { + const path = relativeParts.join("/"); + for (const listingHref of listingHrefs) { + if (listingHref.startsWith(path)) { + return listingHref; + } + } + relativeParts.pop(); + } + + return undefined; + }; + + const manageSidebarVisiblity = (el, placeholderDescriptor) => { + let isVisible = true; + let elRect; + + return (hiddenRegions) => { + if (el === null) { + return; + } + + // Find the last element of the TOC + const lastChildEl = el.lastElementChild; + + if (lastChildEl) { + // Converts the sidebar to a menu + const convertToMenu = () => { + for (const child of el.children) { + child.style.opacity = 0; + child.style.overflow = "hidden"; + child.style.pointerEvents = "none"; + } + + nexttick(() => { + const toggleContainer = window.document.createElement("div"); + toggleContainer.style.width = "100%"; + toggleContainer.classList.add("zindex-over-content"); + toggleContainer.classList.add("quarto-sidebar-toggle"); + toggleContainer.classList.add("headroom-target"); // Marks this to be managed by headeroom + toggleContainer.id = placeholderDescriptor.id; + toggleContainer.style.position = "fixed"; + + const toggleIcon = window.document.createElement("i"); + toggleIcon.classList.add("quarto-sidebar-toggle-icon"); + toggleIcon.classList.add("bi"); + toggleIcon.classList.add("bi-caret-down-fill"); + + const toggleTitle = window.document.createElement("div"); + const titleEl = window.document.body.querySelector( + placeholderDescriptor.titleSelector + ); + if (titleEl) { + toggleTitle.append( + titleEl.textContent || titleEl.innerText, + toggleIcon + ); + } + toggleTitle.classList.add("zindex-over-content"); + toggleTitle.classList.add("quarto-sidebar-toggle-title"); + toggleContainer.append(toggleTitle); + + const toggleContents = window.document.createElement("div"); + toggleContents.classList = el.classList; + toggleContents.classList.add("zindex-over-content"); + toggleContents.classList.add("quarto-sidebar-toggle-contents"); + for (const child of el.children) { + if (child.id === "toc-title") { + continue; + } + + const clone = child.cloneNode(true); + clone.style.opacity = 1; + clone.style.pointerEvents = null; + clone.style.display = null; + toggleContents.append(clone); + } + toggleContents.style.height = "0px"; + const positionToggle = () => { + // position the element (top left of parent, same width as parent) + if (!elRect) { + elRect = el.getBoundingClientRect(); + } + toggleContainer.style.left = `${elRect.left}px`; + toggleContainer.style.top = `${elRect.top}px`; + toggleContainer.style.width = `${elRect.width}px`; + }; + positionToggle(); + + toggleContainer.append(toggleContents); + el.parentElement.prepend(toggleContainer); + + // Process clicks + let tocShowing = false; + // Allow the caller to control whether this is dismissed + // when it is clicked (e.g. sidebar navigation supports + // opening and closing the nav tree, so don't dismiss on click) + const clickEl = placeholderDescriptor.dismissOnClick + ? toggleContainer + : toggleTitle; + + const closeToggle = () => { + if (tocShowing) { + toggleContainer.classList.remove("expanded"); + toggleContents.style.height = "0px"; + tocShowing = false; + } + }; + + // Get rid of any expanded toggle if the user scrolls + window.document.addEventListener( + "scroll", + throttle(() => { + closeToggle(); + }, 50) + ); + + // Handle positioning of the toggle + window.addEventListener( + "resize", + throttle(() => { + elRect = undefined; + positionToggle(); + }, 50) + ); + + window.addEventListener("quarto-hrChanged", () => { + elRect = undefined; + }); + + // Process the click + clickEl.onclick = () => { + if (!tocShowing) { + toggleContainer.classList.add("expanded"); + toggleContents.style.height = null; + tocShowing = true; + } else { + closeToggle(); + } + }; + }); + }; + + // Converts a sidebar from a menu back to a sidebar + const convertToSidebar = () => { + for (const child of el.children) { + child.style.opacity = 1; + child.style.overflow = null; + child.style.pointerEvents = null; + } + + const placeholderEl = window.document.getElementById( + placeholderDescriptor.id + ); + if (placeholderEl) { + placeholderEl.remove(); + } + + el.classList.remove("rollup"); + }; + + if (isReaderMode()) { + convertToMenu(); + isVisible = false; + } else { + // Find the top and bottom o the element that is being managed + const elTop = el.offsetTop; + const elBottom = + elTop + lastChildEl.offsetTop + lastChildEl.offsetHeight; + + if (!isVisible) { + // If the element is current not visible reveal if there are + // no conflicts with overlay regions + if (!inHiddenRegion(elTop, elBottom, hiddenRegions)) { + convertToSidebar(); + isVisible = true; + } + } else { + // If the element is visible, hide it if it conflicts with overlay regions + // and insert a placeholder toggle (or if we're in reader mode) + if (inHiddenRegion(elTop, elBottom, hiddenRegions)) { + convertToMenu(); + isVisible = false; + } + } + } + } + }; + }; + + const tabEls = document.querySelectorAll('a[data-bs-toggle="tab"]'); + for (const tabEl of tabEls) { + const id = tabEl.getAttribute("data-bs-target"); + if (id) { + const columnEl = document.querySelector( + `${id} .column-margin, .tabset-margin-content` + ); + if (columnEl) + tabEl.addEventListener("shown.bs.tab", function (event) { + const el = event.srcElement; + if (el) { + const visibleCls = `${el.id}-margin-content`; + // walk up until we find a parent tabset + let panelTabsetEl = el.parentElement; + while (panelTabsetEl) { + if (panelTabsetEl.classList.contains("panel-tabset")) { + break; + } + panelTabsetEl = panelTabsetEl.parentElement; + } + + if (panelTabsetEl) { + const prevSib = panelTabsetEl.previousElementSibling; + if ( + prevSib && + prevSib.classList.contains("tabset-margin-container") + ) { + const childNodes = prevSib.querySelectorAll( + ".tabset-margin-content" + ); + for (const childEl of childNodes) { + if (childEl.classList.contains(visibleCls)) { + childEl.classList.remove("collapse"); + } else { + childEl.classList.add("collapse"); + } + } + } + } + } + + layoutMarginEls(); + }); + } + } + + // Manage the visibility of the toc and the sidebar + const marginScrollVisibility = manageSidebarVisiblity(marginSidebarEl, { + id: "quarto-toc-toggle", + titleSelector: "#toc-title", + dismissOnClick: true, + }); + const sidebarScrollVisiblity = manageSidebarVisiblity(sidebarEl, { + id: "quarto-sidebarnav-toggle", + titleSelector: ".title", + dismissOnClick: false, + }); + let tocLeftScrollVisibility; + if (leftTocEl) { + tocLeftScrollVisibility = manageSidebarVisiblity(leftTocEl, { + id: "quarto-lefttoc-toggle", + titleSelector: "#toc-title", + dismissOnClick: true, + }); + } + + // Find the first element that uses formatting in special columns + const conflictingEls = window.document.body.querySelectorAll( + '[class^="column-"], [class*=" column-"], aside, [class*="margin-caption"], [class*=" margin-caption"], [class*="margin-ref"], [class*=" margin-ref"]' + ); + + // Filter all the possibly conflicting elements into ones + // the do conflict on the left or ride side + const arrConflictingEls = Array.from(conflictingEls); + const leftSideConflictEls = arrConflictingEls.filter((el) => { + if (el.tagName === "ASIDE") { + return false; + } + return Array.from(el.classList).find((className) => { + return ( + className !== "column-body" && + className.startsWith("column-") && + !className.endsWith("right") && + !className.endsWith("container") && + className !== "column-margin" + ); + }); + }); + const rightSideConflictEls = arrConflictingEls.filter((el) => { + if (el.tagName === "ASIDE") { + return true; + } + + const hasMarginCaption = Array.from(el.classList).find((className) => { + return className == "margin-caption"; + }); + if (hasMarginCaption) { + return true; + } + + return Array.from(el.classList).find((className) => { + return ( + className !== "column-body" && + !className.endsWith("container") && + className.startsWith("column-") && + !className.endsWith("left") + ); + }); + }); + + const kOverlapPaddingSize = 10; + function toRegions(els) { + return els.map((el) => { + const boundRect = el.getBoundingClientRect(); + const top = + boundRect.top + + document.documentElement.scrollTop - + kOverlapPaddingSize; + return { + top, + bottom: top + el.scrollHeight + 2 * kOverlapPaddingSize, + }; + }); + } + + let hasObserved = false; + const visibleItemObserver = (els) => { + let visibleElements = [...els]; + const intersectionObserver = new IntersectionObserver( + (entries, _observer) => { + entries.forEach((entry) => { + if (entry.isIntersecting) { + if (visibleElements.indexOf(entry.target) === -1) { + visibleElements.push(entry.target); + } + } else { + visibleElements = visibleElements.filter((visibleEntry) => { + return visibleEntry !== entry; + }); + } + }); + + if (!hasObserved) { + hideOverlappedSidebars(); + } + hasObserved = true; + }, + {} + ); + els.forEach((el) => { + intersectionObserver.observe(el); + }); + + return { + getVisibleEntries: () => { + return visibleElements; + }, + }; + }; + + const rightElementObserver = visibleItemObserver(rightSideConflictEls); + const leftElementObserver = visibleItemObserver(leftSideConflictEls); + + const hideOverlappedSidebars = () => { + marginScrollVisibility(toRegions(rightElementObserver.getVisibleEntries())); + sidebarScrollVisiblity(toRegions(leftElementObserver.getVisibleEntries())); + if (tocLeftScrollVisibility) { + tocLeftScrollVisibility( + toRegions(leftElementObserver.getVisibleEntries()) + ); + } + }; + + window.quartoToggleReader = () => { + // Applies a slow class (or removes it) + // to update the transition speed + const slowTransition = (slow) => { + const manageTransition = (id, slow) => { + const el = document.getElementById(id); + if (el) { + if (slow) { + el.classList.add("slow"); + } else { + el.classList.remove("slow"); + } + } + }; + + manageTransition("TOC", slow); + manageTransition("quarto-sidebar", slow); + }; + const readerMode = !isReaderMode(); + setReaderModeValue(readerMode); + + // If we're entering reader mode, slow the transition + if (readerMode) { + slowTransition(readerMode); + } + highlightReaderToggle(readerMode); + hideOverlappedSidebars(); + + // If we're exiting reader mode, restore the non-slow transition + if (!readerMode) { + slowTransition(!readerMode); + } + }; + + const highlightReaderToggle = (readerMode) => { + const els = document.querySelectorAll(".quarto-reader-toggle"); + if (els) { + els.forEach((el) => { + if (readerMode) { + el.classList.add("reader"); + } else { + el.classList.remove("reader"); + } + }); + } + }; + + const setReaderModeValue = (val) => { + if (window.location.protocol !== "file:") { + window.localStorage.setItem("quarto-reader-mode", val); + } else { + localReaderMode = val; + } + }; + + const isReaderMode = () => { + if (window.location.protocol !== "file:") { + return window.localStorage.getItem("quarto-reader-mode") === "true"; + } else { + return localReaderMode; + } + }; + let localReaderMode = null; + + const tocOpenDepthStr = tocEl?.getAttribute("data-toc-expanded"); + const tocOpenDepth = tocOpenDepthStr ? Number(tocOpenDepthStr) : 1; + + // Walk the TOC and collapse/expand nodes + // Nodes are expanded if: + // - they are top level + // - they have children that are 'active' links + // - they are directly below an link that is 'active' + const walk = (el, depth) => { + // Tick depth when we enter a UL + if (el.tagName === "UL") { + depth = depth + 1; + } + + // It this is active link + let isActiveNode = false; + if (el.tagName === "A" && el.classList.contains("active")) { + isActiveNode = true; + } + + // See if there is an active child to this element + let hasActiveChild = false; + for (child of el.children) { + hasActiveChild = walk(child, depth) || hasActiveChild; + } + + // Process the collapse state if this is an UL + if (el.tagName === "UL") { + if (tocOpenDepth === -1 && depth > 1) { + // toc-expand: false + el.classList.add("collapse"); + } else if ( + depth <= tocOpenDepth || + hasActiveChild || + prevSiblingIsActiveLink(el) + ) { + el.classList.remove("collapse"); + } else { + el.classList.add("collapse"); + } + + // untick depth when we leave a UL + depth = depth - 1; + } + return hasActiveChild || isActiveNode; + }; + + // walk the TOC and expand / collapse any items that should be shown + if (tocEl) { + updateActiveLink(); + walk(tocEl, 0); + } + + // Throttle the scroll event and walk peridiocally + window.document.addEventListener( + "scroll", + throttle(() => { + if (tocEl) { + updateActiveLink(); + walk(tocEl, 0); + } + if (!isReaderMode()) { + hideOverlappedSidebars(); + } + }, 5) + ); + window.addEventListener( + "resize", + throttle(() => { + if (tocEl) { + updateActiveLink(); + walk(tocEl, 0); + } + if (!isReaderMode()) { + hideOverlappedSidebars(); + } + }, 10) + ); + hideOverlappedSidebars(); + highlightReaderToggle(isReaderMode()); +}); + +// grouped tabsets +window.addEventListener("pageshow", (_event) => { + function getTabSettings() { + const data = localStorage.getItem("quarto-persistent-tabsets-data"); + if (!data) { + localStorage.setItem("quarto-persistent-tabsets-data", "{}"); + return {}; + } + if (data) { + return JSON.parse(data); + } + } + + function setTabSettings(data) { + localStorage.setItem( + "quarto-persistent-tabsets-data", + JSON.stringify(data) + ); + } + + function setTabState(groupName, groupValue) { + const data = getTabSettings(); + data[groupName] = groupValue; + setTabSettings(data); + } + + function toggleTab(tab, active) { + const tabPanelId = tab.getAttribute("aria-controls"); + const tabPanel = document.getElementById(tabPanelId); + if (active) { + tab.classList.add("active"); + tabPanel.classList.add("active"); + } else { + tab.classList.remove("active"); + tabPanel.classList.remove("active"); + } + } + + function toggleAll(selectedGroup, selectorsToSync) { + for (const [thisGroup, tabs] of Object.entries(selectorsToSync)) { + const active = selectedGroup === thisGroup; + for (const tab of tabs) { + toggleTab(tab, active); + } + } + } + + function findSelectorsToSyncByLanguage() { + const result = {}; + const tabs = Array.from( + document.querySelectorAll(`div[data-group] a[id^='tabset-']`) + ); + for (const item of tabs) { + const div = item.parentElement.parentElement.parentElement; + const group = div.getAttribute("data-group"); + if (!result[group]) { + result[group] = {}; + } + const selectorsToSync = result[group]; + const value = item.innerHTML; + if (!selectorsToSync[value]) { + selectorsToSync[value] = []; + } + selectorsToSync[value].push(item); + } + return result; + } + + function setupSelectorSync() { + const selectorsToSync = findSelectorsToSyncByLanguage(); + Object.entries(selectorsToSync).forEach(([group, tabSetsByValue]) => { + Object.entries(tabSetsByValue).forEach(([value, items]) => { + items.forEach((item) => { + item.addEventListener("click", (_event) => { + setTabState(group, value); + toggleAll(value, selectorsToSync[group]); + }); + }); + }); + }); + return selectorsToSync; + } + + const selectorsToSync = setupSelectorSync(); + for (const [group, selectedName] of Object.entries(getTabSettings())) { + const selectors = selectorsToSync[group]; + // it's possible that stale state gives us empty selections, so we explicitly check here. + if (selectors) { + toggleAll(selectedName, selectors); + } + } +}); + +function throttle(func, wait) { + let waiting = false; + return function () { + if (!waiting) { + func.apply(this, arguments); + waiting = true; + setTimeout(function () { + waiting = false; + }, wait); + } + }; +} + +function nexttick(func) { + return setTimeout(func, 0); +} diff --git a/profile/_freeze/blog/posts/causal-recourse/index/libs/quarto-html/tippy.css b/profile/_freeze/blog/posts/causal-recourse/index/libs/quarto-html/tippy.css new file mode 100644 index 0000000..e6ae635 --- /dev/null +++ b/profile/_freeze/blog/posts/causal-recourse/index/libs/quarto-html/tippy.css @@ -0,0 +1 @@ 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a/profile/_freeze/blog/posts/conformal-image-classifier/index/execute-results/html.json b/profile/_freeze/blog/posts/conformal-image-classifier/index/execute-results/html.json index 76f4e19..328d464 100644 --- a/profile/_freeze/blog/posts/conformal-image-classifier/index/execute-results/html.json +++ b/profile/_freeze/blog/posts/conformal-image-classifier/index/execute-results/html.json @@ -1,10 +1,10 @@ { - "hash": "8a96d3a48288fce5e64f2325d2bd8ba6", + "hash": "5d39d096cbd3f9ef49ff70cab9365f26", "result": { - "engine": "jupyter", - "markdown": "---\ntitle: How to Conformalize a Deep Image Classifier\nsubtitle: Conformal Prediction in Julia --- Part 2\ndate: '2022-12-05'\ncategories:\n - conformal prediction\n - uncertainty\n - Julia\ndescription: >-\n A guide demonstrating how to use [`ConformalPrediction.jl`](https://github.com/juliatrustworthyai/ConformalPrediction.jl) to conformalize a deep image classifier in a few lines of code.\nimage: www/intro.gif\njupyter: julia-1.10\ndraft: false\n---\n\n\n\n
    \n
    \n \n
    Conformalized prediction sets for a
    simple Deep Image Classifier.
    \n
    \n
    \n\nDeep Learning is popular and --- for some tasks like image classification --- remarkably powerful. But it is also well-known that Deep Neural Networks (DNN) can be unstable [@goodfellow2014explaining] and poorly calibrated. Conformal Prediction can be used to mitigate these pitfalls. \n\nIn the [first part](../conformal-prediction/index.qmd) of this series of posts on Conformal Prediction, we looked at the basic underlying methodology and how CP can be implemented in Julia using [`ConformalPrediction.jl`](https://github.com/juliatrustworthyai/ConformalPrediction.jl). This second part of the series is a more goal-oriented how-to guide: it demonstrates how you can conformalize a deep learning image classifier built in `Flux.jl` in just a few lines of code. \n\nSince this is meant to be more of a hands-on article, we will avoid diving too deeply into methodological concepts. If you need more colour on this, be sure to check out the [first article](../conformal-prediction/index.qmd) on this topic and also @angelopoulos2021gentle. For a more formal treatment of Conformal Prediction see also @angelopoulos2022uncertainty.\n\n## 🎯 The Task at Hand \n\nThe task at hand is to predict the labels of handwritten images of digits using the famous MNIST dataset [@lecun1998mnist]. Importing this popular machine learning dataset in Julia is made remarkably easy through `MLDatasets.jl`:\n\n::: {#e317685b .cell execution_count=2}\n``` {.julia .cell-code}\nusing MLDatasets\nN = 1000\nXraw, yraw = MNIST(split=:train)[:]\nXraw = Xraw[:,:,1:N]\nyraw = yraw[1:N]\n```\n:::\n\n\n@fig-samples below shows a few random samples from the training data:\n\n::: {#cell-fig-samples .cell execution_count=3}\n``` {.julia .cell-code}\nusing MLJ\nusing Images\nX = map(x -> convert2image(MNIST, x), eachslice(Xraw, dims=3))\ny = coerce(yraw, Multiclass)\n\nn_samples = 10\nmosaic(rand(X, n_samples)..., ncol=n_samples)\n```\n\n::: {#fig-samples .cell-output .cell-output-display execution_count=4}\n```{=html}\n\n```\n\nRandom samples from the MNIST dataset.\n:::\n:::\n\n\n## 🚧 Building the Network\n\nTo model the mapping from image inputs to labels will rely on a simple Multi-Layer Perceptron (MLP). A great Julia library for Deep Learning is `Flux.jl`. But wait ... doesn't `ConformalPrediction.jl` work with models trained in `MLJ.jl`? That's right, but fortunately there exists a `Flux.jl` interface to `MLJ.jl`, namely `MLJFlux.jl`. The interface is still in its early stages, but already very powerful and easily accessible for anyone (like myself) who is used to building Neural Networks in `Flux.jl`. \n\nIn `Flux.jl`, you could build an MLP for this task as follows,\n\n::: {#f1b9de42 .cell execution_count=4}\n``` {.julia .cell-code}\nusing Flux\n\nmlp = Chain(\n Flux.flatten,\n Dense(prod((28,28)), 32, relu),\n Dense(32, 10)\n)\n```\n:::\n\n\nwhere `(28,28)` is just the input dimension (28x28 pixel images). Since we have ten digits, our output dimension is ten.^[For a full tutorial on how to build an MNIST image classifier relying solely on `Flux.jl`, check out this [tutorial](https://fluxml.ai/Flux.jl/stable/tutorials/2021-01-26-mlp/).]\n\nWe can do the exact same thing in `MLJFlux.jl` as follows,\n\n::: {#e1b14f5b .cell execution_count=5}\n``` {.julia .cell-code}\nusing MLJFlux\n\nbuilder = MLJFlux.@builder Chain(\n Flux.flatten,\n Dense(prod(n_in), 32, relu),\n Dense(32, n_out)\n)\n```\n:::\n\n\nwhere here we rely on the `@builder` macro to make the transition from `Flux.jl` to `MLJ.jl` as seamless as possible. Finally, `MLJFlux.jl` already comes with a number of helper functions to define plain-vanilla networks. In this case, we will use the `ImageClassifier` with our custom builder and cross-entropy loss:\n\n::: {#cf09cbcb .cell execution_count=6}\n``` {.julia .cell-code}\nImageClassifier = @load ImageClassifier\nclf = ImageClassifier(\n builder=builder,\n epochs=10,\n loss=Flux.crossentropy\n)\n```\n:::\n\n\nThe generated instance `clf` is a model (in the `MLJ.jl` sense) so from this point on we can rely on standard `MLJ.jl` workflows. For example, we can wrap our model in data to create a machine and then evaluate it on a holdout set as follows:\n\n::: {#b50938d8 .cell execution_count=7}\n``` {.julia .cell-code}\nmach = machine(clf, X, y)\n\nevaluate!(\n mach,\n resampling=Holdout(rng=123, fraction_train=0.8),\n operation=predict_mode,\n measure=[accuracy]\n)\n```\n:::\n\n\nThe accuracy of our very simple model is not amazing, but good enough for the purpose of this tutorial. For each image, our MLP returns a softmax output for each possible digit: 0,1,2,3,...,9. Since each individual softmax output is valued between zero and one, $y_k\\in(0,1)$, this is commonly interpreted as a probability: $y_k \\coloneqq p(y=k|X)$. Edge cases -- that is values close to either zero or one -- indicate high predictive certainty. But this is only a heuristic notion of predictive uncertainty [@angelopoulos2021gentle]. Next, we will turn this heuristic notion of uncertainty into a rigorous one using Conformal Prediction.\n\n## 🔥 Conformalizing the Network\n\nSince `clf` is a model, it is also compatible with our package: `ConformalPrediction.jl`. To conformalize our MLP, we therefore only need to call `conformal_model(clf)`. Since the generated instance `conf_model` is also just a model, we can still rely on standard `MLJ.jl` workflows. Below we first wrap it in data and then fit it. Aaaand ... we're done! Let's look at the results in the next section.\n\n::: {#1a8df175 .cell execution_count=8}\n``` {.julia .cell-code}\nusing ConformalPrediction\nconf_model = conformal_model(clf; method=:simple_inductive, coverage=.95)\nmach = machine(conf_model, X, y)\nfit!(mach)\n```\n:::\n\n\n## 📊 Results\n\n\n\n@fig-plots below presents the results. @fig-plots-1 displays highly certain predictions, now defined in the rigorous sense of Conformal Prediction: in each case, the conformal set (just beneath the image) includes only one label. \n\n@fig-plots-2 and @fig-plots-3 display increasingly uncertain predictions of set size two and three, respectively. They demonstrate that CP is well equipped to deal with samples characterized by high aleatoric uncertainty: digits four (4), seven (7) and nine (9) share certain similarities. So do digits five (5) and six (6) as well as three (3) and eight (8). These may be hard to distinguish from each other even after seeing many examples (and even for a human). It is therefore unsurprising to see that these digits often end up together in conformal sets. \n\n::: {#fig-plots .cell layout-nrow='3' execution_count=10}\n\n::: {#fig-plots-1 .cell-output .cell-output-display}\n```{=html}\n\n\n\n \n \n \n\n\n\n \n \n \n\n\n\n \n \n \n\n\n\n\n\n\n \n \n \n\n\n\n\n\n\n \n \n \n\n\n\n\n\n```\n\nRandomly selected prediction sets of size $|C|=1$.\n:::\n\n::: {#fig-plots-2 .cell-output .cell-output-display}\n```{=html}\n\n\n\n \n \n \n\n\n\n \n \n \n\n\n\n \n \n \n\n\n\n\n\n\n \n \n \n\n\n\n\n\n\n \n \n \n\n\n\n\n\n```\n\nRandomly selected prediction sets of size $|C|=2$.\n:::\n\n::: {#fig-plots-3 .cell-output .cell-output-display}\n```{=html}\n\n\n\n \n \n \n\n\n\n \n \n \n\n\n\n \n \n \n\n\n\n\n\n\n \n \n \n\n\n\n\n\n\n \n \n \n\n\n\n\n\n```\n\nRandomly selected prediction sets of size $|C|=3$.\n:::\n\nConformalized predictions from an image classifier.\n:::\n\n\n\n\n## 🧐 Evaluation\n\nTo evaluate the performance of conformal models, specific performance measures can be used to assess if the model is correctly specified and well-calibrated [@angelopoulos2021gentle]. We will look at this in some more detail in another post in the future. For now, just be aware that these measures are already available in `ConformalPrediction.jl` and we will briefly showcase them here.\n\nAs for many other things, `ConformalPrediction.jl` taps into the existing functionality of `MLJ.jl` for model evaluation. In particular, we will see below how we can use the generic `evaluate!` method on our machine. To assess the correctness of our conformal predictor, we can compute the empirical coverage rate using the custom performance measure `emp_coverage`. With respect to model calibration we will look at the model's conditional coverage. For adaptive, well-calibrated conformal models, conditional coverage is high. One general go-to measure for assessing conditional coverage is size-stratified coverage. The custom measure for this purpose is just called `size_stratified_coverage`, aliased by `ssc`. \n\nThe code below implements the model evaluation using cross-validation. The Simple Inductive Classifier that we used above is not adaptive and hence the attained conditional coverage is low compared to the overall empirical coverage, which is close to $0.95$, so in line with the desired coverage rate specified above.\n\n::: {#1631cd46 .cell execution_count=12}\n``` {.julia .cell-code}\n_eval = evaluate!(\n mach,\n resampling=CV(),\n operation=predict,\n measure=[emp_coverage, ssc]\n)\ndisplay(_eval)\nprintln(\"Empirical coverage: $(round(_eval.measurement[1], digits=3))\")\nprintln(\"SSC: $(round(_eval.measurement[2], digits=3))\")\n```\n\n::: {.cell-output .cell-output-display}\n\n::: {.ansi-escaped-output}\n```{=html}\n
    PerformanceEvaluation object with these fields:\n  measure, operation, measurement, per_fold,\n  per_observation, fitted_params_per_fold,\n  report_per_fold, train_test_rows\nExtract:\n┌──────────────────────────────────────────────┬───────────┬─────────────┬──────\n│ measure                                      │ operation │ measurement │ 1.9 ⋯\n├──────────────────────────────────────────────┼───────────┼─────────────┼──────\n│ ConformalPrediction.emp_coverage             │ predict   │ 0.954       │ 0.0 ⋯\n│ ConformalPrediction.size_stratified_coverage │ predict   │ 0.661       │ 0.3 ⋯\n└──────────────────────────────────────────────┴───────────┴─────────────┴──────\n                                                               2 columns omitted\n
    \n```\n:::\n\n:::\n\n::: {.cell-output .cell-output-stdout}\n```\nEmpirical coverage: 0.954\nSSC: 0.661\n```\n:::\n:::\n\n\n\n\nWe can attain higher adaptivity (SSC) when using adaptive prediction sets:\n\n::: {#2c12655e .cell execution_count=14}\n``` {.julia .cell-code}\nconf_model = conformal_model(clf; method=:adaptive_inductive, coverage=.95)\nmach = machine(conf_model, X, y)\nfit!(mach)\n_eval = evaluate!(\n mach,\n resampling=CV(),\n operation=predict,\n measure=[emp_coverage, ssc]\n)\nresults[:adaptive_inductive] = mach\ndisplay(_eval)\nprintln(\"Empirical coverage: $(round(_eval.measurement[1], digits=3))\")\nprintln(\"SSC: $(round(_eval.measurement[2], digits=3))\")\n```\n\n::: {.cell-output .cell-output-display}\n\n::: {.ansi-escaped-output}\n```{=html}\n
    PerformanceEvaluation object with these fields:\n  measure, operation, measurement, per_fold,\n  per_observation, fitted_params_per_fold,\n  report_per_fold, train_test_rows\nExtract:\n┌──────────────────────────────────────────────┬───────────┬─────────────┬──────\n│ measure                                      │ operation │ measurement │ 1.9 ⋯\n├──────────────────────────────────────────────┼───────────┼─────────────┼──────\n│ ConformalPrediction.emp_coverage             │ predict   │ 0.995       │ 0.0 ⋯\n│ ConformalPrediction.size_stratified_coverage │ predict   │ 0.981       │ 0.0 ⋯\n└──────────────────────────────────────────────┴───────────┴─────────────┴──────\n                                                               2 columns omitted\n
    \n```\n:::\n\n:::\n\n::: {.cell-output .cell-output-stdout}\n```\nEmpirical coverage: 0.995\nSSC: 0.981\n```\n:::\n:::\n\n\nWe can also have a look at the resulting set size for both approaches using a custom `Plots.jl` recipe (fig-setsize). In line with the above, the spread is wider for the adaptive approach, which reflects that \"the procedure is effectively distinguishing between easy and hard inputs\" [@angelopoulos2021gentle].\n\n::: {#cell-fig-setsize .cell execution_count=15}\n``` {.julia .cell-code}\nplt_list = []\nfor (_mod, mach) in results\n push!(plt_list, bar(mach.model, mach.fitresult, X; title=String(_mod)))\nend\nplot(plt_list..., size=(800,300))\nplot(plt_list..., size=(800,300),bg_colour=:transparent)\n```\n\n::: {#fig-setsize .cell-output .cell-output-display execution_count=16}\n```{=html}\n\n\n\n \n \n \n\n\n \n \n \n\n\n \n \n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n \n \n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n```\n\nDistribution of set sizes for both approaches.\n:::\n:::\n\n\n## 🔁 Recap\n\nIn this short guide, we have seen how easy it is to conformalize a deep learning image classifier in Julia using `ConformalPrediction.jl`. Almost any deep neural network trained in `Flux.jl` is compatible with `MLJ.jl` and can therefore be conformalized in just a few lines of code. This makes it remarkably easy to move uncertainty heuristics to rigorous predictive uncertainty estimates. We have also seen a sneak peek at the performance evaluation of conformal predictors. Stay tuned for more!\n\n## 🎓 References\n\n", + "engine": "julia", + "markdown": "---\ntitle: How to Conformalize a Deep Image Classifier\nsubtitle: Conformal Prediction in Julia --- Part 2\ndate: '2022-12-05'\ncategories:\n - conformal prediction\n - uncertainty\n - Julia\ndescription: >-\n A guide demonstrating how to use [`ConformalPrediction.jl`](https://github.com/juliatrustworthyai/ConformalPrediction.jl) to conformalize a deep image classifier in a few lines of code.\nimage: www/intro.gif\nengine: julia\njulia: \n exeflags: [\"--project=./\"]\n---\n\n\n\n\n\n\n
    \n
    \n \n
    Conformalized prediction sets for a
    simple Deep Image Classifier.
    \n
    \n
    \n\nDeep Learning is popular and --- for some tasks like image classification --- remarkably powerful. But it is also well-known that Deep Neural Networks (DNN) can be unstable [@goodfellow2014explaining] and poorly calibrated. Conformal Prediction can be used to mitigate these pitfalls. \n\nIn the [first part](../conformal-prediction/index.qmd) of this series of posts on Conformal Prediction, we looked at the basic underlying methodology and how CP can be implemented in Julia using [`ConformalPrediction.jl`](https://github.com/juliatrustworthyai/ConformalPrediction.jl). This second part of the series is a more goal-oriented how-to guide: it demonstrates how you can conformalize a deep learning image classifier built in `Flux.jl` in just a few lines of code. \n\nSince this is meant to be more of a hands-on article, we will avoid diving too deeply into methodological concepts. If you need more colour on this, be sure to check out the [first article](../conformal-prediction/index.qmd) on this topic and also @angelopoulos2021gentle. For a more formal treatment of Conformal Prediction see also @angelopoulos2022uncertainty.\n\n## 🎯 The Task at Hand \n\nThe task at hand is to predict the labels of handwritten images of digits using the famous MNIST dataset [@lecun1998mnist]. Importing this popular machine learning dataset in Julia is made remarkably easy through `MLDatasets.jl`:\n\n\n\n::: {#4 .cell execution_count=1}\n``` {.julia .cell-code}\nusing MLDatasets\nN = 1000\nXraw, yraw = MNIST(split=:train)[:]\nXraw = Xraw[:,:,1:N]\nyraw = yraw[1:N]\n```\n:::\n\n\n\n\n\n@fig-samples below shows a few random samples from the training data:\n\n\n\n::: {#cell-fig-samples .cell execution_count=1}\n``` {.julia .cell-code}\nusing MLJ\nusing Images\nX = map(x -> convert2image(MNIST, x), eachslice(Xraw, dims=3))\ny = coerce(yraw, Multiclass)\n\nn_samples = 10\nmosaic(rand(X, n_samples)..., ncol=n_samples)\n```\n\n::: {#fig-samples .cell-output .cell-output-display execution_count=1}\n```{=html}\n\n```\n\nRandom samples from the MNIST dataset.\n:::\n:::\n\n\n\n\n\n## 🚧 Building the Network\n\nTo model the mapping from image inputs to labels will rely on a simple Multi-Layer Perceptron (MLP). A great Julia library for Deep Learning is `Flux.jl`. But wait ... doesn't `ConformalPrediction.jl` work with models trained in `MLJ.jl`? That's right, but fortunately there exists a `Flux.jl` interface to `MLJ.jl`, namely `MLJFlux.jl`. The interface is still in its early stages, but already very powerful and easily accessible for anyone (like myself) who is used to building Neural Networks in `Flux.jl`. \n\nIn `Flux.jl`, you could build an MLP for this task as follows,\n\n\n\n::: {#8 .cell execution_count=1}\n``` {.julia .cell-code}\nusing Flux\n\nmlp = Chain(\n Flux.flatten,\n Dense(prod((28,28)), 32, relu),\n Dense(32, 10)\n)\n```\n:::\n\n\n\n\n\nwhere `(28,28)` is just the input dimension (28x28 pixel images). Since we have ten digits, our output dimension is ten.^[For a full tutorial on how to build an MNIST image classifier relying solely on `Flux.jl`, check out this [tutorial](https://fluxml.ai/Flux.jl/stable/tutorials/2021-01-26-mlp/).]\n\nWe can do the exact same thing in `MLJFlux.jl` as follows,\n\n\n\n::: {#10 .cell execution_count=1}\n``` {.julia .cell-code}\nusing MLJFlux\n\nbuilder = MLJFlux.@builder Chain(\n Flux.flatten,\n Dense(prod(n_in), 32, relu),\n Dense(32, n_out)\n)\n```\n:::\n\n\n\n\n\nwhere here we rely on the `@builder` macro to make the transition from `Flux.jl` to `MLJ.jl` as seamless as possible. Finally, `MLJFlux.jl` already comes with a number of helper functions to define plain-vanilla networks. In this case, we will use the `ImageClassifier` with our custom builder and cross-entropy loss:\n\n\n\n::: {#12 .cell execution_count=1}\n``` {.julia .cell-code}\nImageClassifier = @load ImageClassifier\nclf = ImageClassifier(\n builder=builder,\n epochs=10,\n loss=Flux.crossentropy\n)\n```\n:::\n\n\n\n\n\nThe generated instance `clf` is a model (in the `MLJ.jl` sense) so from this point on we can rely on standard `MLJ.jl` workflows. For example, we can wrap our model in data to create a machine and then evaluate it on a holdout set as follows:\n\n\n\n::: {#14 .cell execution_count=1}\n``` {.julia .cell-code}\nmach = machine(clf, X, y)\n\nevaluate!(\n mach,\n resampling=Holdout(rng=123, fraction_train=0.8),\n operation=predict_mode,\n measure=[accuracy]\n)\n```\n:::\n\n\n\n\n\nThe accuracy of our very simple model is not amazing, but good enough for the purpose of this tutorial. For each image, our MLP returns a softmax output for each possible digit: 0,1,2,3,...,9. Since each individual softmax output is valued between zero and one, $y_k\\in(0,1)$, this is commonly interpreted as a probability: $y_k \\coloneqq p(y=k|X)$. Edge cases -- that is values close to either zero or one -- indicate high predictive certainty. But this is only a heuristic notion of predictive uncertainty [@angelopoulos2021gentle]. Next, we will turn this heuristic notion of uncertainty into a rigorous one using Conformal Prediction.\n\n## 🔥 Conformalizing the Network\n\nSince `clf` is a model, it is also compatible with our package: `ConformalPrediction.jl`. To conformalize our MLP, we therefore only need to call `conformal_model(clf)`. Since the generated instance `conf_model` is also just a model, we can still rely on standard `MLJ.jl` workflows. Below we first wrap it in data and then fit it. Aaaand ... we're done! Let's look at the results in the next section.\n\n\n\n::: {#16 .cell execution_count=1}\n``` {.julia .cell-code}\nusing ConformalPrediction\nconf_model = conformal_model(clf; method=:simple_inductive, coverage=.95)\nmach = machine(conf_model, X, y)\nfit!(mach)\n```\n:::\n\n\n\n\n\n## 📊 Results\n\n\n\n\n\n\n\n\n@fig-plots below presents the results. @fig-plots-1 displays highly certain predictions, now defined in the rigorous sense of Conformal Prediction: in each case, the conformal set (just beneath the image) includes only one label. \n\n@fig-plots-2 and @fig-plots-3 display increasingly uncertain predictions of set size two and three, respectively. They demonstrate that CP is well equipped to deal with samples characterized by high aleatoric uncertainty: digits four (4), seven (7) and nine (9) share certain similarities. So do digits five (5) and six (6) as well as three (3) and eight (8). These may be hard to distinguish from each other even after seeing many examples (and even for a human). It is therefore unsurprising to see that these digits often end up together in conformal sets. \n\n\n\n::: {#fig-plots .cell layout-nrow='3' execution_count=1}\n\n::: {#fig-plots-1 .cell-output .cell-output-display}\n```{=html}\n\n\n\n \n \n \n\n\n\n \n \n \n\n\n\n \n \n \n\n\n\n\n\n\n \n \n \n\n\n\n\n\n\n \n \n \n\n\n\n\n\n```\n\nRandomly selected prediction sets of size $|C|=1$.\n:::\n\n::: {#fig-plots-2 .cell-output .cell-output-display}\n```{=html}\n\n\n\n \n \n \n\n\n\n \n \n \n\n\n\n \n \n \n\n\n\n\n\n\n \n \n \n\n\n\n\n\n\n \n \n \n\n\n\n\n\n```\n\nRandomly selected prediction sets of size $|C|=2$.\n:::\n\n::: {#fig-plots-3 .cell-output .cell-output-display}\n```{=html}\n\n\n\n \n \n \n\n\n\n \n \n \n\n\n\n \n \n \n\n\n\n\n\n\n \n \n \n\n\n\n\n\n\n \n \n \n\n\n\n\n\n```\n\nRandomly selected prediction sets of size $|C|=3$.\n:::\n\nConformalized predictions from an image classifier.\n:::\n\n\n\n\n\n\n\n\n## 🧐 Evaluation\n\nTo evaluate the performance of conformal models, specific performance measures can be used to assess if the model is correctly specified and well-calibrated [@angelopoulos2021gentle]. We will look at this in some more detail in another post in the future. For now, just be aware that these measures are already available in `ConformalPrediction.jl` and we will briefly showcase them here.\n\nAs for many other things, `ConformalPrediction.jl` taps into the existing functionality of `MLJ.jl` for model evaluation. In particular, we will see below how we can use the generic `evaluate!` method on our machine. To assess the correctness of our conformal predictor, we can compute the empirical coverage rate using the custom performance measure `emp_coverage`. With respect to model calibration we will look at the model's conditional coverage. For adaptive, well-calibrated conformal models, conditional coverage is high. One general go-to measure for assessing conditional coverage is size-stratified coverage. The custom measure for this purpose is just called `size_stratified_coverage`, aliased by `ssc`. \n\nThe code below implements the model evaluation using cross-validation. The Simple Inductive Classifier that we used above is not adaptive and hence the attained conditional coverage is low compared to the overall empirical coverage, which is close to $0.95$, so in line with the desired coverage rate specified above.\n\n\n\n::: {#24 .cell execution_count=1}\n``` {.julia .cell-code}\n_eval = evaluate!(\n mach,\n resampling=CV(),\n operation=predict,\n measure=[emp_coverage, ssc]\n)\ndisplay(_eval)\nprintln(\"Empirical coverage: $(round(_eval.measurement[1], digits=3))\")\nprintln(\"SSC: $(round(_eval.measurement[2], digits=3))\")\n```\n\n::: {.cell-output .cell-output-stdout}\n```\n\rEvaluating over 6 folds: 33%[========> ] ETA: 0:00:05\rEvaluating over 6 folds: 50%[============> ] ETA: 0:00:03\rEvaluating over 6 folds: 67%[================> ] ETA: 0:00:02\rEvaluating over 6 folds: 83%[====================> ] ETA: 0:00:01\rEvaluating over 6 folds: 100%[=========================] Time: 0:00:05\nEmpirical coverage: 0.959\nSSC: 0.791\n```\n:::\n\n::: {.cell-output .cell-output-display}\n```\nPerformanceEvaluation object with these fields:\n measure, operation, measurement, per_fold,\n per_observation, fitted_params_per_fold,\n report_per_fold, train_test_rows\nExtract:\n┌──────────────────────────────────────────────┬───────────┬─────────────┬──────\n│ measure │ operation │ measurement │ 1.9 ⋯\n├──────────────────────────────────────────────┼───────────┼─────────────┼──────\n│ ConformalPrediction.emp_coverage │ predict │ 0.959 │ 0.0 ⋯\n│ ConformalPrediction.size_stratified_coverage │ predict │ 0.791 │ 0.1 ⋯\n└──────────────────────────────────────────────┴───────────┴─────────────┴──────\n 2 columns omitted\n```\n:::\n:::\n\n\n\n\n\n\n\n\nWe can attain higher adaptivity (SSC) when using adaptive prediction sets:\n\n\n\n::: {#28 .cell execution_count=1}\n``` {.julia .cell-code}\nconf_model = conformal_model(clf; method=:adaptive_inductive, coverage=.95)\nmach = machine(conf_model, X, y)\nfit!(mach)\n_eval = evaluate!(\n mach,\n resampling=CV(),\n operation=predict,\n measure=[emp_coverage, ssc]\n)\nresults[:adaptive_inductive] = mach\ndisplay(_eval)\nprintln(\"Empirical coverage: $(round(_eval.measurement[1], digits=3))\")\nprintln(\"SSC: $(round(_eval.measurement[2], digits=3))\")\n```\n\n::: {.cell-output .cell-output-stdout}\n```\n[ Info: Training machine(AdaptiveInductiveClassifier(model = ImageClassifier(builder = GenericBuilder(apply = #3), …), …), …).\n\rOptimising neural net: 18%[====> ] ETA: 0:00:00\rOptimising neural net: 27%[======> ] ETA: 0:00:01\rOptimising neural net: 36%[=========> ] ETA: 0:00:01\rOptimising neural net: 45%[===========> ] ETA: 0:00:00\rOptimising neural net: 55%[=============> ] ETA: 0:00:00\rOptimising neural net: 64%[===============> ] ETA: 0:00:00\rOptimising neural net: 73%[==================> ] ETA: 0:00:00\rOptimising neural net: 82%[====================> ] ETA: 0:00:00\rOptimising neural net: 91%[======================> ] ETA: 0:00:00\rOptimising neural net: 100%[=========================] Time: 0:00:00\n\rEvaluating over 6 folds: 33%[========> ] ETA: 0:00:03\rEvaluating over 6 folds: 50%[============> ] ETA: 0:00:02\rEvaluating over 6 folds: 67%[================> ] ETA: 0:00:02\rEvaluating over 6 folds: 83%[====================> ] ETA: 0:00:01\rEvaluating over 6 folds: 100%[=========================] Time: 0:00:05\nEmpirical coverage: 0.996\nSSC: 0.983\n```\n:::\n\n::: {.cell-output .cell-output-display}\n```\nPerformanceEvaluation object with these fields:\n measure, operation, measurement, per_fold,\n per_observation, fitted_params_per_fold,\n report_per_fold, train_test_rows\nExtract:\n┌──────────────────────────────────────────────┬───────────┬─────────────┬──────\n│ measure │ operation │ measurement │ 1.9 ⋯\n├──────────────────────────────────────────────┼───────────┼─────────────┼──────\n│ ConformalPrediction.emp_coverage │ predict │ 0.996 │ 0.0 ⋯\n│ ConformalPrediction.size_stratified_coverage │ predict │ 0.983 │ 0.0 ⋯\n└──────────────────────────────────────────────┴───────────┴─────────────┴──────\n 2 columns omitted\n```\n:::\n:::\n\n\n\n\n\nWe can also have a look at the resulting set size for both approaches using a custom `Plots.jl` recipe (fig-setsize). In line with the above, the spread is wider for the adaptive approach, which reflects that \"the procedure is effectively distinguishing between easy and hard inputs\" [@angelopoulos2021gentle].\n\n\n\n::: {#cell-fig-setsize .cell execution_count=1}\n``` {.julia .cell-code}\nplt_list = []\nfor (_mod, mach) in results\n push!(plt_list, bar(mach.model, mach.fitresult, X; title=String(_mod)))\nend\nplot(plt_list..., size=(800,300))\nplot(plt_list..., size=(800,300),bg_colour=:transparent)\n```\n\n::: {#fig-setsize .cell-output .cell-output-display execution_count=1}\n```{=html}\n\n\n\n \n \n \n\n\n \n \n \n\n\n \n \n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n \n \n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n```\n\nDistribution of set sizes for both approaches.\n:::\n:::\n\n\n\n\n\n## 🔁 Recap\n\nIn this short guide, we have seen how easy it is to conformalize a deep learning image classifier in Julia using `ConformalPrediction.jl`. Almost any deep neural network trained in `Flux.jl` is compatible with `MLJ.jl` and can therefore be conformalized in just a few lines of code. This makes it remarkably easy to move uncertainty heuristics to rigorous predictive uncertainty estimates. We have also seen a sneak peek at the performance evaluation of conformal predictors. Stay tuned for more!\n\n## 🎓 References\n\n", "supporting": [ - "index_files" + "index_files/figure-html" ], "filters": [], "includes": { diff --git a/profile/_quarto.yml b/profile/_quarto.yml index 2a0a6b9..576f59e 100644 --- a/profile/_quarto.yml +++ b/profile/_quarto.yml @@ -42,5 +42,7 @@ format: css: styles.css toc: true +bibliography: bib.bib + diff --git a/profile/bib.bib b/profile/bib.bib index 29127ef..f7c3fe9 100644 --- a/profile/bib.bib +++ b/profile/bib.bib @@ -1,37 +1,37 @@ -@Article{ges2003, -author = {Chickering, David Maxwell}, -title = {Optimal structure identification with greedy search}, -year = {2003}, -issue_date = {3/1/2003}, -publisher = {JMLR.org}, -volume = {3}, -number = {null}, -issn = {1532-4435}, -url = {https://doi.org/10.1162/153244303321897717}, -doi = {10.1162/153244303321897717}, -abstract = {In this paper we prove the so-called "Meek Conjecture". In particular, we show that if a DAG H is an independence map of another DAG G, then there exists a finite sequence of edge additions and covered edge reversals in G such that (1) after each edge modification H remains an independence map of G and (2) after all modifications G =H. As shown by Meek (1997), this result has an important consequence for Bayesian approaches to learning Bayesian networks from data: in the limit of large sample size, there exists a two-phase greedy search algorithm that---when applied to a particular sparsely-connected search space---provably identifies a perfect map of the generative distribution if that perfect map is a DAG. We provide a new implementation of the search space, using equivalence classes as states, for which all operators used in the greedy search can be scored efficiently using local functions of the nodes in the domain. Finally, using both synthetic and real-world datasets, we demonstrate that the two-phase greedy approach leads to good solutions when learning with finite sample sizes.}, -journal = {J. Mach. Learn. Res.}, -month = {mar}, -pages = {507–554}, -numpages = {48} -} - -@InProceedings{karimi2021, -author = {Karimi, Amir-Hossein and Sch\"{o}lkopf, Bernhard and Valera, Isabel}, -title = {Algorithmic Recourse: from Counterfactual Explanations to Interventions}, -year = {2021}, -isbn = {9781450383097}, -publisher = {Association for Computing Machinery}, -address = {New York, NY, USA}, -url = {https://doi.org/10.1145/3442188.3445899}, -doi = {10.1145/3442188.3445899}, -abstract = {As machine learning is increasingly used to inform consequential decision-making (e.g., pre-trial bail and loan approval), it becomes important to explain how the system arrived at its decision, and also suggest actions to achieve a favorable decision. Counterfactual explanations -"how the world would have (had) to be different for a desirable outcome to occur"- aim to satisfy these criteria. Existing works have primarily focused on designing algorithms to obtain counterfactual explanations for a wide range of settings. However, it has largely been overlooked that ultimately, one of the main objectives is to allow people to act rather than just understand. In layman's terms, counterfactual explanations inform an individual where they need to get to, but not how to get there. In this work, we rely on causal reasoning to caution against the use of counterfactual explanations as a recommendable set of actions for recourse. Instead, we propose a shift of paradigm from recourse via nearest counterfactual explanations to recourse through minimal interventions, shifting the focus from explanations to interventions.}, -booktitle = {Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency}, -pages = {353–362}, -numpages = {10}, -keywords = {algorithmic recourse, causal inference, consequential recommendations, contrastive explanations, counterfactual explanations, explainable artificial intelligence, minimal interventions}, -location = {Virtual Event, Canada}, -series = {FAccT '21} +@Article{chickering2003optimal, + author = {Chickering, David Maxwell}, + title = {Optimal structure identification with greedy search}, + doi = {10.1162/153244303321897717}, + issn = {1532-4435}, + number = {null}, + pages = {507–554}, + url = {https://doi.org/10.1162/153244303321897717}, + volume = {3}, + abstract = {In this paper we prove the so-called "Meek Conjecture". In particular, we show that if a DAG H is an independence map of another DAG G, then there exists a finite sequence of edge additions and covered edge reversals in G such that (1) after each edge modification H remains an independence map of G and (2) after all modifications G =H. As shown by Meek (1997), this result has an important consequence for Bayesian approaches to learning Bayesian networks from data: in the limit of large sample size, there exists a two-phase greedy search algorithm that---when applied to a particular sparsely-connected search space---provably identifies a perfect map of the generative distribution if that perfect map is a DAG. We provide a new implementation of the search space, using equivalence classes as states, for which all operators used in the greedy search can be scored efficiently using local functions of the nodes in the domain. Finally, using both synthetic and real-world datasets, we demonstrate that the two-phase greedy approach leads to good solutions when learning with finite sample sizes.}, + issue_date = {3/1/2003}, + journal = {J. Mach. Learn. Res.}, + month = {mar}, + numpages = {48}, + publisher = {JMLR.org}, + year = {2003}, +} + +@InProceedings{karimi2021algorithmic, + author = {Karimi, Amir-Hossein and Sch\"{o}lkopf, Bernhard and Valera, Isabel}, + booktitle = {Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency}, + title = {Algorithmic Recourse: from Counterfactual Explanations to Interventions}, + doi = {10.1145/3442188.3445899}, + isbn = {9781450383097}, + location = {Virtual Event, Canada}, + pages = {353–362}, + publisher = {Association for Computing Machinery}, + series = {FAccT '21}, + url = {https://doi.org/10.1145/3442188.3445899}, + abstract = {As machine learning is increasingly used to inform consequential decision-making (e.g., pre-trial bail and loan approval), it becomes important to explain how the system arrived at its decision, and also suggest actions to achieve a favorable decision. Counterfactual explanations -"how the world would have (had) to be different for a desirable outcome to occur"- aim to satisfy these criteria. Existing works have primarily focused on designing algorithms to obtain counterfactual explanations for a wide range of settings. However, it has largely been overlooked that ultimately, one of the main objectives is to allow people to act rather than just understand. In layman's terms, counterfactual explanations inform an individual where they need to get to, but not how to get there. In this work, we rely on causal reasoning to caution against the use of counterfactual explanations as a recommendable set of actions for recourse. Instead, we propose a shift of paradigm from recourse via nearest counterfactual explanations to recourse through minimal interventions, shifting the focus from explanations to interventions.}, + address = {New York, NY, USA}, + keywords = {algorithmic recourse, causal inference, consequential recommendations, contrastive explanations, counterfactual explanations, explainable artificial intelligence, minimal interventions}, + numpages = {10}, + year = {2021}, } @Book{pearl2009book, @@ -1534,16 +1534,6 @@ @Misc{karimi2020survey year = {2021}, } -@InProceedings{karimi2021algorithmic, - author = {Karimi, Amir-Hossein and Sch{\"o}lkopf, Bernhard and Valera, Isabel}, - booktitle = {Proceedings of the 2021 {{ACM Conference}} on {{Fairness}}, {{Accountability}}, and {{Transparency}}}, - title = {Algorithmic Recourse: From Counterfactual Explanations to Interventions}, - pages = {353--362}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - year = {2021}, -} - @InProceedings{kaur2020interpreting, author = {Kaur, Harmanpreet and Nori, Harsha and Jenkins, Samuel and Caruana, Rich and Wallach, Hanna and Wortman Vaughan, Jennifer}, booktitle = {Proceedings of the 2020 {{CHI}} Conference on Human Factors in Computing Systems}, diff --git a/profile/blog/posts/_metadata.yml b/profile/blog/posts/_metadata.yml index 62b7907..a1d1b66 100755 --- a/profile/blog/posts/_metadata.yml +++ b/profile/blog/posts/_metadata.yml @@ -17,8 +17,7 @@ author: comments: utterances: repo: pat-alt/pat-alt.github.io - -bibliography: https://raw.githubusercontent.com/pat-alt/bib/main/bib.bib + citation: true crossref: diff --git a/profile/blog/posts/a-new-tool-for-explainable-ai/index.html b/profile/blog/posts/a-new-tool-for-explainable-ai/index.html deleted file mode 100644 index 3f0039f..0000000 --- a/profile/blog/posts/a-new-tool-for-explainable-ai/index.html +++ /dev/null @@ -1,779 +0,0 @@ - - - - - - - - - - - -A new tool for explainable AI - - - - - - - - - - - - - - - - - - - - - - - -     - - - - - \ No newline at end of file diff --git a/profile/blog/posts/a-new-tool-for-explainable-ai/index.qmd b/profile/blog/posts/a-new-tool-for-explainable-ai/index.qmd index 2b03908..bc729c1 100644 --- a/profile/blog/posts/a-new-tool-for-explainable-ai/index.qmd +++ b/profile/blog/posts/a-new-tool-for-explainable-ai/index.qmd @@ -12,7 +12,6 @@ image: www/intro.gif execute: eval: false echo: true -draft: false --- ```{julia} diff --git a/profile/blog/posts/causal-recourse/Manifest.toml b/profile/blog/posts/causal-recourse/Manifest.toml new file mode 100644 index 0000000..cc05f85 --- /dev/null +++ b/profile/blog/posts/causal-recourse/Manifest.toml @@ -0,0 +1,1654 @@ +# This file is machine-generated - editing it directly is not advised + +julia_version = "1.10.5" +manifest_format = "2.0" +project_hash = "25611679d220fb8d8ed8d4ecc80ba962141010d1" + +[[deps.AbstractTrees]] +git-tree-sha1 = "2d9c9a55f9c93e8887ad391fbae72f8ef55e1177" +uuid = 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"d8fb68d0-12a3-5cfd-a85a-d49703b185fd" +version = "1.4.1+1" diff --git a/profile/blog/posts/causal-recourse/Project.toml b/profile/blog/posts/causal-recourse/Project.toml new file mode 100644 index 0000000..cfc4483 --- /dev/null +++ b/profile/blog/posts/causal-recourse/Project.toml @@ -0,0 +1,5 @@ +[deps] +CausalInference = "8e462317-f959-576b-b3c1-403f26cec956" +GraphRecipes = "bd48cda9-67a9-57be-86fa-5b3c104eda73" +Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" +Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" diff --git a/profile/blog/posts/causal-recourse/bib.bib b/profile/blog/posts/causal-recourse/bib.bib deleted file mode 100644 index 29127ef..0000000 --- a/profile/blog/posts/causal-recourse/bib.bib +++ /dev/null @@ -1,3464 +0,0 @@ -@Article{ges2003, -author = {Chickering, David Maxwell}, -title = {Optimal structure identification with greedy search}, -year = {2003}, -issue_date = {3/1/2003}, -publisher = {JMLR.org}, -volume = {3}, -number = {null}, -issn = {1532-4435}, -url = {https://doi.org/10.1162/153244303321897717}, -doi = {10.1162/153244303321897717}, -abstract = {In this paper we prove the so-called "Meek Conjecture". In particular, we show that if a DAG H is an independence map of another DAG G, then there exists a finite sequence of edge additions and covered edge reversals in G such that (1) after each edge modification H remains an independence map of G and (2) after all modifications G =H. As shown by Meek (1997), this result has an important consequence for Bayesian approaches to learning Bayesian networks from data: in the limit of large sample size, there exists a two-phase greedy search algorithm that---when applied to a particular sparsely-connected search space---provably identifies a perfect map of the generative distribution if that perfect map is a DAG. We provide a new implementation of the search space, using equivalence classes as states, for which all operators used in the greedy search can be scored efficiently using local functions of the nodes in the domain. Finally, using both synthetic and real-world datasets, we demonstrate that the two-phase greedy approach leads to good solutions when learning with finite sample sizes.}, -journal = {J. Mach. Learn. Res.}, -month = {mar}, -pages = {507–554}, -numpages = {48} -} - -@InProceedings{karimi2021, -author = {Karimi, Amir-Hossein and Sch\"{o}lkopf, Bernhard and Valera, Isabel}, -title = {Algorithmic Recourse: from Counterfactual Explanations to Interventions}, -year = {2021}, -isbn = {9781450383097}, -publisher = {Association for Computing Machinery}, -address = {New York, NY, USA}, -url = {https://doi.org/10.1145/3442188.3445899}, -doi = {10.1145/3442188.3445899}, -abstract = {As machine learning is increasingly used to inform consequential decision-making (e.g., pre-trial bail and loan approval), it becomes important to explain how the system arrived at its decision, and also suggest actions to achieve a favorable decision. Counterfactual explanations -"how the world would have (had) to be different for a desirable outcome to occur"- aim to satisfy these criteria. Existing works have primarily focused on designing algorithms to obtain counterfactual explanations for a wide range of settings. However, it has largely been overlooked that ultimately, one of the main objectives is to allow people to act rather than just understand. In layman's terms, counterfactual explanations inform an individual where they need to get to, but not how to get there. In this work, we rely on causal reasoning to caution against the use of counterfactual explanations as a recommendable set of actions for recourse. Instead, we propose a shift of paradigm from recourse via nearest counterfactual explanations to recourse through minimal interventions, shifting the focus from explanations to interventions.}, -booktitle = {Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency}, -pages = {353–362}, -numpages = {10}, -keywords = {algorithmic recourse, causal inference, consequential recommendations, contrastive explanations, counterfactual explanations, explainable artificial intelligence, minimal interventions}, -location = {Virtual Event, Canada}, -series = {FAccT '21} -} - -@Book{pearl2009book, -author = {Pearl, Judea}, -title = {Causality: Models, Reasoning and Inference}, -year = {2009}, -isbn = {052189560X}, -publisher = {Cambridge University Press}, -address = {USA}, -edition = {2nd}, -abstract = {Written by one of the preeminent researchers in the field, this book provides a comprehensive exposition of modern analysis of causation. It shows how causality has grown from a nebulous concept into a mathematical theory with significant applications in the fields of statistics, artificial intelligence, economics, philosophy, cognitive science, and the health and social sciences. Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections and statistical associations. The book will open the way for including causal analysis in the standard curricula of statistics, artificial intelligence, business, epidemiology, social sciences, and economics. Students in these fields will find natural models, simple inferential procedures, and precise mathematical definitions of causal concepts that traditional texts have evaded or made unduly complicated. The first edition of Causality has led to a paradigmatic change in the way that causality is treated in statistics, philosophy, computer science, social science, and economics. Cited in more than 3,000 scientific publications, it continues to liberate scientists from the traditional molds of statistical thinking. In this revised edition, Judea Pearl elucidates thorny issues, answers readers' questions, and offers a panoramic view of recent advances in this field of research. Causality will be of interests to students and professionals in a wide variety of fields. Anyone who wishes to elucidate meaningful relationships from data, predict effects of actions and policies, assess explanations of reported events, or form theories of causal understanding and causal speech will find this book stimulating and invaluable.} -} - -@TechReport{xu2022conformal, - author = {Xu, Chen and Xie, Yao}, - date = {2022-06}, - institution = {arXiv}, - title = {Conformal prediction set for time-series}, - doi = {10.48550/arXiv.2206.07851}, - note = {arXiv:2206.07851 [cs, stat] type: article}, - url = {http://arxiv.org/abs/2206.07851}, - urldate = {2023-07-22}, - abstract = {When building either prediction intervals for regression (with real-valued response) or prediction sets for classification (with categorical responses), uncertainty quantification is essential to studying complex machine learning methods. In this paper, we develop Ensemble Regularized Adaptive Prediction Set (ERAPS) to construct prediction sets for time-series (with categorical responses), based on the prior work of [Xu and Xie, 2021]. In particular, we allow unknown dependencies to exist within features and responses that arrive in sequence. Method-wise, ERAPS is a distribution-free and ensemble-based framework that is applicable for arbitrary classifiers. Theoretically, we bound the coverage gap without assuming data exchangeability and show asymptotic set convergence. Empirically, we demonstrate valid marginal and conditional coverage by ERAPS, which also tends to yield smaller prediction sets than competing methods.}, - annotation = {Comment: Strongly accepted by the Workshop on Distribution-Free Uncertainty Quantification at ICML 2022}, - file = {arXiv Fulltext PDF:https\://arxiv.org/pdf/2206.07851.pdf:application/pdf}, - keywords = {Statistics - Machine Learning, Computer Science - Machine Learning, Statistics - Methodology}, -} - -@Article{kingma2014adam, - author = {Kingma, Diederik P and Ba, Jimmy}, - title = {Adam: A method for stochastic optimization}, - journal = {arXiv preprint arXiv:1412.6980}, - year = {2014}, -} - -@Misc{xiao2017fashion, - author = {Han Xiao and Kashif Rasul and Roland Vollgraf}, - title = {Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms}, - eprint = {1708.07747}, - archiveprefix = {arXiv}, - primaryclass = {cs.LG}, - year = {2017}, -} - -@Online{mw2023fidelity, - author = {Merriam-Webster}, - title = {"Fidelity"}, - url = {https://www.merriam-webster.com/dictionary/fidelity}, - language = {en}, - organization = {Merriam-Webster}, - urldate = {2023-03-23}, - abstract = {the quality or state of being faithful; accuracy in details : exactness; the degree to which an electronic device (such as a record player, radio, or television) accurately reproduces its effect (such as sound or picture)… See the full definition}, -} - -@InProceedings{altmeyer2023endogenous, - author = {Altmeyer, Patrick and Angela, Giovan and Buszydlik, Aleksander and Dobiczek, Karol and van Deursen, Arie and Liem, Cynthia CS}, - booktitle = {2023 IEEE Conference on Secure and Trustworthy Machine Learning (SaTML)}, - title = {Endogenous Macrodynamics in Algorithmic Recourse}, - organization = {IEEE}, - pages = {418--431}, - year = {2023}, -} - -%% This BibTeX bibliography file was created using BibDesk. -%% https://bibdesk.sourceforge.io/ - -%% Created for Patrick Altmeyer at 2022-12-13 12:58:22 +0100 - - -%% Saved with string encoding Unicode (UTF-8) - - - -@Article{abadie2002instrumental, - author = {Abadie, Alberto and Angrist, Joshua and Imbens, Guido}, - title = {Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings}, - doi = {10.2139/ssrn.195733}, - number = {1}, - pages = {91--117}, - volume = {70}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {Econometrica : journal of the Econometric Society}, - shortjournal = {Econometrica}, - year = {2002}, -} - -@Article{abadie2003economic, - author = {Abadie, Alberto and Gardeazabal, Javier}, - title = {The Economic Costs of Conflict: {{A}} Case Study of the {{Basque Country}}}, - number = {1}, - pages = {113--132}, - volume = {93}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {American economic review}, - year = {2003}, -} - -@InProceedings{ackerman2021machine, - author = {Ackerman, Samuel and Dube, Parijat and Farchi, Eitan and Raz, Orna and Zalmanovici, Marcel}, - booktitle = {2021 {{IEEE}}/{{ACM Third International Workshop}} on {{Deep Learning}} for {{Testing}} and {{Testing}} for {{Deep Learning}} ({{DeepTest}})}, - title = {Machine {{Learning Model Drift Detection Via Weak Data Slices}}}, - doi = {10.1109/deeptest52559.2021.00007}, - pages = {1--8}, - publisher = {{IEEE}}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - year = {2021}, -} - -@Article{allen2017referencedependent, - author = {Allen, Eric J and Dechow, Patricia M and Pope, Devin G and Wu, George}, - title = {Reference-Dependent Preferences: {{Evidence}} from Marathon Runners}, - doi = {10.3386/w20343}, - number = {6}, - pages = {1657--1672}, - volume = {63}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {Management Science}, - year = {2017}, -} - -@Article{altmeyer2018option, - author = {Altmeyer, Patrick and Grapendal, Jacob Daniel and Pravosud, Makar and Quintana, Gand Derry}, - title = {Option Pricing in the {{Heston}} Stochastic Volatility Model: An Empirical Evaluation}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - year = {2018}, -} - -@Article{altmeyer2021deep, - author = {Altmeyer, Patrick and Agusti, Marc and Vidal-Quadras Costa, Ignacio}, - title = {Deep {{Vector Autoregression}} for {{Macroeconomic Data}}}, - url = {https://thevoice.bse.eu/wp-content/uploads/2021/07/ds21-project-agusti-et-al.pdf}, - bdsk-url-1 = {https://thevoice.bse.eu/wp-content/uploads/2021/07/ds21-project-agusti-et-al.pdf}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - year = {2021}, -} - -@Book{altmeyer2021deepvars, - author = {Altmeyer, Patrick}, - title = {Deepvars: {{Deep Vector Autoregession}}}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - year = {2021}, -} - -@Misc{altmeyer2022counterfactualexplanations, - author = {Altmeyer, Patrick}, - title = {{{CounterfactualExplanations}}.Jl - a {{Julia}} Package for {{Counterfactual Explanations}} and {{Algorithmic Recourse}}}, - url = {https://github.com/pat-alt/CounterfactualExplanations.jl}, - bdsk-url-1 = {https://github.com/pat-alt/CounterfactualExplanations.jl}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - year = {2022}, -} - -@Software{altmeyerCounterfactualExplanationsJlJulia2022, - author = {Altmeyer, Patrick}, - title = {{{CounterfactualExplanations}}.Jl - a {{Julia}} Package for {{Counterfactual Explanations}} and {{Algorithmic Recourse}}}, - url = {https://github.com/pat-alt/CounterfactualExplanations.jl}, - version = {0.1.2}, - bdsk-url-1 = {https://github.com/pat-alt/CounterfactualExplanations.jl}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - year = {2022}, -} - -@Misc{angelopoulos2021gentle, - author = {Anastasios N. Angelopoulos and Stephen Bates}, - title = {A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification}, - eprint = {2107.07511}, - archiveprefix = {arXiv}, - primaryclass = {cs.LG}, - year = {2022}, -} - -@Misc{angelopoulos2022uncertainty, - author = {Angelopoulos, Anastasios and Bates, Stephen and Malik, Jitendra and Jordan, Michael I.}, - title = {Uncertainty {{Sets}} for {{Image Classifiers}} Using {{Conformal Prediction}}}, - eprint = {2009.14193}, - eprinttype = {arxiv}, - abstract = {Convolutional image classifiers can achieve high predictive accuracy, but quantifying their uncertainty remains an unresolved challenge, hindering their deployment in consequential settings. Existing uncertainty quantification techniques, such as Platt scaling, attempt to calibrate the network's probability estimates, but they do not have formal guarantees. We present an algorithm that modifies any classifier to output a predictive set containing the true label with a user-specified probability, such as 90\%. The algorithm is simple and fast like Platt scaling, but provides a formal finite-sample coverage guarantee for every model and dataset. Our method modifies an existing conformal prediction algorithm to give more stable predictive sets by regularizing the small scores of unlikely classes after Platt scaling. In experiments on both Imagenet and Imagenet-V2 with ResNet-152 and other classifiers, our scheme outperforms existing approaches, achieving coverage with sets that are often factors of 5 to 10 smaller than a stand-alone Platt scaling baseline.}, - archiveprefix = {arXiv}, - bdsk-url-1 = {http://arxiv.org/abs/2009.14193}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - file = {:/Users/FA31DU/Zotero/storage/5BYIRBR2/Angelopoulos et al. - 2022 - Uncertainty Sets for Image Classifiers using Confo.pdf:;:/Users/FA31DU/Zotero/storage/2QJAKFKV/2009.html:}, - keywords = {Computer Science - Computer Vision and Pattern Recognition, Mathematics - Statistics Theory, Statistics - Machine Learning}, - month = sep, - number = {arXiv:2009.14193}, - primaryclass = {cs, math, stat}, - publisher = {{arXiv}}, - year = {2022}, -} - -@Article{angelucci2009indirect, - author = {Angelucci, Manuela and De Giorgi, Giacomo}, - title = {Indirect Effects of an Aid Program: How Do Cash Transfers Affect Ineligibles' Consumption?}, - doi = {10.1257/aer.99.1.486}, - number = {1}, - pages = {486--508}, - volume = {99}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {American economic review}, - year = {2009}, -} - -@Article{angrist1990lifetime, - author = {Angrist, Joshua D}, - title = {Lifetime Earnings and the {{Vietnam}} Era Draft Lottery: Evidence from Social Security Administrative Records}, - pages = {313--336}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {The American Economic Review}, - year = {1990}, -} - -@Unpublished{antoran2020getting, - author = {Antor{\'a}n, Javier and Bhatt, Umang and Adel, Tameem and Weller, Adrian and Hern{\'a}ndez-Lobato, Jos{\'e} Miguel}, - title = {Getting a Clue: {{A}} Method for Explaining Uncertainty Estimates}, - archiveprefix = {arXiv}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - eprint = {2006.06848}, - eprinttype = {arxiv}, - year = {2020}, -} - -@Article{arcones1992bootstrap, - author = {Arcones, Miguel A and Gine, Evarist}, - title = {On the Bootstrap of {{U}} and {{V}} Statistics}, - pages = {655--674}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {The Annals of Statistics}, - year = {1992}, -} - -@Article{ariely2003coherent, - author = {Ariely, Dan and Loewenstein, George and Prelec, Drazen}, - title = {``{{Coherent}} Arbitrariness'': {{Stable}} Demand Curves without Stable Preferences}, - doi = {10.1017/cbo9780511618031.014}, - number = {1}, - pages = {73--106}, - volume = {118}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {The Quarterly journal of economics}, - year = {2003}, -} - -@Article{ariely2006tom, - author = {Ariely, Dan and Loewenstein, George and Prelec, Drazen}, - title = {Tom {{Sawyer}} and the Construction of Value}, - doi = {10.1017/cbo9780511618031.015}, - number = {1}, - 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archiveprefix = {arXiv}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - eprint = {2006.06831}, - eprinttype = {arxiv}, - year = {2020}, -} - -@Misc{karimi2020survey, - author = {Amir-Hossein Karimi and Gilles Barthe and Bernhard Schölkopf and Isabel Valera}, - title = {A survey of algorithmic recourse: definitions, formulations, solutions, and prospects}, - eprint = {2010.04050}, - archiveprefix = {arXiv}, - primaryclass = {cs.LG}, - year = {2021}, -} - -@InProceedings{karimi2021algorithmic, - author = {Karimi, Amir-Hossein and Sch{\"o}lkopf, Bernhard and Valera, Isabel}, - booktitle = {Proceedings of the 2021 {{ACM Conference}} on {{Fairness}}, {{Accountability}}, and {{Transparency}}}, - title = {Algorithmic Recourse: From Counterfactual Explanations to Interventions}, - pages = {353--362}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - year = {2021}, -} - -@InProceedings{kaur2020interpreting, - author = {Kaur, Harmanpreet and Nori, Harsha and Jenkins, Samuel and Caruana, Rich and Wallach, Hanna and Wortman Vaughan, Jennifer}, - booktitle = {Proceedings of the 2020 {{CHI}} Conference on Human Factors in Computing Systems}, - title = {Interpreting Interpretability: Understanding Data Scientists' Use of Interpretability Tools for Machine Learning}, - doi = {10.1145/3313831.3376219}, - pages = {1--14}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - year = {2020}, -} - -@Article{kehoe2021defence, - author = {Kehoe, Aidan and Wittek, Peter and Xue, Yanbo and Pozas-Kerstjens, Alejandro}, - title = {Defence against Adversarial Attacks Using Classical and Quantum-Enhanced {{Boltzmann}} Machines}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {Machine Learning: Science and Technology}, - year = {2021}, -} - -@Unpublished{kendall2017what, - author = {Kendall, Alex and Gal, Yarin}, - title = {What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?}, - archiveprefix = {arXiv}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - eprint = {1703.04977}, - eprinttype = {arxiv}, - year = {2017}, -} - -@Article{kihoro2004seasonal, - author = {Kihoro, J and Otieno, RO and Wafula, C}, - title = {Seasonal Time Series Forecasting: {{A}} Comparative Study of {{ARIMA}} and {{ANN}} Models}, - doi = {10.4314/ajst.v5i2.15330}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - year = {2004}, -} - -@Book{kilian2017structural, - author = {Kilian, Lutz and L{\"u}tkepohl, Helmut}, - title = {Structural Vector Autoregressive Analysis}, - publisher = {{Cambridge University Press}}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - year = {2017}, -} - -@Article{kirsch2019batchbald, - author = {Kirsch, Andreas and Van Amersfoort, Joost and Gal, Yarin}, - title = {Batchbald: {{Efficient}} and Diverse Batch Acquisition for Deep Bayesian Active Learning}, - pages = {7026--7037}, - volume = {32}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {Advances in neural information processing systems}, - year = {2019}, -} - -@Unpublished{kuiper2021exploring, - author = {Kuiper, Ouren and van den Berg, Martin and van den Burgt, Joost and Leijnen, Stefan}, - title = {Exploring {{Explainable AI}} in the {{Financial Sector}}: {{Perspectives}} of {{Banks}} and {{Supervisory Authorities}}}, - archiveprefix = {arXiv}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - doi = {10.1007/978-3-030-93842-0_6}, - eprint = {2111.02244}, - eprinttype = {arxiv}, - year = {2021}, -} - -@Article{kydland1982time, - author = {Kydland, Finn E and Prescott, Edward C}, - title = {Time to Build and Aggregate Fluctuations}, - pages = {1345--1370}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {Econometrica: Journal of the Econometric Society}, - year = {1982}, -} - -@Unpublished{lachapelle2019gradientbased, - author = {Lachapelle, S{\'e}bastien and Brouillard, Philippe and Deleu, Tristan and Lacoste-Julien, Simon}, - title = {Gradient-Based Neural Dag Learning}, - archiveprefix = {arXiv}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - eprint = {1906.02226}, - eprinttype = {arxiv}, - year = {2019}, -} - -@InProceedings{lakkaraju2020how, - author = {Lakkaraju, Himabindu and Bastani, Osbert}, - booktitle = {Proceedings of the {{AAAI}}/{{ACM Conference}} on {{AI}}, {{Ethics}}, and {{Society}}}, - title = {" {{How}} Do {{I}} Fool You?" {{Manipulating User Trust}} via {{Misleading Black Box Explanations}}}, - pages = {79--85}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - year = {2020}, -} - -@InProceedings{lakkaraju2020how, - author = {Lakkaraju, Himabindu and Bastani, Osbert}, - booktitle = {Proceedings of the {{AAAI}}/{{ACM Conference}} on {{AI}}, {{Ethics}}, and {{Society}}}, - title = {" {{How Do I Fool You}}?" {{Manipulating User Trust}} via {{Misleading Black Box Explanations}}}, - pages = {79--85}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - year = {2020}, -} - -@Article{lakshminarayanan2016simple, - author = {Lakshminarayanan, Balaji and Pritzel, Alexander and Blundell, Charles}, - title = {Simple and scalable predictive uncertainty estimation using deep ensembles}, - volume = {30}, - journal = {Advances in neural information processing systems}, - year = {2017}, -} - -@Unpublished{laugel2017inverse, - author = {Laugel, Thibault and Lesot, Marie-Jeanne and Marsala, Christophe and Renard, Xavier and Detyniecki, Marcin}, - title = {Inverse Classification for Comparison-Based Interpretability in Machine Learning}, - archiveprefix = {arXiv}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - eprint = {1712.08443}, - eprinttype = {arxiv}, - shortjournal = {arXiv preprint arXiv:1712.08443}, - year = {2017}, -} - -@Thesis{lawrence2001variational, - author = {Lawrence, Neil David}, - title = {Variational Inference in Probabilistic Models}, - type = {phdthesis}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - school = {{University of Cambridge}}, - year = {2001}, -} - -@Misc{lecun1998mnist, - author = {LeCun, Yann}, - title = {The MNIST database of handwritten digits}, - howpublished = {http://yann.lecun.com/exdb/mnist/}, - note = {Accessed: 2024-01-10}, - year = {1998}, -} - -@Article{lee2003best, - author = {Lee, Lung-fei}, - title = {Best Spatial Two-Stage Least Squares Estimators for a Spatial Autoregressive Model with Autoregressive Disturbances}, - doi = {10.1081/etc-120025891}, - number = {4}, - pages = {307--335}, - volume = {22}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {Econometric Reviews}, - year = {2003}, -} - -@Article{lerner2013financial, - author = {Lerner, Jennifer S and Li, Ye and Weber, Elke U}, - title = {The Financial Costs of Sadness}, - doi = {10.1177/0956797612450302}, - number = {1}, - pages = {72--79}, - volume = {24}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {Psychological science}, - year = {2013}, -} - -@Article{list2004neoclassical, - author = {List, John A}, - title = {Neoclassical Theory versus Prospect Theory: {{Evidence}} from the Marketplace}, - doi = {10.3386/w9736}, - number = {2}, - pages = {615--625}, - volume = {72}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {Econometrica : journal of the Econometric Society}, - shortjournal = {Econometrica}, - year = {2004}, -} - -@Article{lucas1976econometric, - author = {Lucas, JR}, - title = {Econometric Policy Evaluation: A Critique `, in {{K}}. {{Brunner}} and {{A Meltzer}}, {{The Phillips}} Curve and Labor Markets, {{North Holland}}}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - year = {1976}, -} - -@InProceedings{lundberg2017unified, - author = {Lundberg, Scott M and Lee, Su-In}, - booktitle = {Proceedings of the 31st International Conference on Neural Information Processing Systems}, - title = {A Unified Approach to Interpreting Model Predictions}, - pages = {4768--4777}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - year = {2017}, -} - -@Book{lutkepohl2005new, - author = {L{\"u}tkepohl, Helmut}, - title = {New Introduction to Multiple Time Series Analysis}, - publisher = {{Springer Science \& Business Media}}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - year = {2005}, -} - -@Article{madrian2001power, - author = {Madrian, Brigitte C and Shea, Dennis F}, - title = {The Power of Suggestion: {{Inertia}} in 401 (k) Participation and Savings Behavior}, - doi = {10.3386/w7682}, - number = {4}, - pages = {1149--1187}, - volume = {116}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {The Quarterly journal of economics}, - year = {2001}, -} - -@Book{manning2008introduction, - author = {Manning, Christopher D and Sch{\"u}tze, Hinrich and Raghavan, Prabhakar}, - title = {Introduction to Information Retrieval}, - publisher = {{Cambridge university press}}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - year = {2008}, -} - -@Software{manokhin2022awesome, - author = {Manokhin, Valery}, - title = {Awesome Conformal Prediction}, - doi = {10.5281/zenodo.6467205}, - howpublished = {https://doi.org/10.5281/zenodo.6467205}, - note = {Accessed: 2023-12-24}, - url = {https://doi.org/10.5281/zenodo.6467205}, - version = {v1.0.0}, - month = apr, - publisher = {Zenodo}, - year = {2022}, -} - -@Article{manski1993identification, - author = {Manski, Charles F}, - title = {Identification of Endogenous Social Effects: {{The}} Reflection Problem}, - doi = {10.2307/2298123}, - number = {3}, - pages = {531--542}, - volume = {60}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {The review of economic studies}, - year = {1993}, -} - -@Article{markle2018goals, - author = {Markle, Alex and Wu, George and White, Rebecca and Sackett, Aaron}, - title = {Goals as Reference Points in Marathon Running: {{A}} Novel Test of Reference Dependence}, - doi = {10.2139/ssrn.2523510}, - number = {1}, - pages = {19--50}, - volume = {56}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {Journal of Risk and Uncertainty}, - year = {2018}, -} - -@Article{masini2021machine, - author = {Masini, Ricardo P and Medeiros, Marcelo C and Mendes, Eduardo F}, - title = {Machine Learning Advances for Time Series Forecasting}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {Journal of Economic Surveys}, - year = {2021}, -} - -@Article{mccracken2016fredmd, - author = {McCracken, Michael W and Ng, Serena}, - title = {{{FRED-MD}}: {{A}} Monthly Database for Macroeconomic Research}, - doi = {10.20955/wp.2015.012}, - number = {4}, - pages = {574--589}, - volume = {34}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {Journal of Business \& Economic Statistics}, - year = {2016}, -} - -@Article{mcculloch1990logical, - author = {McCulloch, Warren S and Pitts, Walter}, - title = {A Logical Calculus of the Ideas Immanent in Nervous Activity}, - number = {1}, - pages = {99--115}, - volume = {52}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {Bulletin of mathematical biology}, - year = {1990}, -} - -@Article{migut2015visualizing, - author = {Migut, MA and Worring, Marcel and Veenman, Cor J}, - title = {Visualizing Multi-Dimensional Decision Boundaries in {{2D}}}, - doi = {10.1007/s10618-013-0342-x}, - number = {1}, - pages = {273--295}, - volume = {29}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {Data Mining and Knowledge Discovery}, - year = {2015}, -} - -@Article{miller2019explanation, - author = {Miller, Tim}, - title = {Explanation in Artificial Intelligence: {{Insights}} from the Social Sciences}, - doi = {10.1016/j.artint.2018.07.007}, - pages = {1--38}, - volume = {267}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {Artificial intelligence}, - year = {2019}, -} - -@InProceedings{miller2020strategic, - author = {Miller, John and Milli, Smitha and Hardt, Moritz}, - booktitle = {Proceedings of the 37th {{International Conference}} on {{Machine Learning}}}, - title = {Strategic {{Classification}} Is {{Causal Modeling}} in {{Disguise}}}, - eventtitle = {International {{Conference}} on {{Machine Learning}}}, - pages = {6917--6926}, - publisher = {{PMLR}}, - url = {https://proceedings.mlr.press/v119/miller20b.html}, - urldate = {2022-11-03}, - abstract = {Consequential decision-making incentivizes individuals to strategically adapt their behavior to the specifics of the decision rule. While a long line of work has viewed strategic adaptation as gaming and attempted to mitigate its effects, recent work has instead sought to design classifiers that incentivize individuals to improve a desired quality. Key to both accounts is a cost function that dictates which adaptations are rational to undertake. In this work, we develop a causal framework for strategic adaptation. Our causal perspective clearly distinguishes between gaming and improvement and reveals an important obstacle to incentive design. We prove any procedure for designing classifiers that incentivize improvement must inevitably solve a non-trivial causal inference problem. We show a similar result holds for designing cost functions that satisfy the requirements of previous work. With the benefit of hindsight, our results show much of the prior work on strategic classification is causal modeling in disguise.}, - bdsk-url-1 = {https://proceedings.mlr.press/v119/miller20b.html}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - file = {:/Users/FA31DU/Zotero/storage/46I2QMPI/Miller et al. - 2020 - Strategic Classification is Causal Modeling in Dis.pdf:;:/Users/FA31DU/Zotero/storage/NWREET6B/Miller et al. - 2020 - Strategic Classification is Causal Modeling in Dis.pdf:}, - issn = {2640-3498}, - langid = {english}, - month = nov, - year = {2020}, -} - -@Article{mischel1988nature, - author = {Mischel, Walter and Shoda, Yuichi and Peake, Philip K}, - title = {The Nature of Adolescent Competencies Predicted by Preschool Delay of Gratification.}, - doi = {10.1037/0022-3514.54.4.687}, - number = {4}, - pages = {687}, - volume = {54}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {Journal of personality and social psychology}, - year = {1988}, -} - -@InProceedings{mittelstadt2019explaining, - author = {Mittelstadt, Brent and Russell, Chris and Wachter, Sandra}, - booktitle = {Proceedings of the Conference on Fairness, Accountability, and Transparency}, - title = {Explaining Explanations in {{AI}}}, - doi = {10.1145/3287560.3287574}, - pages = {279--288}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - year = {2019}, -} - -@Book{molnar2022interpretable, - author = {Christoph Molnar}, - title = {Interpretable Machine Learning}, - edition = {2}, - subtitle = {A Guide for Making Black Box Models Explainable}, - url = {https://christophm.github.io/interpretable-ml-book}, - year = {2022}, -} - -@Book{morgan2015counterfactuals, - author = {Morgan, Stephen L and Winship, Christopher}, - title = {Counterfactuals and Causal Inference}, - publisher = {{Cambridge University Press}}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - year = {2015}, -} - 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date-modified = {2022-12-13 12:58:01 +0100}, - year = {2012}, -} - -@Book{murphy2012machine, - author = {Murphy, Kevin P}, - title = {Machine Learning: {{A}} Probabilistic Perspective}, - publisher = {{MIT press}}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - year = {2012}, -} - -@Book{murphy2022probabilistic, - author = {Murphy, Kevin P}, - title = {Probabilistic {{Machine Learning}}: {{An}} Introduction}, - publisher = {{MIT Press}}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - year = {2022}, -} - -@Article{nagel1995unraveling, - author = {Nagel, Rosemarie}, - title = {Unraveling in Guessing Games: {{An}} Experimental Study}, - number = {5}, - pages = {1313--1326}, - volume = {85}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {The American Economic Review}, - year = {1995}, -} - -@Unpublished{navarro-martinez2021bridging, - author = {Navarro-Martinez, Daniel and Wang, Xinghua}, - title = {Bridging the Gap between the Lab and the Field: {{Dictator}} Games and Donations}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - year = {2021}, -} - -@InProceedings{nelson2015evaluating, - author = {Nelson, Kevin and Corbin, George and Anania, Mark and Kovacs, Matthew and Tobias, Jeremy and Blowers, Misty}, - booktitle = {2015 {{IEEE Symposium}} on {{Computational Intelligence}} for {{Security}} and {{Defense Applications}} ({{CISDA}})}, - title = {Evaluating Model Drift in Machine Learning Algorithms}, - doi = {10.1109/cisda.2015.7208643}, - pages = {1--8}, - publisher = {{IEEE}}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - year = {2015}, -} - -@Book{nocedal2006numerical, - author = {Nocedal, Jorge and Wright, Stephen}, - title = {Numerical Optimization}, - publisher = {{Springer Science \& Business Media}}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - 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date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - publisher = {{OECD}}, - year = {2021}, -} - -@Book{oneil2016weapons, - author = {O'Neil, Cathy}, - title = {Weapons of Math Destruction: {{How}} Big Data Increases Inequality and Threatens Democracy}, - publisher = {{Crown}}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - year = {2016}, -} - -@Article{pace1997sparse, - author = {Pace, R Kelley and Barry, Ronald}, - title = {Sparse Spatial Autoregressions}, - doi = {10.1016/s0167-7152(96)00140-x}, - number = {3}, - pages = {291--297}, - volume = {33}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {Statistics \& Probability Letters}, - year = {1997}, -} - -@Unpublished{parr2018matrix, - author = {Parr, Terence and Howard, Jeremy}, - title = {The Matrix Calculus You Need for Deep Learning}, - archiveprefix = {arXiv}, - date-added = {2022-12-13 12:58:01 +0100}, - 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Dickerson and Chirag Shah}, - title = {Counterfactual Explanations and Algorithmic Recourses for Machine Learning: A Review}, - eprint = {2010.10596}, - archiveprefix = {arXiv}, - primaryclass = {cs.LG}, - year = {2022}, -} - -@Article{verstyuk2020modeling, - author = {Verstyuk, Sergiy}, - title = {Modeling Multivariate Time Series in Economics: {{From}} Auto-Regressions to Recurrent Neural Networks}, - doi = {10.2139/ssrn.3589337}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {Available at SSRN 3589337}, - year = {2020}, -} - -@Article{wachter2017counterfactual, - author = {Wachter, Sandra and Mittelstadt, Brent and Russell, Chris}, - title = {Counterfactual Explanations without Opening the Black Box: {{Automated}} Decisions and the {{GDPR}}}, - doi = {10.2139/ssrn.3063289}, - pages = {841}, - volume = {31}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {Harv. 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G.}, - title = {Epidemiological Data from the {{COVID-19}} Outbreak, Real-Time Case Information}, - doi = {doi.org/10.1038/s41597-020-0448-0}, - number = {106}, - volume = {7}, - bdsk-url-1 = {https://doi.org/10.1038/s41597-020-0448-0}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {Scientific Data}, - year = {2020}, -} - -@Article{yeh2009comparisons, - author = {Yeh, I-Cheng and Lien, Che-hui}, - title = {The Comparisons of Data Mining Techniques for the Predictive Accuracy of Probability of Default of Credit Card Clients}, - doi = {10.1016/j.eswa.2007.12.020}, - number = {2}, - pages = {2473--2480}, - volume = {36}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {Expert systems with applications}, - year = {2009}, -} - -@Article{zhang1998forecasting, - author = {Zhang, Guoqiang and Patuwo, B Eddy and Hu, Michael Y}, - title = {Forecasting with Artificial Neural Networks:: {{The}} State of the Art}, - number = {1}, - pages = {35--62}, - volume = {14}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {International journal of forecasting}, - year = {1998}, -} - -@Article{zhang2003time, - author = {Zhang, G Peter}, - title = {Time Series Forecasting Using a Hybrid {{ARIMA}} and Neural Network Model}, - doi = {10.1016/s0925-2312(01)00702-0}, - pages = {159--175}, - volume = {50}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {Neurocomputing}, - year = {2003}, -} - -@Unpublished{zheng2018dags, - author = {Zheng, Xun and Aragam, Bryon and Ravikumar, Pradeep and Xing, Eric P}, - title = {Dags with No Tears: {{Continuous}} Optimization for Structure Learning}, - archiveprefix = {arXiv}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - eprint = {1803.01422}, - eprinttype = {arxiv}, - year = {2018}, -} - -@Article{zhu2015optimal, - author = {Zhu, Rong and Ma, Ping and Mahoney, Michael W and Yu, Bin}, - title = {Optimal Subsampling Approaches for Large Sample Linear Regression}, - pages = {arXiv--1509}, - date-added = {2022-12-13 12:58:01 +0100}, - date-modified = {2022-12-13 12:58:01 +0100}, - journal = {arXiv}, - year = {2015}, -} - -@Article{barber2021predictive, - author = {Barber, Rina Foygel and Candès, Emmanuel J. and Ramdas, Aaditya and Tibshirani, Ryan J.}, - title = {Predictive inference with the jackknife+}, - doi = {10.1214/20-AOS1965}, - issn = {0090-5364, 2168-8966}, - number = {1}, - pages = {486--507}, - urldate = {2022-12-13}, - volume = {49}, - abstract = {This paper introduces the jackknife+, which is a novel method for constructing predictive confidence intervals. Whereas the jackknife outputs an interval centered at the predicted response of a test point, with the width of the interval determined by the quantiles of leave-one-out residuals, the jackknife+ also uses the leave-one-out predictions at the test point to account for the variability in the fitted regression function. Assuming exchangeable training samples, we prove that this crucial modification permits rigorous coverage guarantees regardless of the distribution of the data points, for any algorithm that treats the training points symmetrically. Such guarantees are not possible for the original jackknife and we demonstrate examples where the coverage rate may actually vanish. Our theoretical and empirical analysis reveals that the jackknife and the jackknife+ intervals achieve nearly exact coverage and have similar lengths whenever the fitting algorithm obeys some form of stability. Further, we extend the jackknife+ to \$K\$-fold cross validation and similarly establish rigorous coverage properties. Our methods are related to cross-conformal prediction proposed by Vovk (Ann. Math. Artif. Intell. 74 (2015) 9–28) and we discuss connections.}, - file = {:Barber2021 - Predictive Inference with the Jackknife+.pdf:PDF}, - journal = {The Annals of Statistics}, - keywords = {62F40, 62G08, 62G09, conformal inference, cross-validation, distribution-free, jackknife, leave-one-out, stability}, - month = feb, - publisher = {Institute of Mathematical Statistics}, - year = {2021}, -} - -@TechReport{chouldechova2018frontiers, - author = {Chouldechova, Alexandra and Roth, Aaron}, - title = {The {Frontiers} of {Fairness} in {Machine} {Learning}}, - doi = {10.48550/arXiv.1810.08810}, - eprint = {1810.08810}, - note = {arXiv:1810.08810 [cs, stat] type: article}, - abstract = {The last few years have seen an explosion of academic and popular interest in algorithmic fairness. Despite this interest and the volume and velocity of work that has been produced recently, the fundamental science of fairness in machine learning is still in a nascent state. In March 2018, we convened a group of experts as part of a CCC visioning workshop to assess the state of the field, and distill the most promising research directions going forward. This report summarizes the findings of that workshop. Along the way, it surveys recent theoretical work in the field and points towards promising directions for research.}, - archiveprefix = {arxiv}, - file = {:chouldechova2018frontiers - The Frontiers of Fairness in Machine Learning.pdf:PDF}, - keywords = {Computer Science - Machine Learning, Computer Science - Data Structures and Algorithms, Computer Science - Computer Science and Game Theory, Statistics - Machine Learning}, - month = oct, - school = {arXiv}, - year = {2018}, -} - -@Misc{pawelczyk2022probabilistically, - author = {Martin Pawelczyk and Teresa Datta and Johannes van-den-Heuvel and Gjergji Kasneci and Himabindu Lakkaraju}, - title = {Probabilistically Robust Recourse: Navigating the Trade-offs between Costs and Robustness in Algorithmic Recourse}, - eprint = {2203.06768}, - archiveprefix = {arXiv}, - primaryclass = {cs.LG}, - year = {2023}, -} - -@Misc{stutz2022learning, - author = {David Stutz and Krishnamurthy and Dvijotham and Ali Taylan Cemgil and Arnaud Doucet}, - title = {Learning Optimal Conformal Classifiers}, - eprint = {2110.09192}, - archiveprefix = {arXiv}, - primaryclass = {cs.LG}, - year = {2022}, -} - -@InProceedings{grathwohl2020your, - author = {Grathwohl, Will and Wang, Kuan-Chieh and Jacobsen, Joern-Henrik and Duvenaud, David and Norouzi, Mohammad and Swersky, Kevin}, - booktitle = {International Conference on Learning Representations}, - title = {Your classifier is secretly an energy based model and you should treat it like one}, - year = {2020}, -} - -@Book{murphy2023probabilistic, - author = {Murphy, Kevin P}, - title = {Probabilistic machine learning: Advanced topics}, - publisher = {MIT press}, - year = {2023}, -} - -@InProceedings{artelt2021evaluating, - author = {Artelt, Andr{\'e} and Vaquet, Valerie and Velioglu, Riza and Hinder, Fabian and Brinkrolf, Johannes and Schilling, Malte and Hammer, Barbara}, - booktitle = {2021 IEEE Symposium Series on Computational Intelligence (SSCI)}, - title = {Evaluating robustness of counterfactual explanations}, - organization = {IEEE}, - pages = {01--09}, - year = {2021}, -} - -@Article{guidotti2022counterfactual, - author = {Guidotti, Riccardo}, - title = {Counterfactual explanations and how to find them: literature review and benchmarking}, - pages = {1--55}, - journal = {Data Mining and Knowledge Discovery}, - publisher = {Springer}, - year = {2022}, -} - -@Misc{mahajan2019preserving, - author = {Divyat Mahajan and Chenhao Tan and Amit Sharma}, - title = {Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifiers}, - eprint = {1912.03277}, - archiveprefix = {arXiv}, - primaryclass = {cs.LG}, - year = {2020}, -} - -@TechReport{antoran2023sampling, - author = {Antorán, Javier and Padhy, Shreyas and Barbano, Riccardo and Nalisnick, Eric and Janz, David and Hernández-Lobato, José Miguel}, - date = {2023-03}, - institution = {arXiv}, - title = {Sampling-based inference for large linear models, with application to linearised {Laplace}}, - note = {arXiv:2210.04994 [cs, stat] type: article}, - url = {http://arxiv.org/abs/2210.04994}, - urldate = {2023-03-25}, - abstract = {Large-scale linear models are ubiquitous throughout machine learning, with contemporary application as surrogate models for neural network uncertainty quantification; that is, the linearised Laplace method. Alas, the computational cost associated with Bayesian linear models constrains this method's application to small networks, small output spaces and small datasets. We address this limitation by introducing a scalable sample-based Bayesian inference method for conjugate Gaussian multi-output linear models, together with a matching method for hyperparameter (regularisation) selection. Furthermore, we use a classic feature normalisation method (the g-prior) to resolve a previously highlighted pathology of the linearised Laplace method. Together, these contributions allow us to perform linearised neural network inference with ResNet-18 on CIFAR100 (11M parameters, 100 outputs x 50k datapoints), with ResNet-50 on Imagenet (50M parameters, 1000 outputs x 1.2M datapoints) and with a U-Net on a high-resolution tomographic reconstruction task (2M parameters, 251k output{\textasciitilde}dimensions).}, - annotation = {Comment: Published at ICLR 2023. This latest Arxiv version is extended with a demonstration of the proposed methods on the Imagenet dataset}, - file = {arXiv Fulltext PDF:https\://arxiv.org/pdf/2210.04994.pdf:application/pdf}, - keywords = {Statistics - Machine Learning, Computer Science - Artificial Intelligence, Computer Science - Machine Learning}, -} - -@Misc{altmeyer2022conformal, - author = {Altmeyer, Patrick}, - date = {2022-10}, - title = {{Conformal} {Prediction} in {Julia}}, - language = {en}, - url = {https://www.paltmeyer.com/blog/posts/conformal-prediction/}, - urldate = {2023-03-27}, - abstract = {A (very) gentle introduction to Conformal Prediction in Julia using my new package ConformalPrediction.jl.}, -} - -@InProceedings{welling2011bayesian, - author = {Welling, Max and Teh, Yee W}, - booktitle = {Proceedings of the 28th international conference on machine learning (ICML-11)}, - title = {Bayesian learning via stochastic gradient Langevin dynamics}, - organization = {Citeseer}, - pages = {681--688}, - year = {2011}, -} - -@Article{gill2010circular, - author = {Gill, Jeff and Hangartner, Dominik}, - title = {Circular data in political science and how to handle it}, - number = {3}, - pages = {316--336}, - volume = {18}, - journal = {Political Analysis}, - publisher = {Cambridge University Press}, - year = {2010}, -} - -@InProceedings{liu2022goggle, - author = {Liu, Tennison and Qian, Zhaozhi and Berrevoets, Jeroen and van der Schaar, Mihaela}, - booktitle = {The Eleventh International Conference on Learning Representations}, - title = {GOGGLE: Generative modelling for tabular data by learning relational structure}, - year = {2022}, -} - -@Misc{du2019implicit, - author = {Yilun Du and Igor Mordatch}, - title = {Implicit Generation and Generalization in Energy-Based Models}, - eprint = {1903.08689}, - archiveprefix = {arXiv}, - primaryclass = {cs.LG}, - year = {2020}, -} - -@InProceedings{krizhevsky2009learning, - author = {Krizhevsky, A.}, - date = {2009}, - title = {Learning {Multiple} {Layers} of {Features} from {Tiny} {Images}}, - url = {https://www.semanticscholar.org/paper/Learning-Multiple-Layers-of-Features-from-Tiny-Krizhevsky/5d90f06bb70a0a3dced62413346235c02b1aa086}, - urldate = {2023-06-21}, - abstract = {Groups at MIT and NYU have collected a dataset of millions of tiny colour images from the web. It is, in principle, an excellent dataset for unsupervised training of deep generative models, but previous researchers who have tried this have found it dicult to learn a good set of lters from the images. We show how to train a multi-layer generative model that learns to extract meaningful features which resemble those found in the human visual cortex. Using a novel parallelization algorithm to distribute the work among multiple machines connected on a network, we show how training such a model can be done in reasonable time. A second problematic aspect of the tiny images dataset is that there are no reliable class labels which makes it hard to use for object recognition experiments. We created two sets of reliable labels. The CIFAR-10 set has 6000 examples of each of 10 classes and the CIFAR-100 set has 600 examples of each of 100 non-overlapping classes. Using these labels, we show that object recognition is signicantly improved by pre-training a layer of features on a large set of unlabeled tiny images.}, - annotation = {[TLDR] It is shown how to train a multi-layer generative model that learns to extract meaningful features which resemble those found in the human visual cortex, using a novel parallelization algorithm to distribute the work among multiple machines connected on a network.}, - file = {Semantic Scholar Link:https\://www.semanticscholar.org/paper/Learning-Multiple-Layers-of-Features-from-Tiny-Krizhevsky/5d90f06bb70a0a3dced62413346235c02b1aa086:text/html;Full Text PDF:http\://www.cs.toronto.edu/~kriz/learning-features-2009-TR.pdf:application/pdf}, -} - -@Misc{becker1996adult, - author = {Barry Becker, Ronny Kohavi}, - date = {1996}, - title = {Adult}, - doi = {10.24432/C5XW20}, - note = {Type: dataset}, - url = {https://archive.ics.uci.edu/dataset/2}, - urldate = {2023-06-21}, - publisher = {UCI Machine Learning Repository}, -} - -@InProceedings{tolomei2017interpretable, - author = {Tolomei, Gabriele and Silvestri, Fabrizio and Haines, Andrew and Lalmas, Mounia}, - booktitle = {Proceedings of the 23rd {ACM} {SIGKDD} {International} {Conference} on {Knowledge} {Discovery} and {Data} {Mining}}, - date = {2017-08}, - title = {Interpretable {Predictions} of {Tree}-based {Ensembles} via {Actionable} {Feature} {Tweaking}}, - doi = {10.1145/3097983.3098039}, - note = {arXiv:1706.06691 [stat]}, - pages = {465--474}, - url = {http://arxiv.org/abs/1706.06691}, - urldate = {2023-06-21}, - abstract = {Machine-learned models are often described as "black boxes". In many real-world applications however, models may have to sacrifice predictive power in favour of human-interpretability. When this is the case, feature engineering becomes a crucial task, which requires significant and time-consuming human effort. Whilst some features are inherently static, representing properties that cannot be influenced (e.g., the age of an individual), others capture characteristics that could be adjusted (e.g., the daily amount of carbohydrates taken). Nonetheless, once a model is learned from the data, each prediction it makes on new instances is irreversible - assuming every instance to be a static point located in the chosen feature space. There are many circumstances however where it is important to understand (i) why a model outputs a certain prediction on a given instance, (ii) which adjustable features of that instance should be modified, and finally (iii) how to alter such a prediction when the mutated instance is input back to the model. In this paper, we present a technique that exploits the internals of a tree-based ensemble classifier to offer recommendations for transforming true negative instances into positively predicted ones. We demonstrate the validity of our approach using an online advertising application. First, we design a Random Forest classifier that effectively separates between two types of ads: low (negative) and high (positive) quality ads (instances). Then, we introduce an algorithm that provides recommendations that aim to transform a low quality ad (negative instance) into a high quality one (positive instance). Finally, we evaluate our approach on a subset of the active inventory of a large ad network, Yahoo Gemini.}, - annotation = {Comment: 10 pages, KDD 2017}, - file = {arXiv Fulltext PDF:https\://arxiv.org/pdf/1706.06691.pdf:application/pdf}, - keywords = {Statistics - Machine Learning, 68T01, I.2.0, I.5.1}, -} - -@TechReport{dandl2023counterfactuals, - author = {Dandl, Susanne and Hofheinz, Andreas and Binder, Martin and Bischl, Bernd and Casalicchio, Giuseppe}, - date = {2023-04}, - institution = {arXiv}, - title = {counterfactuals: {An} {R} {Package} for {Counterfactual} {Explanation} {Methods}}, - note = {arXiv:2304.06569 [cs, stat] type: article}, - url = {http://arxiv.org/abs/2304.06569}, - urldate = {2023-06-21}, - abstract = {Counterfactual explanation methods provide information on how feature values of individual observations must be changed to obtain a desired prediction. Despite the increasing amount of proposed methods in research, only a few implementations exist whose interfaces and requirements vary widely. In this work, we introduce the counterfactuals R package, which provides a modular and unified R6-based interface for counterfactual explanation methods. We implemented three existing counterfactual explanation methods and propose some optional methodological extensions to generalize these methods to different scenarios and to make them more comparable. We explain the structure and workflow of the package using real use cases and show how to integrate additional counterfactual explanation methods into the package. In addition, we compared the implemented methods for a variety of models and datasets with regard to the quality of their counterfactual explanations and their runtime behavior.}, - file = {arXiv Fulltext PDF:https\://arxiv.org/pdf/2304.06569.pdf:application/pdf}, - keywords = {Statistics - Machine Learning, Computer Science - Machine Learning, Statistics - Computation}, - shorttitle = {counterfactuals}, -} - -@TechReport{laugel2017inversea, - author = {Laugel, Thibault and Lesot, Marie-Jeanne and Marsala, Christophe and Renard, Xavier and Detyniecki, Marcin}, - date = {2017-12}, - institution = {arXiv}, - title = {Inverse {Classification} for {Comparison}-based {Interpretability} in {Machine} {Learning}}, - doi = {10.48550/arXiv.1712.08443}, - note = {arXiv:1712.08443 [cs, stat] type: article}, - url = {http://arxiv.org/abs/1712.08443}, - urldate = {2023-06-21}, - abstract = {In the context of post-hoc interpretability, this paper addresses the task of explaining the prediction of a classifier, considering the case where no information is available, neither on the classifier itself, nor on the processed data (neither the training nor the test data). It proposes an instance-based approach whose principle consists in determining the minimal changes needed to alter a prediction: given a data point whose classification must be explained, the proposed method consists in identifying a close neighbour classified differently, where the closeness definition integrates a sparsity constraint. This principle is implemented using observation generation in the Growing Spheres algorithm. Experimental results on two datasets illustrate the relevance of the proposed approach that can be used to gain knowledge about the classifier.}, - annotation = {Comment: preprint}, - file = {arXiv Fulltext PDF:https\://arxiv.org/pdf/1712.08443.pdf:application/pdf}, - keywords = {Statistics - Machine Learning, Computer Science - Artificial Intelligence, Computer Science - Machine Learning}, -} - -@TechReport{delaney2021uncertainty, - author = {Delaney, Eoin and Greene, Derek and Keane, Mark T.}, - date = {2021-07}, - institution = {arXiv}, - title = {Uncertainty {Estimation} and {Out}-of-{Distribution} {Detection} for {Counterfactual} {Explanations}: {Pitfalls} and {Solutions}}, - note = {arXiv:2107.09734 [cs] type: article}, - url = {http://arxiv.org/abs/2107.09734}, - urldate = {2023-06-23}, - abstract = {Whilst an abundance of techniques have recently been proposed to generate counterfactual explanations for the predictions of opaque black-box systems, markedly less attention has been paid to exploring the uncertainty of these generated explanations. This becomes a critical issue in high-stakes scenarios, where uncertain and misleading explanations could have dire consequences (e.g., medical diagnosis and treatment planning). Moreover, it is often difficult to determine if the generated explanations are well grounded in the training data and sensitive to distributional shifts. This paper proposes several practical solutions that can be leveraged to solve these problems by establishing novel connections with other research works in explainability (e.g., trust scores) and uncertainty estimation (e.g., Monte Carlo Dropout). Two experiments demonstrate the utility of our proposed solutions.}, - file = {arXiv Fulltext PDF:https\://arxiv.org/pdf/2107.09734.pdf:application/pdf}, - keywords = {Computer Science - Machine Learning, Computer Science - Artificial Intelligence}, - shorttitle = {Uncertainty {Estimation} and {Out}-of-{Distribution} {Detection} for {Counterfactual} {Explanations}}, -} - -@InProceedings{casanueva2020efficient, - author = {Casanueva, Iñigo and Temčinas, Tadas and Gerz, Daniela and Henderson, Matthew and Vulić, Ivan}, - booktitle = {Proceedings of the 2nd {Workshop} on {Natural} {Language} {Processing} for {Conversational} {AI}}, - date = {2020-07}, - title = {Efficient {Intent} {Detection} with {Dual} {Sentence} {Encoders}}, - doi = {10.18653/v1/2020.nlp4convai-1.5}, - location = {Online}, - pages = {38--45}, - publisher = {Association for Computational Linguistics}, - url = {https://aclanthology.org/2020.nlp4convai-1.5}, - urldate = {2023-06-27}, - abstract = {Building conversational systems in new domains and with added functionality requires resource-efficient models that work under low-data regimes (i.e., in few-shot setups). Motivated by these requirements, we introduce intent detection methods backed by pretrained dual sentence encoders such as USE and ConveRT. We demonstrate the usefulness and wide applicability of the proposed intent detectors, showing that: 1) they outperform intent detectors based on fine-tuning the full BERT-Large model or using BERT as a fixed black-box encoder on three diverse intent detection data sets; 2) the gains are especially pronounced in few-shot setups (i.e., with only 10 or 30 annotated examples per intent); 3) our intent detectors can be trained in a matter of minutes on a single CPU; and 4) they are stable across different hyperparameter settings. In hope of facilitating and democratizing research focused on intention detection, we release our code, as well as a new challenging single-domain intent detection dataset comprising 13,083 annotated examples over 77 intents.}, - file = {Full Text PDF:https\://aclanthology.org/2020.nlp4convai-1.5.pdf:application/pdf}, -} - -@TechReport{liu2019roberta, - author = {Liu, Yinhan and Ott, Myle and Goyal, Naman and Du, Jingfei and Joshi, Mandar and Chen, Danqi and Levy, Omer and Lewis, Mike and Zettlemoyer, Luke and Stoyanov, Veselin}, - date = {2019-07}, - institution = {arXiv}, - title = {{RoBERTa}: {A} {Robustly} {Optimized} {BERT} {Pretraining} {Approach}}, - doi = {10.48550/arXiv.1907.11692}, - note = {arXiv:1907.11692 [cs] type: article}, - url = {http://arxiv.org/abs/1907.11692}, - urldate = {2023-06-27}, - abstract = {Language model pretraining has led to significant performance gains but careful comparison between different approaches is challenging. Training is computationally expensive, often done on private datasets of different sizes, and, as we will show, hyperparameter choices have significant impact on the final results. We present a replication study of BERT pretraining (Devlin et al., 2019) that carefully measures the impact of many key hyperparameters and training data size. We find that BERT was significantly undertrained, and can match or exceed the performance of every model published after it. Our best model achieves state-of-the-art results on GLUE, RACE and SQuAD. These results highlight the importance of previously overlooked design choices, and raise questions about the source of recently reported improvements. We release our models and code.}, - file = {arXiv Fulltext PDF:https\://arxiv.org/pdf/1907.11692.pdf:application/pdf}, - keywords = {Computer Science - Computation and Language}, - shorttitle = {{RoBERTa}}, -} - -@TechReport{kunstner2020limitations, - author = {Kunstner, Frederik and Balles, Lukas and Hennig, Philipp}, - date = {2020-06}, - institution = {arXiv}, - title = {Limitations of the {Empirical} {Fisher} {Approximation} for {Natural} {Gradient} {Descent}}, - doi = {10.48550/arXiv.1905.12558}, - note = {arXiv:1905.12558 [cs, stat] type: article}, - url = {http://arxiv.org/abs/1905.12558}, - urldate = {2023-06-30}, - abstract = {Natural gradient descent, which preconditions a gradient descent update with the Fisher information matrix of the underlying statistical model, is a way to capture partial second-order information. Several highly visible works have advocated an approximation known as the empirical Fisher, drawing connections between approximate second-order methods and heuristics like Adam. We dispute this argument by showing that the empirical Fisher---unlike the Fisher---does not generally capture second-order information. We further argue that the conditions under which the empirical Fisher approaches the Fisher (and the Hessian) are unlikely to be met in practice, and that, even on simple optimization problems, the pathologies of the empirical Fisher can have undesirable effects.}, - annotation = {Comment: V3: Minor corrections (typographic errors)}, - file = {arXiv Fulltext PDF:https\://arxiv.org/pdf/1905.12558.pdf:application/pdf}, - keywords = {Computer Science - Machine Learning, Statistics - Machine Learning}, -} - -@TechReport{botev2017practical, - author = {Botev, Aleksandar and Ritter, Hippolyt and Barber, David}, - date = {2017-06}, - institution = {arXiv}, - title = {Practical {Gauss}-{Newton} {Optimisation} for {Deep} {Learning}}, - doi = {10.48550/arXiv.1706.03662}, - note = {arXiv:1706.03662 [stat] type: article}, - url = {http://arxiv.org/abs/1706.03662}, - urldate = {2023-06-30}, - abstract = {We present an efficient block-diagonal ap- proximation to the Gauss-Newton matrix for feedforward neural networks. Our result- ing algorithm is competitive against state- of-the-art first order optimisation methods, with sometimes significant improvement in optimisation performance. Unlike first-order methods, for which hyperparameter tuning of the optimisation parameters is often a labo- rious process, our approach can provide good performance even when used with default set- tings. A side result of our work is that for piecewise linear transfer functions, the net- work objective function can have no differ- entiable local maxima, which may partially explain why such transfer functions facilitate effective optimisation.}, - annotation = {Comment: ICML 2017}, - file = {arXiv Fulltext PDF:https\://arxiv.org/pdf/1706.03662.pdf:application/pdf}, - keywords = {Statistics - Machine Learning}, -} - -@TechReport{sharma2021sketching, - author = {Sharma, Apoorva and Azizan, Navid and Pavone, Marco}, - date = {2021-02}, - institution = {arXiv}, - title = {Sketching {Curvature} for {Efficient} {Out}-of-{Distribution} {Detection} for {Deep} {Neural} {Networks}}, - doi = {10.48550/arXiv.2102.12567}, - note = {arXiv:2102.12567 [cs] type: article}, - url = {http://arxiv.org/abs/2102.12567}, - urldate = {2023-06-30}, - abstract = {In order to safely deploy Deep Neural Networks (DNNs) within the perception pipelines of real-time decision making systems, there is a need for safeguards that can detect out-of-training-distribution (OoD) inputs both efficiently and accurately. Building on recent work leveraging the local curvature of DNNs to reason about epistemic uncertainty, we propose Sketching Curvature of OoD Detection (SCOD), an architecture-agnostic framework for equipping any trained DNN with a task-relevant epistemic uncertainty estimate. Offline, given a trained model and its training data, SCOD employs tools from matrix sketching to tractably compute a low-rank approximation of the Fisher information matrix, which characterizes which directions in the weight space are most influential on the predictions over the training data. Online, we estimate uncertainty by measuring how much perturbations orthogonal to these directions can alter predictions at a new test input. We apply SCOD to pre-trained networks of varying architectures on several tasks, ranging from regression to classification. We demonstrate that SCOD achieves comparable or better OoD detection performance with lower computational burden relative to existing baselines.}, - file = {arXiv Fulltext PDF:https\://arxiv.org/pdf/2102.12567.pdf:application/pdf}, - keywords = {Computer Science - Machine Learning}, -} - -@TechReport{amini2019spatial, - author = {Amini, Alexander and Soleimany, Ava and Karaman, Sertac and Rus, Daniela}, - date = {2019-05}, - institution = {arXiv}, - title = {Spatial {Uncertainty} {Sampling} for {End}-to-{End} {Control}}, - doi = {10.48550/arXiv.1805.04829}, - note = {arXiv:1805.04829 [cs] type: article}, - url = {http://arxiv.org/abs/1805.04829}, - urldate = {2023-06-30}, - abstract = {End-to-end trained neural networks (NNs) are a compelling approach to autonomous vehicle control because of their ability to learn complex tasks without manual engineering of rule-based decisions. However, challenging road conditions, ambiguous navigation situations, and safety considerations require reliable uncertainty estimation for the eventual adoption of full-scale autonomous vehicles. Bayesian deep learning approaches provide a way to estimate uncertainty by approximating the posterior distribution of weights given a set of training data. Dropout training in deep NNs approximates Bayesian inference in a deep Gaussian process and can thus be used to estimate model uncertainty. In this paper, we propose a Bayesian NN for end-to-end control that estimates uncertainty by exploiting feature map correlation during training. This approach achieves improved model fits, as well as tighter uncertainty estimates, than traditional element-wise dropout. We evaluate our algorithms on a challenging dataset collected over many different road types, times of day, and weather conditions, and demonstrate how uncertainties can be used in conjunction with a human controller in a parallel autonomous setting.}, - annotation = {Comment: Originally published in Neural Information Processing Systems (NIPS) Workshop on Bayesian Deep Learning 2017}, - file = {arXiv Fulltext PDF:https\://arxiv.org/pdf/1805.04829.pdf:application/pdf}, - keywords = {Computer Science - Artificial Intelligence, Computer Science - Machine Learning, Computer Science - Robotics}, -} - -@InProceedings{lecun1989optimal, - author = {LeCun, Yann and Denker, John and Solla, Sara}, - booktitle = {Advances in {Neural} {Information} {Processing} {Systems}}, - date = {1989}, - title = {Optimal {Brain} {Damage}}, - publisher = {Morgan-Kaufmann}, - url = {https://proceedings.neurips.cc/paper/1989/hash/6c9882bbac1c7093bd25041881277658-Abstract.html}, - urldate = {2023-06-30}, - volume = {2}, - abstract = {We have used information-theoretic ideas to derive a class of prac(cid:173) tical and nearly optimal schemes for adapting the size of a neural network. By removing unimportant weights from a network, sev(cid:173) eral improvements can be expected: better generalization, fewer training examples required, and improved speed of learning and/or classification. The basic idea is to use second-derivative informa(cid:173) tion to make a tradeoff between network complexity and training set error. Experiments confirm the usefulness of the methods on a real-world application.}, - file = {Full Text PDF:https\://proceedings.neurips.cc/paper_files/paper/1989/file/6c9882bbac1c7093bd25041881277658-Paper.pdf:application/pdf}, -} - -@TechReport{martens2020optimizing, - author = {Martens, James and Grosse, Roger}, - date = {2020-06}, - institution = {arXiv}, - title = {Optimizing {Neural} {Networks} with {Kronecker}-factored {Approximate} {Curvature}}, - doi = {10.48550/arXiv.1503.05671}, - note = {arXiv:1503.05671 [cs, stat] type: article}, - url = {http://arxiv.org/abs/1503.05671}, - urldate = {2023-06-30}, - abstract = {We propose an efficient method for approximating natural gradient descent in neural networks which we call Kronecker-Factored Approximate Curvature (K-FAC). K-FAC is based on an efficiently invertible approximation of a neural network's Fisher information matrix which is neither diagonal nor low-rank, and in some cases is completely non-sparse. It is derived by approximating various large blocks of the Fisher (corresponding to entire layers) as being the Kronecker product of two much smaller matrices. While only several times more expensive to compute than the plain stochastic gradient, the updates produced by K-FAC make much more progress optimizing the objective, which results in an algorithm that can be much faster than stochastic gradient descent with momentum in practice. And unlike some previously proposed approximate natural-gradient/Newton methods which use high-quality non-diagonal curvature matrices (such as Hessian-free optimization), K-FAC works very well in highly stochastic optimization regimes. This is because the cost of storing and inverting K-FAC's approximation to the curvature matrix does not depend on the amount of data used to estimate it, which is a feature typically associated only with diagonal or low-rank approximations to the curvature matrix.}, - annotation = {Comment: Reduction ratio formula corrected. Removed incorrect claim about geodesics in footnote}, - file = {arXiv Fulltext PDF:https\://arxiv.org/pdf/1503.05671.pdf:application/pdf}, - keywords = {Computer Science - Machine Learning, Computer Science - Neural and Evolutionary Computing, Statistics - Machine Learning}, -} - -@TechReport{fong2021conformal, - author = {Fong, Edwin and Holmes, Chris}, - date = {2021-06}, - institution = {arXiv}, - title = {Conformal {Bayesian} {Computation}}, - doi = {10.48550/arXiv.2106.06137}, - note = {arXiv:2106.06137 [stat] type: article}, - url = {http://arxiv.org/abs/2106.06137}, - urldate = {2023-07-19}, - abstract = {We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, \$p(y {\textbackslash}mid x)\$, characterize subjective beliefs on outcomes of interest, \$y\$, conditional on predictors, \$x\$. Bayesian prediction is well-calibrated when the model is true, but the predictive intervals may exhibit poor empirical coverage when the model is misspecified, under the so called \$\{{\textbackslash}cal\{M\}\}\$-open perspective. In contrast, conformal inference provides finite sample frequentist guarantees on predictive confidence intervals without the requirement of model fidelity. Using 'add-one-in' importance sampling, we show that conformal Bayesian predictive intervals are efficiently obtained from re-weighted posterior samples of model parameters. Our approach contrasts with existing conformal methods that require expensive refitting of models or data-splitting to achieve computational efficiency. We demonstrate the utility on a range of examples including extensions to partially exchangeable settings such as hierarchical models.}, - annotation = {Comment: 19 pages, 4 figures, 12 tables; added references and fixed typos}, - file = {arXiv Fulltext PDF:https\://arxiv.org/pdf/2106.06137.pdf:application/pdf}, - keywords = {Statistics - Methodology, Statistics - Computation}, -} - -@Book{hyndman2018forecasting, - author = {Hyndman, Rob J. and Athanasopoulos, George}, - date = {2018-05}, - title = {Forecasting: principles and practice}, - isbn = {9780987507112}, - language = {en}, - note = {Google-Books-ID: \_bBhDwAAQBAJ}, - publisher = {OTexts}, - abstract = {Forecasting is required in many situations. Stocking an inventory may require forecasts of demand months in advance. Telecommunication routing requires traffic forecasts a few minutes ahead. Whatever the circumstances or time horizons involved, forecasting is an important aid in effective and efficient planning.This textbook provides a comprehensive introduction to forecasting methods and presents enough information about each method for readers to use them sensibly.}, - file = {Google Books Link:https\://books.google.com/books?id=_bBhDwAAQBAJ:text/html}, - keywords = {Business \& Economics / Forecasting, Business \& Economics / Statistics, Computers / Databases / Data Mining, Computers / Mathematical \& Statistical Software}, - shorttitle = {Forecasting}, -} - -@InProceedings{xu2021conformal, - author = {Xu, Chen and Xie, Yao}, - date = {2021-07}, - title = {Conformal prediction interval for dynamic time-series}, - language = {en}, - pages = {11559--11569}, - publisher = {PMLR}, - url = {https://proceedings.mlr.press/v139/xu21h.html}, - urldate = {2023-07-24}, - abstract = {We develop a method to construct distribution-free prediction intervals for dynamic time-series, called {\textbackslash}Verb{\textbar}EnbPI{\textbar} that wraps around any bootstrap ensemble estimator to construct sequential prediction intervals. {\textbackslash}Verb{\textbar}EnbPI{\textbar} is closely related to the conformal prediction (CP) framework but does not require data exchangeability. Theoretically, these intervals attain finite-sample, {\textbackslash}textit\{approximately valid\} marginal coverage for broad classes of regression functions and time-series with strongly mixing stochastic errors. Computationally, {\textbackslash}Verb{\textbar}EnbPI{\textbar} avoids overfitting and requires neither data-splitting nor training multiple ensemble estimators; it efficiently aggregates bootstrap estimators that have been trained. In general, {\textbackslash}Verb{\textbar}EnbPI{\textbar} is easy to implement, scalable to producing arbitrarily many prediction intervals sequentially, and well-suited to a wide range of regression functions. We perform extensive real-data analyses to demonstrate its effectiveness.}, - file = {Full Text PDF:http\://proceedings.mlr.press/v139/xu21h/xu21h.pdf:application/pdf}, - issn = {2640-3498}, -} - -@Book{howard2020deep, - author = {Howard, Jeremy and Gugger, Sylvain}, - date = {2020-06}, - title = {Deep {Learning} for {Coders} with fastai and {PyTorch}}, - isbn = {9781492045496}, - language = {en}, - note = {Google-Books-ID: yATuDwAAQBAJ}, - publisher = {"O'Reilly Media, Inc."}, - abstract = {Deep learning is often viewed as the exclusive domain of math PhDs and big tech companies. But as this hands-on guide demonstrates, programmers comfortable with Python can achieve impressive results in deep learning with little math background, small amounts of data, and minimal code. How? With fastai, the first library to provide a consistent interface to the most frequently used deep learning applications.Authors Jeremy Howard and Sylvain Gugger, the creators of fastai, show you how to train a model on a wide range of tasks using fastai and PyTorch. You’ll also dive progressively further into deep learning theory to gain a complete understanding of the algorithms behind the scenes.Train models in computer vision, natural language processing, tabular data, and collaborative filteringLearn the latest deep learning techniques that matter most in practiceImprove accuracy, speed, and reliability by understanding how deep learning models workDiscover how to turn your models into web applicationsImplement deep learning algorithms from scratchConsider the ethical implications of your workGain insight from the foreword by PyTorch cofounder, Soumith Chintala}, - file = {Google Books Link:https\://books.google.nl/books?id=yATuDwAAQBAJ:text/html}, - keywords = {Computers / Data Science / Machine Learning, Computers / Image Processing, Computers / Computer Science, Computers / Machine Theory, Computers / Data Science / Neural Networks, Computers / Programming / General, Computers / Languages / Python, Computers / Data Science / Data Visualization}, -} - -@Article{samoilescu2021model, - author = {Samoilescu, Robert-Florian and Van Looveren, Arnaud and Klaise, Janis}, - title = {Model-agnostic and scalable counterfactual explanations via reinforcement learning}, - journal = {arXiv preprint arXiv:2106.02597}, - year = {2021}, -} - -@Article{chen2021seven, - author = {Chen, Jiahao and Storchan, Victor}, - title = {Seven challenges for harmonizing explainability requirements}, - journal = {arXiv preprint arXiv:2108.05390}, - year = {2021}, -} - -@InProceedings{wang2003multiscale, - author = {Wang, Zhou and Simoncelli, Eero P and Bovik, Alan C}, - booktitle = {The Thrity-Seventh Asilomar Conference on Signals, Systems \& Computers, 2003}, - title = {Multiscale structural similarity for image quality assessment}, - organization = {Ieee}, - pages = {1398--1402}, - volume = {2}, - year = {2003}, -} - -@Article{dhurandhar2018explanations, - author = {Dhurandhar, Amit and Chen, Pin-Yu and Luss, Ronny and Tu, Chun-Chen and Ting, Paishun and Shanmugam, Karthikeyan and Das, Payel}, - title = {Explanations based on the missing: Towards contrastive explanations with pertinent negatives}, - volume = {31}, - journal = {Advances in neural information processing systems}, - year = {2018}, -} - -@InProceedings{liem2023treat, - author = {Liem, Cynthia CS and Demetriou, Andrew M}, - booktitle = {2023 IEEE/ACM 45th International Conference on Software Engineering: Software Engineering in Society (ICSE-SEIS)}, - title = {Treat societally impactful scientific insights as open-source software artifacts}, - organization = {IEEE}, - pages = {150--156}, - year = {2023}, -} - -@InProceedings{altmeyer2023explaining, - author = {Altmeyer, Patrick and van Deursen, Arie and others}, - booktitle = {Proceedings of the JuliaCon Conferences}, - title = {Explaining Black-Box Models through Counterfactuals}, - number = {1}, - pages = {130}, - volume = {1}, - year = {2023}, -} - -@Article{anand2022explainable, - author = {Anand, Avishek and Lyu, Lijun and Idahl, Maximilian and Wang, Yumeng and Wallat, Jonas and Zhang, Zijian}, - title = {Explainable Information Retrieval: A Survey}, - journal = {arXiv preprint arXiv:2211.02405}, - year = {2022}, -} - -@Article{leonhardt2023extractive, - author = {Leonhardt, Jurek and Rudra, Koustav and Anand, Avishek}, - title = {Extractive explanations for interpretable text ranking}, - number = {4}, - pages = {1--31}, - volume = {41}, - journal = {ACM Transactions on Information Systems}, - publisher = {ACM New York, NY, USA}, - year = {2023}, -} - -@Article{porsius2023private, - author = {Porsius Martins, C{\'e}lio}, - title = {Private cycle detection in financial transactions}, - year = {2023}, -} - -@Article{van2021one, - author = {van der Werf, Daan}, - title = {One Step Ahead: A weakly-supervised approach to training robust machine learning models for transaction monitoring}, - year = {2021}, -} - -@InProceedings{yang2018leveraging, - author = {Yang, Jie and Drake, Thomas and Damianou, Andreas and Maarek, Yoelle}, - booktitle = {Proceedings of the 2018 World Wide Web Conference}, - title = {Leveraging crowdsourcing data for deep active learning an application: Learning intents in alexa}, - pages = {23--32}, - year = {2018}, -} - -@Article{smirnova2022nessy, - author = {Smirnova, Alisa and Yang, Jie and Yang, Dingqi and Cudre-Mauroux, Philippe}, - title = {Nessy: A Neuro-Symbolic System for Label Noise Reduction}, - journal = {IEEE Transactions on Knowledge and Data Engineering}, - publisher = {IEEE}, - year = {2022}, -} - -@InProceedings{arous2021marta, - author = {Arous, Ines and Dolamic, Ljiljana and Yang, Jie and Bhardwaj, Akansha and Cuccu, Giuseppe and Cudr{\'e}-Mauroux, Philippe}, - booktitle = {Proceedings of the AAAI conference on artificial intelligence}, - title = {Marta: Leveraging human rationales for explainable text classification}, - number = {7}, - pages = {5868--5876}, - volume = {35}, - year = {2021}, -} - -@Article{agusti2021deep, - author = {Agust{\'\i}, Marc and Altmeyer, Patrick and Vidal-Quadras, Ignacio}, - title = {Deep vector autoregression for macroeconomic data}, - year = {2021}, -} - -@Article{altmeyer2023yield, - author = {Altmeyer, Patrick and Boneva, Lena and Kinston, Rafael and Saha, Shreyosi and Stoja, Evarist}, - title = {Yield curve sensitivity to investor positioning around economic shocks}, - year = {2023}, -} - -@Misc{DHPC2022, - author = {{D}elft {H}igh {P}erformance {C}omputing {C}entre ({DHPC})}, - title = {{D}elft{B}lue {S}upercomputer ({P}hase 1)}, - howpublished = {\url{https://www.tudelft.nl/dhpc/ark:/44463/DelftBluePhase1}}, - note = {Accessed: 2024-01-10}, - year = {2022}, -} - -@Article{lecun1998gradient, - author = {LeCun, Yann and Bottou, L{\'e}on and Bengio, Yoshua and Haffner, Patrick}, - title = {Gradient-based learning applied to document recognition}, - number = {11}, - pages = {2278--2324}, - volume = {86}, - journal = {Proceedings of the IEEE}, - publisher = {IEEE}, - year = {1998}, -} - -@Misc{alain2018understanding, - author = {Guillaume Alain and Yoshua Bengio}, - title = {Understanding intermediate layers using linear classifier probes}, - eprint = {1610.01644}, - archiveprefix = {arXiv}, - primaryclass = {stat.ML}, - year = {2018}, -} - -@Misc{belinkov2021probing, - author = {Yonatan Belinkov}, - title = {Probing Classifiers: Promises, Shortcomings, and Advances}, - eprint = {2102.12452}, - archiveprefix = {arXiv}, - primaryclass = {cs.CL}, - year = {2021}, -} - -@Misc{gurnee2023language, - author = {Wes Gurnee and Max Tegmark}, - title = {Language Models Represent Space and Time}, - eprint = {2310.02207}, - archiveprefix = {arXiv}, - primaryclass = {cs.LG}, - year = {2023}, -} - -@Misc{shah2023trillion, - author = {Agam Shah and Suvan Paturi and Sudheer Chava}, - title = {Trillion Dollar Words: A New Financial Dataset, Task & Market Analysis}, - eprint = {2305.07972}, - archiveprefix = {arXiv}, - primaryclass = {cs.CL}, - year = {2023}, -} - -@Misc{liu2019roberta, - author = {Yinhan Liu and Myle Ott and Naman Goyal and Jingfei Du and Mandar Joshi and Danqi Chen and Omer Levy and Mike Lewis and Luke Zettlemoyer and Veselin Stoyanov}, - title = {RoBERTa: A Robustly Optimized BERT Pretraining Approach}, - eprint = {1907.11692}, - archiveprefix = {arXiv}, - primaryclass = {cs.CL}, - year = {2019}, -} - -@Misc{altmeyer2023faithful, - author = {Patrick Altmeyer and Mojtaba Farmanbar and Arie van Deursen and Cynthia C. S. Liem}, - title = {Faithful Model Explanations through Energy-Constrained Conformal Counterfactuals}, - eprint = {2312.10648}, - archiveprefix = {arXiv}, - primaryclass = {cs.LG}, - year = {2023}, -} - -@Misc{touvron2023llama, - author = {Hugo Touvron and Thibaut Lavril and Gautier Izacard and Xavier Martinet and Marie-Anne Lachaux and Timothée Lacroix and Baptiste Rozière and Naman Goyal and Eric Hambro and Faisal Azhar and Aurelien Rodriguez and Armand Joulin and Edouard Grave and Guillaume Lample}, - title = {{LLaMA: Open and Efficient Foundation Language Models}}, - eprint = {2302.13971}, - archiveprefix = {arXiv}, - primaryclass = {cs.CL}, - year = {2023}, -} - -@Misc{dasgupta2013experiments, - author = {Sanjoy Dasgupta}, - title = {{Experiments with Random Projection}}, - eprint = {1301.3849}, - archiveprefix = {arXiv}, - primaryclass = {cs.LG}, - year = {2013}, -} - -@Misc{altmeyer2024position, - author = {Patrick Altmeyer and Andrew M. Demetriou and Antony Bartlett and Cynthia C. S. Liem}, - title = {Position Paper: Against Spurious Sparks-Dovelating Inflated AI Claims}, - eprint = {2402.03962}, - archiveprefix = {arXiv}, - primaryclass = {cs.AI}, - year = {2024}, -} - -@Article{he2023how, - author = {He, Gaole and Buijsman, Stefan and Gadiraju, Ujwal}, - title = {How Stated Accuracy of an AI System and Analogies to Explain Accuracy Affect Human Reliance on the System}, - doi = {10.1145/3610067}, - number = {CSCW2}, - url = {https://doi.org/10.1145/3610067}, - volume = {7}, - abstract = {AI systems are increasingly being used to support human decision making. It is important that AI advice is followed appropriately. However, according to existing literature, users typically under-rely or over-rely on AI systems, and this leads to sub-optimal team performance. In this context, we investigate the role of stated system accuracy by contrasting the lack of system information with the presence of system accuracy in a loan prediction task. We explore how the degree to which humans understand system accuracy influences their reliance on the AI system, by investigating numeracy levels and with the aid of analogies to explain system accuracy in a first of its kind between-subjects study (N=281). We found that explaining the stated accuracy of a system using analogies failed to help users rely on the AI systemappropriately (i.e., the tendency of users to rely on the system when the system is correct, or on themselves otherwise). To eliminate the impact of subjective attitudes towards analogy domains, we conducted a within-subjects study (N=248) where each participant worked on tasks with analogy-based explanations from different domains. Results from this second study confirmed that explaining stated accuracy of the system with analogies was not sufficient to facilitate appropriate reliance on the AI system in the context of loan prediction tasks, irrespective of individual user differences. Based on our findings from the two studies, we reason that the under-reliance on the AI system may be a result of users' overestimation of their own ability to solve the given task. Thus, although familiar analogies can be effective in improving the intelligibility of stated accuracy of the system, an improved understanding of system accuracy does not necessarily lead to improved system reliance and team performance.}, - address = {New York, NY, USA}, - articleno = {276}, - issue_date = {October 2023}, - journal = {Proc. ACM Hum.-Comput. Interact.}, - keywords = {analogy, human-subjects experiment, reliance, trust}, - month = {oct}, - numpages = {29}, - publisher = {Association for Computing Machinery}, - year = {2023}, -} - -@Article{london2019artificial, - author = {London, Alex John}, - title = {Artificial intelligence and black-box medical decisions: accuracy versus explainability}, - number = {1}, - pages = {15--21}, - volume = {49}, - journal = {Hastings Center Report}, - publisher = {Wiley Online Library}, - year = {2019}, -} - -@Article{robbins2019misdirected, - author = {Robbins, Scott}, - title = {A misdirected principle with a catch: explicability for AI}, - number = {4}, - pages = {495--514}, - volume = {29}, - journal = {Minds and Machines}, - publisher = {Springer}, - year = {2019}, -} - -@InProceedings{biswas2022chime, - author = {Biswas, Shreyan and Corti, Lorenzo and Buijsman, Stefan and Yang, Jie}, - booktitle = {Proceedings of the AAAI Conference on Human Computation and Crowdsourcing}, - title = {CHIME: Causal Human-in-the-Loop Model Explanations}, - number = {1}, - pages = {27--39}, - volume = {10}, - year = {2022}, -} - -@InProceedings{alufaisan2021does, - author = {Alufaisan, Yasmeen and Marusich, Laura R and Bakdash, Jonathan Z and Zhou, Yan and Kantarcioglu, Murat}, - booktitle = {Proceedings of the AAAI Conference on Artificial Intelligence}, - title = {Does explainable artificial intelligence improve human decision-making?}, - number = {8}, - pages = {6618--6626}, - volume = {35}, - year = {2021}, -} - -@InProceedings{altmeyer2024faithful, - author = {Altmeyer, Patrick and Farmanbar, Mojtaba and van Deursen, Arie and Liem, Cynthia CS}, - booktitle = {Proceedings of the AAAI Conference on Artificial Intelligence}, - title = {Faithful Model Explanations through Energy-Constrained Conformal Counterfactuals}, - number = {10}, - pages = {10829--10837}, - volume = {38}, - year = {2024}, -} - -@Misc{hengst2024conformal, - author = {Floris den Hengst and Ralf Wolter and Patrick Altmeyer and Arda Kaygan}, - title = {Conformal Intent Classification and Clarification for Fast and Accurate Intent Recognition}, - eprint = {2403.18973}, - archiveprefix = {arXiv}, - primaryclass = {cs.CL}, - year = {2024}, -} - -@Comment{jabref-meta: databaseType:biblatex;} - -@Comment{jabref-meta: keypatterndefault:[auth:lower][year][veryshorttitle:lower];} - -@Comment{jabref-meta: saveActions:disabled; -all-text-fields[identity] -date[normalize_date] -month[normalize_month] -pages[normalize_page_numbers] -;} diff --git a/profile/blog/posts/causal-recourse/index.html b/profile/blog/posts/causal-recourse/index.html deleted file mode 100644 index 1597120..0000000 --- a/profile/blog/posts/causal-recourse/index.html +++ /dev/null @@ -1,778 +0,0 @@ - - - - - - - - - - - - -When Causal meets Recourse - - - - - - - - - - - - - - - - - - - - - - - -
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    Counterfactual Explanations through Structural Causal Models

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    This post introduces a new tool in CounterfactualExplanations.jl, enhancing the package with causal reasoning to generate counterfactual explanations. The functionality can be used to explain machine learning algorithms developed in Julia and other popular programming languages like Python and R. Unlike traditional counterfactual generators, this approach utilizes causal information to perturb features intelligently.

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    Jorge Luiz Franco

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    Introduction

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    In recent years, the need for interpretable and explainable AI has surged, particularly in high-stakes domains. Counterfactual explanations provide a means to understand how changes to input features could alter the outcomes of machine learning models. This blog post presents a new tool in the CounterfactualExplanations.jl package, developed during my JSoC (Julia Summer of Code) project, which incorporates causal reasoning into counterfactual generation.

    -
    -
    -

    Project Overview

    -

    This project aimed to enhance the CounterfactualExplanations.jl package by infusing it with a robust mathematical foundation for minimal algorithmic recourse, based on the principles of causal reasoning (Karimi, Schölkopf, and Valera 2021).

    -
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    Key Contributions

    -

    During the project, I contributed to two key repositories:

    -
      -

    1. CounterfactualExplanations.jl: Developed a new tool for generating counterfactual explanations using causal information. This allows users to create smarter perturbations rather than random adjustments, ultimately providing more meaningful insights.

      2. -

    2. CausalInference.jl: Implemented a Structural Causal Model (SCM) structure that extracts information from data, laying the groundwork for the causal reasoning capabilities in CounterfactualExplanations.jl.

      3. -
    -

    This was an amazing experience, not just experience contribute to two repositories simultaneously, but also to work with the mantainers of these repos. I learned a lot about the Julia language and the Julia community. This was possible because of the mentorship of Patrick Altmeyer(CounterfactualExplanations) and Moritz Schauer (CausalInference), who guided me throughout the project and are amazing researchers.

    -
    -
    -

    The MINTGenerator

    -

    In this project, we developed the MINTGenerator, a counterfactual generator based on the Recourse through Minimal Intervention (MINT) method proposed by Karimi, Schölkopf, and Valera (2021).

    -
    -
    -

    Description

    -

    The MINTGenerator incorporates causal reeasoning in algorithm recourse to achieve minimal interventions when generating a counterfactual explanation. In this sense, the main ideia is that just perturbating a black box model without taking into account the causal relations in the data can guide to misleading recommendations. Here we now shift to a perspective where every action/pertubation is an intervetion in the causal graph of the problem, thus the change is not made just in the intervened upon variable, but also in its childs in the causal structure. The generator utilizes a Structural Causal Model(SCM) to encode the variables in a way that causal effects are propagated and uses a generic gradient-based generator to create the search path, that is, any gradient-base generator (ECCo, REVISE, Watcher, …) can be used with the MINT SCM encoder to generate counterfactual samples in latent space for minimal intervetions algorithm recourse.

    -

    The MINT algorithm minimizes a loss function that combines the causal constraints of the SCM and the distance between the generated counterfactual and the original input. Since we want a gradient-based generator, we need to pass the constrained optimizaiton problem into an unconstrained one and we do this by using the Lagrangian. Initially, as defined in (Karimi, Schölkopf, and Valera 2021), we aim to aim to find the minimal cost set of actions \(A\) (in the form of structural interventions) that results in a counterfactual instance yielding the favorable output from \(h\),

    -\[\begin{aligned} - -A^* \in \arg\min_A \text{cost}(A; \mathbf{x}_F)\\ -\textrm{s.t.} \quad h(\mathbf{x}_{SCF}) \neq h(\mathbf{x}_F) \; \; \text{,}\\ - -\end{aligned}\] -

    where \(\mathbf{x}_F\) is the original input, \(\mathbf{x}_{SCF}\) is the counterfactual instance, and \(h\) is the black-box model. We use the \(\mathbf{x}_{SCF}\) terminology because the counterfactual is derived from the SCM,

    -

    \[\begin{equation} - -x_{SCF_i} = -\begin{cases} -x_{F_i} + \delta_i, & \text{if } i \in I \\ -x_{F_i} + f_i(\text{pa}_{SCF_i}) - f_i(\text{pa}_{F_i}), & \text{if } i \notin I \; \; \text{,} -\end{cases} - -\end{equation}\]

    -

    where \(I\) is the set of intervened upon variables, \(f_i\) is the function that generates the value of the variable \(i\) given its parents, and \(\text{pa}_{SCF_i}\) and \(\text{pa}_{F_i}\) are the parents of the variable \(i\) in the counterfactual and original instance, respectively. This closed formula for the decision variable \(\mathbf{x}_{SCF}\) is what makes possible to use a gradient-based generator, since with it the lagrangian is differentiable,

    -

    \[\begin{equation} -\mathcal{L}(A ; \lambda) = \text{cost}(A; \mathbf{x}_F) + \lambda \left(h(\mathbf{x}_{SCF}) - h(\mathbf{x}_F) \right) \; \; \text{,} -\end{equation}\]

    -

    or in simple terms and more standard, since \(\lambda\) is constant,

    -

    \[\begin{equation} -\mathcal{L_{\texttt{MINT}}}(\mathbf{x}_{SCF}) = \lambda \text{cost}(\mathbf{x}_{SCF}; \mathbf{x}_F) + \text{yloss}(\mathbf{x}_{SCF},y^*) \; \; \text{,} -\end{equation}\]

    -

    where \(y^*\) is clearly \(h(x_F)\) and \(\text{yloss}\) is :

    -

    \[\begin{equation} -\text{yloss}(\mathbf{x}_{SCF}, y^*) = h \left(\left\{ x_{F_i} + \delta_i [i \in I] + \left(f_i(\text{pa}_{SCF_i}) - f_i(\text{pa}_{F_i}) \right) [i \notin I] \right\}_{i=1}^n \right) - y^* \; \; \text{.} -\end{equation}\]

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    Implementation

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    CausalInference.jl

    -

    In terms of implementation, we need to capture the causal relations from the data, that’s where CausalInference.jl comes in. However, before the project, the package did not have a SCM structure, in the sense that the methods just captured the topological Directed Acyclic Graph (DAG) that showed the causality ruling the data, that is, no causal structural equations were provided,

    -
    -
    using CausalInference
-using Plots, GraphRecipes
-using Random
-Random.seed!(1)
-
-N = 2000 # number of data points
-
-x = randn(N)
-v = x + randn(N)*0.25
-w = x + randn(N)*0.25
-z = v + w + randn(N)*0.25
-s = z + randn(N)*0.25
-
-df = (x=x, v=v, w=w, z=z, s=s)
-
-est_g, score = ges(df; penalty=1.0, parallel=true)
-
-graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)])
    -
    -

    So, our goal was given the DAG provided by the ges method in the causal discovery (Chickering 2003), generate equations that rules each of these causal relations, represented in the DAG as directed edges. The SCM is the union of the DAG and these causal equations, that is, the SCM is a tuple \((G, \mathbf{f})\), where \(G\) is the DAG and \(\mathbf{f}\) is the set of functions that generates the value of each variable given its parents.

    -

    Our solution for constructing the structural causal equations was to assume that the data was generated by a linear model, ie, the causal relations were linear. For the DAG provided in the code example we derive

    -

    \[ v = \mathcal{b}_v \]

    -

    \[ x = \mathcal{a}_{v \to x} v + \mathcal{b}_x \]

    -

    \[ w = \mathcal{a}_{x \to w} x + \mathcal{b}_w \]

    -

    \[ z = \mathcal{a}_{v \to z} v+ \mathcal{a}_{w \to z} w + \mathcal{b}_z \]

    -

    \[ s = \mathcal{a}_{z \to s} z + \mathcal{b}_s \]

    -

    and that’s the tricky thing, as we can see these causal equations are different than the ones that generated the data, but they are the ones that respect the causal system obtained from the obtained DAG. Here \(\mathcal{b}_i\) and \(\mathcal{a}_{i \to j}\) are the intercept term and the coefficient obtained from the linear regression, respectively. To correctly solve the linear regression respecting the dependencies of the causal graph, we use topological_sort_by_dfs from Graphs.jl.

    -

    Now, with the SCM structure in hand, we see that the representation could be a struct containing the DAG and the coefficients/intercepts of the causal equations, this maps exactly the tuple \((G, \mathbf{f})\) that we defined. However, since we need these equations to be differentiable, we need to define a function that takes the SCM and returns the value of the variable given its parents and using just the coefficients and the DAG, lead to errors, because AutoDiff does not deal well with functions that are conditioned (if statements). So, we need to define a way to retrieve the system of causal equations in a smooth way and that’s where the causal_effects matrix comes to the rescue.

    -

    Let the factual vector of features be denoted as:

    -

    \[ -\mathbf{x}_F = -\begin{bmatrix} -x_{F_1} \\ -x_{F_2} \\ -x_{F_3} \\ -\vdots \\ -x_{F_n} -\end{bmatrix} -\]

    -

    Let the causal_effects matrix be:

    -

    \[ -\mathbf{C} = -\begin{bmatrix} -a_{11} & a_{12} & \cdots & a_{1n} & b_1 \\ -a_{21} & a_{22} & \cdots & a_{2n} & b_2 \\ -a_{31} & a_{32} & \cdots & a_{3n} & b_3 \\ -\vdots & \vdots & \ddots & \vdots & \vdots \\ -a_{n1} & a_{n2} & \cdots & a_{nn} & b_n \\ -\end{bmatrix} -\]

    -

    Here, \(a_{ij}\) represents the coefficient from the causal effect of \(x_{F_j}\) on \(x_{F_i}\), and \(b_i\) represents the intercept term for the variable \(x_{F_i}\).

    -

    The matrix multiplication of the causal_effects matrix with the factual vector (excluding the bias term) is given by:

    -

    \[ -\mathbf{C}_{:, 1:n} \cdot \mathbf{x}_F = -\begin{bmatrix} -a_{11} & a_{12} & \cdots & a_{1n} \\ -a_{21} & a_{22} & \cdots & a_{2n} \\ -a_{31} & a_{32} & \cdots & a_{3n} \\ -\vdots & \vdots & \ddots & \vdots \\ -a_{n1} & a_{n2} & \cdots & a_{nn} -\end{bmatrix} -\begin{bmatrix} -x_{F_1} \\ -x_{F_2} \\ -x_{F_3} \\ -\vdots \\ -x_{F_n} -\end{bmatrix} -\]

    -

    Finally, we add the bias term:

    -

    \[ -\mathbf{x}_{SCF} = \mathbf{C}_{:, 1:n} \cdot \mathbf{x}_F + -\begin{bmatrix} -b_1 \\ -b_2 \\ -b_3 \\ -\vdots \\ -b_n -\end{bmatrix} -\]

    -

    In expanded form:

    -

    \[ -\mathbf{x}_{SCF_i} = a_{i1} x_{F_1} + a_{i2} x_{F_2} + \cdots + a_{in} x_{F_n} + b_i, \quad \forall i = 1, 2, \dots, n -\]

    -

    This equation shows how each counterfactual variable \(x_{SCF_i}\) is generated as a linear combination of the factual inputs \(x_{F_j}\) based on the causal effects matrix, with an intercept term \(b_i\) added for each variable.

    -

    One can note that the orphan nodes, that is, the nodes that do not have parents in the DAG, are going to be equal to the intercept term \(\mathcal{b}_\hat{o}\). The intuition behind this is that when we do the linear regression, variables that have no causal parents are just equal to the unconditional mean of the variable, i.e, we get \(x_{SCF_\hat{o}} = \mathbb{E}(x_\hat{o})\). Because of this, in some cases a better understanding of the regression is needed, so the residuals are also part of the SCM structure,

    -
    -
    struct SCM
-    variables::Vector{String}
-    coefficients::Vector{Vector{Float64}}
-    residuals::Vector{Vector{Float64}}
-    dag::DiGraph
-    causal_effects::Matrix{Float64}
-end
    -
    -
    -
    -

    CounterfactualExplanations.jl

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    Conclusion

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    - - -
    - -

    References

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    -Chickering, David Maxwell. 2003. “Optimal Structure Identification with Greedy Search.” J. Mach. Learn. Res. 3 (null): 507–54. https://doi.org/10.1162/153244303321897717. -
    -
    -Karimi, Amir-Hossein, Bernhard Schölkopf, and Isabel Valera. 2021. “Algorithmic Recourse: From Counterfactual Explanations to Interventions.” In Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency, 353–62. FAccT ’21. New York, NY, USA: Association for Computing Machinery. https://doi.org/10.1145/3442188.3445899. -
    -
    - - -
    - - - - - \ No newline at end of file diff --git a/profile/blog/posts/causal-recourse/index.qmd b/profile/blog/posts/causal-recourse/index.qmd index cc2bb1d..8aa42f3 100644 --- a/profile/blog/posts/causal-recourse/index.qmd +++ b/profile/blog/posts/causal-recourse/index.qmd @@ -1,10 +1,9 @@ --- -title: "When Causal meets Recourse" +title: "When Causality meets Recourse" subtitle: "Counterfactual Explanations through Structural Causal Models" -bibliography: bib.bib -date: '2024-09-03' +date: '2024-09-17' description: | - This post introduces a new tool in CounterfactualExplanations.jl, enhancing the package with causal reasoning to generate counterfactual explanations. The functionality can be used to explain machine learning algorithms developed in Julia and other popular programming languages like Python and R. Unlike traditional counterfactual generators, this approach utilizes causal information to perturb features intelligently. + This post introduces a new tool in CounterfactualExplanations.jl, enhancing the package with causal reasoning to generate counterfactual explanations. author: - name: Jorge Luiz Franco url: https://www.linkedin.com/in/jorgelwyz/ @@ -13,11 +12,14 @@ categories: - explainable AI - causality - Julia -image: www/intro.gif +image: www/intro.png execute: - eval: false + eval: true echo: true -draft: false +engine: julia +julia: + exeflags: ["--project=./"] +code-fold: show --- # Introduction @@ -26,7 +28,7 @@ In recent years, the need for interpretable and explainable AI has surged, parti # Project Overview -This project aimed to enhance the CounterfactualExplanations.jl package by infusing it with a robust mathematical foundation for minimal algorithmic recourse, based on the principles of causal reasoning [@karimi2021]. +This project aimed to enhance the CounterfactualExplanations.jl package by infusing it with a robust mathematical foundation for minimal algorithmic recourse, based on the principles of causal reasoning [@karimi2021algorithmic]. ## Key Contributions @@ -36,60 +38,55 @@ During the project, I contributed to two key repositories: 2. **CausalInference.jl**: Implemented a Structural Causal Model (SCM) structure that extracts information from data, laying the groundwork for the causal reasoning capabilities in CounterfactualExplanations.jl. -This was an amazing experience, not just experience contribute to two repositories simultaneously, but also to work with the mantainers of these repos. I learned a lot about the Julia language and the Julia community. This was possible because of the mentorship of Patrick Altmeyer(CounterfactualExplanations) and Moritz Schauer (CausalInference), who guided me throughout the project and are amazing researchers. - - +This was an amazing experience, not just experience contribute to two repositories simultaneously, but also to work with the mantainers of these repos. I learned a lot about the Julia language and the Julia community. This was possible because of the mentorship of Patrick Altmeyer (CounterfactualExplanations) and Moritz Schauer (CausalInference), who guided me throughout the project and are amazing researchers. ## The `MINTGenerator` In this project, we developed the MINTGenerator, a counterfactual generator based on the Recourse through Minimal -Intervention (MINT) method proposed by @karimi2021. +Intervention (MINT) method proposed by @karimi2021algorithmic. ## Description The MINTGenerator incorporates causal reeasoning in algorithm recourse to achieve minimal interventions when generating a counterfactual explanation. In this sense, the main ideia is that just perturbating a black box model without taking into account the causal relations in the data can guide to misleading recommendations. Here we now shift to a perspective where every action/pertubation is an intervetion in the causal graph of the problem, thus the change is not made just in the intervened upon variable, but also in its childs in the causal structure. The generator utilizes a Structural Causal Model(SCM) to encode the variables in a way that causal effects are propagated and uses a generic gradient-based generator to create the search path, that is, any gradient-base generator (ECCo, REVISE, Watcher, ...) can be used with the MINT SCM encoder to generate counterfactual samples in latent space for minimal intervetions algorithm recourse. -The MINT algorithm minimizes a loss function that combines the causal constraints of the SCM and the distance between the generated counterfactual and the original input. Since we want a gradient-based generator, we need to pass the constrained optimizaiton problem into an unconstrained one and we do this by using the Lagrangian. Initially, as defined in [@karimi2021], we aim to aim to find the minimal cost set of actions $A$ (in the form of structural interventions) that results in a counterfactual instance yielding the favorable output from $h$, - +The MINT algorithm minimizes a loss function that combines the causal constraints of the SCM and the distance between the generated counterfactual and the original input. Since we want a gradient-based generator, we need to pass the constrained optimizaiton problem into an unconstrained one and we do this by using the Lagrangian. Initially, as defined in [@karimi2021algorithmic], we aim to aim to find the minimal cost set of actions $A$ (in the form of structural interventions) that results in a counterfactual instance yielding the favorable output from $h$, +$$ \begin{aligned} A^* \in \arg\min_A \text{cost}(A; \mathbf{x}_F)\\ \textrm{s.t.} \quad h(\mathbf{x}_{SCF}) \neq h(\mathbf{x}_F) \; \; \text{,}\\ \end{aligned} +$$ where $\mathbf{x}_F$ is the original input, $\mathbf{x}_{SCF}$ is the counterfactual instance, and $h$ is the black-box model. We use the $\mathbf{x}_{SCF}$ terminology because the counterfactual is derived from the SCM, -\begin{equation} - +$$ x_{SCF_i} = \begin{cases} x_{F_i} + \delta_i, & \text{if } i \in I \\ x_{F_i} + f_i(\text{pa}_{SCF_i}) - f_i(\text{pa}_{F_i}), & \text{if } i \notin I \; \; \text{,} \end{cases} - -\end{equation} +$$ where $I$ is the set of intervened upon variables, $f_i$ is the function that generates the value of the variable $i$ given its parents, and $\text{pa}_{SCF_i}$ and $\text{pa}_{F_i}$ are the parents of the variable $i$ in the counterfactual and original instance, respectively. This closed formula for the decision variable $\mathbf{x}_{SCF}$ is what makes possible to use a gradient-based generator, since with it the lagrangian is differentiable, -\begin{equation} +$$ \mathcal{L}(A ; \lambda) = \text{cost}(A; \mathbf{x}_F) + \lambda \left(h(\mathbf{x}_{SCF}) - h(\mathbf{x}_F) \right) \; \; \text{,} -\end{equation} +$$ or in simple terms and more standard, since $\lambda$ is constant, -\begin{equation} +$$ \mathcal{L_{\texttt{MINT}}}(\mathbf{x}_{SCF}) = \lambda \text{cost}(\mathbf{x}_{SCF}; \mathbf{x}_F) + \text{yloss}(\mathbf{x}_{SCF},y^*) \; \; \text{,} -\end{equation} +$$ where $y^*$ is clearly $h(x_F)$ and $\text{yloss}$ is : -\begin{equation} +$$ \text{yloss}(\mathbf{x}_{SCF}, y^*) = h \left(\left\{ x_{F_i} + \delta_i [i \in I] + \left(f_i(\text{pa}_{SCF_i}) - f_i(\text{pa}_{F_i}) \right) [i \notin I] \right\}_{i=1}^n \right) - y^* \; \; \text{.} -\end{equation} - - +$$ ## Implementation @@ -98,6 +95,8 @@ where $y^*$ is clearly $h(x_F)$ and $\text{yloss}$ is : In terms of implementation, we need to capture the causal relations from the data, that's where `CausalInference.jl` comes in. However, before the project, the package did not have a SCM structure, in the sense that the methods just captured the topological Directed Acyclic Graph (DAG) that showed the causality ruling the data, that is, no causal structural equations were provided, ```{julia} +#| output: true + using CausalInference using Plots, GraphRecipes using Random @@ -115,14 +114,15 @@ df = (x=x, v=v, w=w, z=z, s=s) est_g, score = ges(df; penalty=1.0, parallel=true) -graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)]) +plt = graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)], size=(500,500), nodesize=0.3) +savefig(plt, "www/intro.png") +display(plt) ``` -So, our goal was given the DAG provided by the `ges` method in the causal discovery [@ges2003], generate equations that rules each of these causal relations, represented in the DAG as directed edges. The SCM is the union of the DAG and these causal equations, that is, the SCM is a tuple $(G, \mathbf{f})$, where $G$ is the DAG and $\mathbf{f}$ is the set of functions that generates the value of each variable given its parents. +So, our goal was given the DAG provided by the `ges` method in the causal discovery [@chickering2003optimal], generate equations that rules each of these causal relations, represented in the DAG as directed edges. The SCM is the union of the DAG and these causal equations, that is, the SCM is a tuple $(G, \mathbf{f})$, where $G$ is the DAG and $\mathbf{f}$ is the set of functions that generates the value of each variable given its parents. Our solution for constructing the structural causal equations was to assume that the data was generated by a linear model, ie, the causal relations were linear. For the DAG provided in the code example we derive - $$ v = \mathcal{b}_v $$ $$ x = \mathcal{a}_{v \to x} v + \mathcal{b}_x $$ @@ -209,6 +209,8 @@ This equation shows how each counterfactual variable $x_{SCF_i}$ is generated as One can note that the `orphan` nodes, that is, the nodes that do not have parents in the DAG, are going to be equal to the intercept term $\mathcal{b}_\hat{o}$. The intuition behind this is that when we do the linear regression, variables that have no causal parents are just equal to the unconditional mean of the variable, i.e, we get $x_{SCF_\hat{o}} = \mathbb{E}(x_\hat{o})$. Because of this, in some cases a better understanding of the regression is needed, so the residuals are also part of the SCM structure, ```{julia} +#| eval: false + struct SCM variables::Vector{String} coefficients::Vector{Vector{Float64}} diff --git a/profile/blog/posts/causal-recourse/www/intro.png b/profile/blog/posts/causal-recourse/www/intro.png new file mode 100644 index 0000000000000000000000000000000000000000..db4d335ed11189b2f351481d3f8f1d2b3373a44d GIT binary patch literal 20746 zcmd?Rhd*pt=`9Z-LKbu-Pe6x&+Be{r6s)}X}))wC$*Kw`R^IqX^5B0*ltgHtgoLI7gF+HB%xm)N<`<$pmU2%oJ^Drnp;OQOyPSG3v zw$n~y=y)Dthu?T2Q_@uaQ_hb?Lwgc(T@xE_|KZa(I$A7lG9}uR@y!1p{WF3Yg{C<1 z{Q2`^>sk7^F-MC6X2N#&q{PGy%V%gznfskpPiM9_W#OEx0IrZ>JR^u8Xk6&f=#!2I9rxzHxhiZF z>W2mIj919sODdlI9_@sO#`dNcZ-?;iU9}3O-Ee_Bbeu+MOXTc^5|&ehe>M^xsef=H zLbG`dpW*7UeDFbhq@GWmG%dY3B34s@z{61V z{2hT#I#K3v*qnVU-_myUX(&z2{_sL>e?UM$$<^=S849y=b5k_cd}eL2)hrtYWq)1& zwoyP@MZeRg=2tt@httRkQ+@T9T`R_XTw~rMEjZi8i`s`^^Wqf7LkqoO=^PcpppdTW 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    Paving the Way Towards Low-Overhead Uncertainty Calibration

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    An Accessible Intro to Laplace Approximations in Julia for Bayesian Deep Learning

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    bayesian deep learning
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    laplace approximation
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    guest post
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    - A guest blog post by a team of students from TU Delft, who have contributed multiple improvements to LaplaceRedux.jl. -
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    Authors
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    Severin Bratus

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    Mark Ardman

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    Adelina Cazacu

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    Andrei Ionescu

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    Ivan Makarov

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    Patrick Altmeyer

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    Published
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    July 4, 2023

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    -Guest Blog Post -
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    This blog post was originally written by Severin Bratus and colleagues from TU Delft and published on Medium. This version of the post includes only minor edits. If you would like to contribute a guest blog post, please get in touch.

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    This post summarizes a quarter-long second-year BSc coursework project at TU Delft. Our team of five students has made multiple improvements to LaplaceRedux.jl, due to Patrick Altmeyer. Inspired by its Pythonic counterpart, laplacet-torch, this Julia library aims to provide low-overhead Bayesian uncertainty calibration to deep neural networks via Laplace Approximations [@daxberger2021laplace].

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    A nice image to attract your attention. The exact inverse Fisher information matrix for a MNIST classifier network (left), its block-diagonal and tri-block-diagonal approximations (middle), and the absolute error (right). Source: Martens & Grosse (2015)
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    We will begin by demystifying the technical terms in the last sentence, in order to explain our contributions to the library and highlight some impressions from the experience. Note that our team has begun working on this PhD-tier subject only having had some introductory courses on probability and statistics, machine learning, and computational intelligence, without any prior exposure to Julia.

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    Bayesian Learning

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    Uncertainty calibration remains a crucial issue in safety-critical applications of modern AI, as, for instance, in autonomous driving. You would want your car autopilot not only to make accurate predictions but also to indicate when a model prediction is uncertain, to give control back to the human driver.

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    A model is well-calibrated if the confidence of a prediction matches its true error rate. Note that you can have well-fit models that are badly calibrated, and vice versa (just like in life, you meet smart people, yet annoyingly arrogant).

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    The standard deep learning training process of gradient descent converges at a weight configuration that minimizes the loss function. The model obtained may be great, yet it is only a point estimate of what the weight parameters should look like.

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    However, with the sheer immensity of the weight space, neural networks are probably underspecified by the data (or, overfit). As neural networks can approximate highly complex functions, many weight configurations would yield roughly the same training loss, yet with varying abilities to generalize outside the training dataset. This is why there are so many regularization methods out there, to keep the models simpler. One radical, yet effective approach is described by @lecun1989optimal:

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    … it is possible to take a perfectly reasonable network, delete half (or more) of the weights and wind up with a network that works just as well, or better.

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    -Figure 1: The loss landscape. One can imagine gradient descent as a particle, let’s say a ball, or a grain of sand, rolling to the bottom of a pit. Then for Bayesian Learning, we have as if a pile of sand poured around at that bottom point, with the pile being thicker where loss is lower. This proverbial sand pile would represent the posterior parameter distribution. Figure due to @amini2019spatial -
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    The way gradient is usually illustrated is with a picture like the one shown in Figure 1 above a curved terrain of the loss function across the parameter space. Each point of the horizontal plane corresponds to some configuration of parameters. Gradient descent seeks the point at the bottom of this terrain, as the point with the lowest loss, however as the loss-curvature is highly non-convex and high-dimensional there are many directions in which we could move and still maintain a low loss. Thus instead of a singular point we would like to specify a probability distribution around that optimal point. Bayesian methods, and in particular Laplace Approximations, allow us to do this!

    -

    Firstly, the Bayesian approach to neural network uncertainty calibration is that of modelling the posterior using Bayes’ Theorem:

    -

    \[ -p(\theta \mid \mathcal{D}) = \tfrac{1}{Z} \,p(\mathcal{D} \mid \theta) \, p(\theta), \qquad Z:= p(\mathcal{D}) = \textstyle\int p(\mathcal{D} \mid \theta) \, p(\theta) \,d\theta -\]

    -

    Here \(p(\mathcal{D} \mid \theta)\) is the likelihood of the data given by the parameters \(\theta\). The prior distribution \(p(\theta)\) specifies our beliefs about what the model parameters would be prior to observing the data. Finally, the intractable constant \(Z\) is called the evidence: it characterizes the probability of observing \(\mathcal{D}\) as a whole, across all possible parameter settings (see here for details).

    -

    For models returning a probability distribution (e.g. classifiers), the loss is commonly defined as the negative log-likelihood. Thus if gradient descent minimizes loss, it maximizes the likelihood, producing the maximum likelihood estimate (MLE), which (assuming a uniform prior) also maximizes the posterior. This is why we call this point the maximum a posteriori, or the MAP. It makes sense to model this point as the mode of the posterior distribution, which could, for example, be a normal Gaussian distribution (see also the introductory post on this blog).

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    Laplace Approximations

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    We do this by a simple-yet-smart trick introduced back in the late 18th century by Pierre-Simon Laplace, the self-proclaimed “greatest French mathematician of his time”. In general, the Laplace Approximation (LA) aims to find a Gaussian approximation to a probability density (in our case, the posterior) defined over a set of continuous variables (in our case, the weights) [@bishop2006pattern]. We can then estimate the loss (negative log-likelihood) as its second-order Taylor expansion:

    -

    \[ -\mathcal{L}(\mathcal{D}; \theta) \approx \mathcal{L}(\mathcal{D}; \theta_\text{MAP}) + \tfrac{1}{2} (\theta - \theta_\text{MAP})^\intercal \left( \nabla^2 _\theta \mathcal{L}(\mathcal{D}; \theta) \vert_{\theta_\text{MAP}} \right)(\theta - \theta_\text{MAP}) -\]

    -

    Note that the first-order Taylor term vanishes at the MAP since it contains the gradient, and the gradient is zero at MAP, since MAP is a maximum, by definition. What remains is the constant (zeroth-order) term, and the second-order term, containing the Hessian, which is a matrix of partial second-order derivatives.

    -

    Then from this approximation, we can derive the long-sought multivariate normal distribution with the MAP as the mean, and the inverted Hessian as the covariance:

    -

    \[ -p(\theta \mid \mathcal{D}) \approx N(\theta; \theta_\text{MAP}, \varSigma) \qquad\text{with}\qquad \varSigma := \left( \nabla^2_\theta \mathcal{L}(\mathcal{D};\theta) \vert_{\theta_\text{MAP}} \right)^{-1} -\]

    -

    The evidence \(Z\) is now also tractably approximated in closed form, allowing us to apply the Bayes’ theorem, to obtain the posterior distribution \(p(\theta \mid \mathcal{D})\). We can then express the posterior predictive distribution, for an input \(x_*\), prediction \(f(x_*)\), to obtain the probability for an output \(y\).

    -

    The evidence \(Z\) is now also tractably approximated in closed form, allowing us to apply the Bayes’ theorem, to obtain the posterior distribution \(p(\theta \mid \mathcal{D})\). We can then express the posterior predictive distribution, to obtain the probability for an output \(y\), given a prediction \(f(x_*)\) for an input \(x_*\).

    -

    \[ -p(y \mid f(x_*), \mathcal{D}) = \int p(y \mid f_\theta(x_*)) \, p(\theta \mid \mathcal{D}) \,d\theta -\]

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    This is what we are really after, after all — instead of giving one singular point-estimate prediction \(\widehat{y} = f(x_*)\), we make the neural network give a distribution over \(y\).

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    However, since the Hessian, a square matrix, defines the covariance between all model parameters (upon inversion), of which there may be millions or billions, the computation and storage of the Hessian (not to speak of inversion!) become intractable, as its size scales quadratically with the number of parameters involved. Thus to apply Laplace approximations to large models, we must make some simplifications — which brings us to…

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    Hessian approximations

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    Multiple techniques to approximate the Hessian have arisen from a field adjacent, yet distinct from Bayesian learning — that of second-order optimization, where Hessians are used to accelerate gradient descent convergence.

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    One such approximation is the Fisher information matrix, or simply the Fisher:

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    \[ -F := \textstyle\sum_{n=1}^N \mathbb{E}_{\widehat{y} \sim p(y \mid f_\theta(x_n))} \left[ gg^\intercal \right] \quad\text{with}\quad g = \nabla_\theta \log p(\widehat{y} \mid f_\theta(x_n)) \large\vert_{\theta_\text{MAP}} -\]

    -

    Note that if instead of sampling the prediction \(\widehat{y} ~ p(y \mid f(x_n))\) from the model-defined distribution, we take the actual training-set label \(y_n\), the resulting matrix is called the empirical Fisher, which is distinct from the Fisher, yet aligns with it under some conditions, and does not generally capture second-order information. See Kunstner et al. (2019) for an excellent discussion on the distinction.

    -

    Instead of the Fisher, one can use the Generalized Gauss-Newton (GGN):

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    \[ -G := \textstyle\sum_{n=1}^N J(x_n) \left( \nabla^2_{f} \log p(y_n \mid f) \Large\vert_{f=f_{\theta_\text{map}}(x_n)} \right) J(x_n)^\intercal -\text{with}\qquad J(x_n) := \nabla_\theta f_\theta(x_n) \vert_{\theta_\text{map}} -\]

    -

    Here \(J(x_n)\) represents the Jacobian of the model output w.r.t. the parameters. The middle factor \(\nabla^2 …\) is a Hessian of log-likelihood of \(y_n\) w.r.t. model output. Note that the model does not necessarily output ready target probabilities — for instance, classifiers output logits, values that define a probability distribution only after the application of the soft-max.

    -

    Unlike the Fisher, GGN does not require the network to define a probabilistic model on its output [@botev2017practical]. For models defining an exponential family distribution over the output, the two coincide [@kunstner2020limitations]. This applies to classifiers since they define a categorical distribution over the output, but not to simple regression models.

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    These matrices are quadratically large, it is infeasible to store them in full. The simplest estimation is to model the matrix as a diagonal — however one can easily contemplate how crude this approximation can be: for 100 parameters, only 1% of the full Hessian is captured.

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    A more sophisticated approach, due to Martens and Grosse (2015), is inspired by the observation that in practice the covariance matrices (i.e. inverted Hessians) for neural networks are block-diagonal-dominant. Thus we can effectively model the covariance matrix (and hence the Fisher) as a block-diagonal matrix, where blocks correspond to parameters grouped by layers. Additionally, each block is decomposed into two Kronecker factors, reducing the size of data stored several magnitudes more, at a cost of another assumption.

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    Lastly, a novel approach is to sketch a low-rank approximation of the Fisher [@sharma2021sketching]. Figure 2 shows four Hessian approximation structures:

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    -Figure 2: (a) Hessian in full, intractable for large networks. (b) Low-rank. (c) Kronecker-factored Approximate Curvature, a block-diagonal method. (d) Diagonal. Source: @daxberger2021laplace -
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    It is also possible to cut the costs by treating only a subset of the model parameters, i.e. a subnetwork, probabilistically, fixing the remaining parameters at their MAP-estimated values. One special case of subnetwork Laplace that was found to perform well in practice is last-layer Laplace, where the selected subnetwork contains only the weights and biases of the last layer.

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    Our contributions to LaplaceRedux.jl

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    In the scope of the project we have added support for: - multi-class classification, in addition to regression and binary classification; - GGN, in addition to empirical Fisher; - hardware-parallelized batched computation of both the empirical Fisher and the GGN; - subnetwork and last-layer Laplace; - KFAC for multi-class classification with Fisher; and - interfacing with MLJ, a common machine learning framework for Julia.

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    We have also made quality assurance / quality-of-life additions to the repository, adding: - a formatting check in the CI/CD pipeline; - an extensive test suite comparing the results of LaplaceRedux.jl against those of its Python counter-part package laplace-torch; and - a benchmark pipeline tracking possible downturns in performance.

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    Methodology

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    We adhered to the Agile/Scrum practices, with two-week-long sprints, and weekly meetings with our formal client, Patrick Altmeyer. We have prioritized the expected requirements by the Moscow method into must-, could-, should-, and won’t-haves. This is all fairly standard for BSc software projects at TU Delft. By the end of the project, we have completed all of our self-assigned must-haves and should-haves.

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    Pain Points

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    Here we list some obstacles we have encountered along the way: - Julia is slow to compile and load dependencies on less powerful machines. - Stack traces are sometimes rather obscure, though it seems to be the price to pay for macros. - Zygote.jl, the automatic differentiation library, is not self-autodifferentiable – it cannot differentiate its own functions. We would want this since we apply Zygote.jacobians when making predictions with the LA. - There is no accessible tool reporting branch coverage on tests – only line coverage is available. - Limited LSP and Unicode support for Jupyter Lab. - Conversion between Flux and ONNX is not yet implemented. - There is no extension library for Zygote equivalent to BackPACK or ASDL for second-order information.

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    • Zygote.jl, the automatic differentiation library, is not self-autodifferentiable: issue. We would want this since we apply Zygote.jacobians when making predictions with the LA.
      • -
    • There is no accessible tool reporting branch coverage on tests – only line coverage is available.
      • -
    • Limited LSP and Unicode support for Jupyter Lab.
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    • No conversion between Flux and ONNX is implemented yet ONNX.jl
      • -
    • There is no extension library for Zygote equivalent to BackPACK or ASDL for second-order information.
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    Highlights

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    And here is what we found refreshing: - Metaprogramming and first-class support for macros are something completely different for students who are used to Java & Python. - The Julia standard API, and Flux/Zygote, are fairly straightforward to use, and well-thought-out for numerical computing and machine learning.

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    Conclusions

    -

    We have covered some elements of the theory behind Laplace Approximations, laid down our additions to the LaplaceRedux.jl package, and brought out some difficulties we, as complete newcomers to Julia, came across. Hope you have enjoyed the tour, and hopefully it has intrigued you enough to look deeper into Bayesian learning and/or Julia since both are developing at a lively pace. You can check out LaplaceRedux on the JuliaTrustworthyAI GitHub page here. Contributions and comments are welcome!

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    Acknowedgements

    -

    Our team members are Mark Ardman, Severin Bratus, Adelina Cazacu, Andrei Ionescu, and Ivan Makarov. We would like to thank Patrick Altmeyer for the opportunity to work on this unique project and for the continuous guidance throughout the development process. We are also grateful to Sebastijan Dumančić, our coach, Sven van der Voort, our TA mentor, and Antony Bartlett, our supporting advisor.

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    References

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    - - - - - \ No newline at end of file From 0a37fef886cbffc276cd4e3ba1c44db67ec1055a Mon Sep 17 00:00:00 2001 From: pat-alt Date: Tue, 17 Sep 2024 09:13:10 +0200 Subject: [PATCH 05/13] a few fixes --- docs/blog/index.html | 58 +- docs/blog/index.xml | 2350 ++++++++------- .../a-new-tool-for-explainable-ai/index.html | 743 +++-- docs/blog/posts/causal-recourse/index.html | 1274 +++++++++ docs/blog/posts/causal-recourse/www/intro.png | Bin 0 -> 20746 bytes .../conformal-image-classifier/index.html | 2525 ++++++++--------- .../conformal-image-classifier/www/intro.gif | Bin 158239 -> 156116 bytes .../conformal-image-classifier/www/medium.gif | Bin 479170 -> 469884 bytes .../new-package-energysamplers/index.html | 5 +- docs/content/research.html | 46 +- docs/listings.json | 1 + docs/search.json | 269 +- docs/sitemap.xml | 46 +- 13 files changed, 4517 insertions(+), 2800 deletions(-) create mode 100644 docs/blog/posts/causal-recourse/index.html create mode 100644 docs/blog/posts/causal-recourse/www/intro.png diff --git a/docs/blog/index.html b/docs/blog/index.html index c783eca..ff22fcd 100644 --- a/docs/blog/index.html +++ b/docs/blog/index.html @@ -184,7 +184,7 @@ +
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    Taija’s Blog

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    +

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    +When Causality meets Recourse +

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    +Counterfactual Explanations through Structural Causal Models +
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    +This post introduces a new tool in CounterfactualExplanations.jl, enhancing the package with causal reasoning to generate counterfactual explanations. +
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    + +
    +Sep 17, 2024 +
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    +Patrick Altmeyer, Jorge Luiz Franco +
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    +8 min +
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    +9/17/24, 9:07:54 AM +
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    7 min

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    12 min

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    diff --git a/docs/blog/index.xml b/docs/blog/index.xml index 0a71227..c9f0d3a 100644 --- a/docs/blog/index.xml +++ b/docs/blog/index.xml @@ -10,7 +10,371 @@ quarto-1.5.57 -Thu, 05 Sep 2024 22:00:00 GMT +Mon, 16 Sep 2024 22:00:00 GMT + + When Causality meets Recourse + Patrick Altmeyer + Jorge Luiz Franco + https://www.taija.org/blog/posts/causal-recourse/ + +

    Introduction

    +

    In recent years, the need for interpretable and explainable AI has surged, particularly in high-stakes domains. Counterfactual explanations provide a means to understand how changes to input features could alter the outcomes of machine learning models. This blog post presents a new tool in the CounterfactualExplanations.jl package, developed during my JSoC (Julia Summer of Code) project, which incorporates causal reasoning into counterfactual generation.

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    A new tool for explainable AI

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    Counterfactual Explanations in Julia — Part I

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    This post introduces a new Julia package for generating counterfactual explanations. The package can be used to explain machine learning algorithms developed and trained in Julia as well as other popular programming languages like Python and R.

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    April 20, 2022

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    -Turning a 9 (nine) into a 4 (four). -
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    Counterfactual explanations, which I introduced in one of my previous posts1, offer a simple and intuitive way to explain black-box models without opening them. Still, as of today there exists only one open-source library that provides a unifying approach to generate and benchmark counterfactual explanations for models built and trained in Python [@pawelczyk2021carla]. This is great, but of limited use to users of other programming languages 🥲.

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    Enter CounterfactualExplanations.jl: a Julia package that can be used to explain machine learning algorithms developed and trained in Julia, Python and R. Counterfactual explanations fall into the broader category of explainable artificial intelligence (XAI).

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    Explainable AI typically involves models that are not inherently interpretable but require additional tools to be explainable to humans. Examples of the latter include ensembles, support vector machines and deep neural networks. This is not to be confused with interpretable AI, which involves models that are inherently interpretable and transparent such as general additive models (GAM), decision trees and rule-based models.

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    Some would argue that we best avoid explaining black-box models altogether [@rudin2019stop] and instead focus solely on interpretable AI. While I agree that initial efforts should always be geared towards interpretable models, stopping there would entail missed opportunities and anyway is probably not very realistic in times of DALL\(\cdot\)E and Co.

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    Even though […] interpretability is of great importance and should be pursued, explanations can, in principle, be offered without opening the “black box.”

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    — @wachter2017counterfactual

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    This post introduces the main functionality of the new Julia package. Following a motivating example using a model trained in Julia, we will see how easy the package can be adapted to work with models trained in Python and R. Since the motivation for this post is also to hopefully attract contributors, the final section outlines some of the exciting developments we have planned.

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    Counterfactuals for image data 🖼

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    To introduce counterfactual explanations I used a simple binary classification problem in my previous post. It involved a linear classifier and a linearly separable, synthetic data set with just two features. This time we are going to step it up a notch: we will generate counterfactual explanations MNIST data. The MNIST dataset contains 60,000 training samples of handwritten digits in the form of 28x28 pixel grey-scale images [@lecun1998mnist]. Each image is associated with a label indicating the digit (0-9) that the image represents.

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    The CounterfactualExplanations.jl package ships with two black-box models that were trained to predict labels for this data: firstly, a simple multi-layer perceptron (MLP) and, secondly, a corresponding deep ensemble. Originally proposed by @lakshminarayanan2016simple, deep ensembles are really just ensembles of deep neural networks. They are still among the most popular approaches to Bayesian deep learning.2

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    Black-box models

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    The code below loads relevant packages along with the MNIST data and pre-trained models.

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    # Load package, models and data:
-using CounterfactualExplanations, Flux
-using CounterfactualExplanations.Data: mnist_data, mnist_model, mnist_ensemble
-data, X, ys = mnist_data()
-model = mnist_model()
-ensemble = mnist_ensemble()
-counterfactual_data = CounterfactualData(X,ys;domain=(0,1))
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    While the package can currently handle a few simple classification models natively, it is designed to be easily extensible through users and contributors. Extending the package to deal with custom models typically involves only two simple steps:

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    1. Subtyping: the custom model needs to be declared as a subtype of the package-internal type AbstractFittedModel.
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    2. Multiple dispatch: the package-internal functions logits and probs need to be extended through custom methods for the new model type.
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    The following code implements these two steps first for the MLP and then for the deep ensemble.

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    using CounterfactualExplanations.Models
-import CounterfactualExplanations.Models: logits, probs
-# MLP:
-# Step 1)
-struct NeuralNetwork <: Models.AbstractFittedModel
-    model::Any
-end
-# Step 2)
-logits(M::NeuralNetwork, X::AbstractArray) = M.model(X)
-probs(M::NeuralNetwork, X::AbstractArray)= softmax(logits(M, X))
-M = NeuralNetwork(model)
-
-# Deep ensemble:
-using Flux: stack
-# Step 1)
-struct FittedEnsemble <: Models.AbstractFittedModel
-    ensemble::AbstractArray
-end
-# Step 2)
-using Statistics
-logits(M::FittedEnsemble, X::AbstractArray) = mean(stack([m(X) for m in M.ensemble],3),dims=3)
-probs(M::FittedEnsemble, X::AbstractArray) = mean(stack([softmax(m(X)) for m in M.ensemble],3),dims=3)
-M_ensemble = FittedEnsemble(ensemble)
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    Counterfactual generators

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    Next, we need to specify the counterfactual generators we want to use. The package currently ships with two default generators that both need gradient access: firstly, the generic generator introduced by @wachter2017counterfactual and, secondly, a greedy generator introduced by @schut2021generating.

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    The greedy generator is designed to be used with models that incorporate uncertainty in their predictions such as the deep ensemble introduced above. It works for probabilistic (Bayesian) models, because they only produce high-confidence predictions in regions of the feature domain that are populated by training samples. As long as the model is expressive enough and well-specified, counterfactuals in these regions will always be realistic and unambiguous since by construction they should look very similar to training samples. Other popular approaches to counterfactual explanations like REVISE [@joshi2019realistic] and CLUE [@antoran2020getting] also play with this simple idea.

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    The following code instantiates the two generators for the problem at hand.

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    generic = GenericGenerator(;loss=:logitcrossentropy)
-greedy = GreedyGenerator(;loss=:logitcrossentropy)
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    Explanations

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    Once the model and counterfactual generator are specified, running counterfactual search is very easy using the package. For a given factual (x), target class (target) and data set (counterfactual_data), simply running

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    generate_counterfactual(x, target, counterfactual_data, M, generic)
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    will generate the results, in this case using the generic generator (generic) for the MLP (M). Since we have specified two different black-box models and two different counterfactual generators, we have four combinations of a model and a generator in total. For each of these combinations I have used the generate_counterfactual function to produce the results in Figure 1.

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    In every case the desired label switch is in fact achieved, but arguably from a human perspective only the counterfactuals for the deep ensemble look like a four. The generic generator produces mild perturbations in regions that seem irrelevant from a human perspective, but nonetheless yields a counterfactual that can pass as a four. The greedy approach clearly targets pixels at the top of the handwritten nine and yields the best result overall. For the non-Bayesian MLP, both the generic and the greedy approach generate counterfactuals that look much like adversarial examples: they perturb pixels in seemingly random regions on the image.

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    -Figure 1: Counterfactual explanations for MNIST: turning a nine (9) into a four (4). -
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    Language interoperability 👥

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    The Julia language offers unique support for programming language interoperability. For example, calling R or Python is made remarkably easy through RCall.jl and PyCall.jl, respectively. This functionality can be leveraged to use CounterfactualExplanations.jl to generate explanations for models that were developed in other programming languages. At this time there is no native support for foreign programming languages, but the following example involving a torch neural network trained in R demonstrates how versatile the package is.3

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    Explaining a torch model

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    We will consider a simple MLP trained for a binary classification task. As before we first need to adapt this custom model for use with our package. The code below the two necessary steps - sub-typing and method extension. Logits are returned by the torch model and copied from the R environment into the Julia scope. Probabilities are then computed inside the Julia scope by passing the logits through the sigmoid function.

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    using Flux
-using CounterfactualExplanations, CounterfactualExplanations.Models
-import CounterfactualExplanations.Models: logits, probs # import functions in order to extend
-
-# Step 1)
-struct TorchNetwork <: Models.AbstractFittedModel
-    nn::Any
-end
-
-# Step 2)
-function logits(M::TorchNetwork, X::AbstractArray)
-  nn = M.nn
-  y = rcopy(R"as_array($nn(torch_tensor(t($X))))")
-  y = isa(y, AbstractArray) ? y : [y]
-  return y'
-end
-function probs(M::TorchNetwork, X::AbstractArray)
-  return σ.(logits(M, X))
-end
-M = TorchNetwork(R"model")
    -
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    Compared to models trained in Julia, we need to do a little more work at this point. Since our counterfactual generators need gradient access, we essentially need to allow our package to communicate with the R torch library. While this may sound daunting, it turns out to be quite manageable: all we have to do is respecify the function that computes the gradient with respect to the counterfactual loss function so that it can deal with the TorchNetwork type we defined above. That is all the adjustment needed to use CounterfactualExplanations.jl for our custom R model. Figure 2 shows a counterfactual path for a randomly chosen sample with respect to the MLP trained in R.

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    You may have stumbled across the term respecify above: does it really seem like a good idea to just replace an existing function from our package? Surely not! There are certainly better ways to go about this, which we will consider when adding native support for Python and R models in future package releases. Which brings us to our final section …

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    import CounterfactualExplanations.Generators: ∂ℓ
-using LinearAlgebra
-
-# Countefactual loss:
-function ∂ℓ(
-    generator::AbstractGradientBasedGenerator, 
-    counterfactual_state::CounterfactualState) 
-  M = counterfactual_state.M
-  nn = M.nn
-  x′ = counterfactual_state.x′
-  t = counterfactual_state.target_encoded
-  R"""
-  x <- torch_tensor($x′, requires_grad=TRUE)
-  output <- $nn(x)
-  loss_fun <- nnf_binary_cross_entropy_with_logits
-  obj_loss <- loss_fun(output,$t)
-  obj_loss$backward()
-  """
-  grad = rcopy(R"as_array(x$grad)")
-  return grad
-end
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    -Figure 2: Counterfactual path using the generic counterfactual generator for a model trained in R. -
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    -
    -

    We need you! 🫵

    -

    The ambition for CounterfactualExplanations.jl is to provide a go-to place for counterfactual explanations to the Julia community and beyond. This is a grand ambition, especially for a package that has so far been built by a single developer who has little prior experience with Julia. We would therefore very much like to invite community contributions. If you have an interest in trustworthy AI, the open-source community and Julia, please do get involved! This package is still in its early stages of development, so any kind of contribution is welcome: advice on the core package architecture, pull requests, issues, discussions and even just comments below would be much appreciated.

    -

    To give you a flavor of what type of future developments we envision, here is a non-exhaustive list:

    -
      -
    1. Native support for additional counterfactual generators and predictive models including those built and trained in Python or R.
      2. -
    2. Additional datasets for testing, evaluation and benchmarking.
      3. -
    3. Improved preprocessing including native support for categorical features.
      4. -
    4. Support for regression models.
      5. -
    -

    Finally, if you like this project but don’t have much time, then simply sharing this article or starring the repo on GitHub would also go a long way.

    -
    -
    -

    Further reading 📚

    -

    If you’re interested in learning more about this development, feel free to check out the following resources:

    - -
    - - -

    Footnotes

    - -
      -

    1. See: [TDS], [blog]↩︎

      2. -

    2. For more information on Bayesian deep learning see my previous post: [TDS], [blog].↩︎

      3. -

    3. The corresponding example involving PyTorch is analogous and therefore not included here. You may find it here.↩︎

      4. -
    -
    - - -
    +
    +

    Project Overview

    +

    This project aimed to enhance the CounterfactualExplanations.jl package by infusing it with a robust mathematical foundation for minimal algorithmic recourse, based on the principles of causal reasoning (Karimi, Schölkopf, and Valera 2021).

    +
    +

    Key Contributions

    +

    During the project, I contributed to two key repositories:

    +
      +

    1. CounterfactualExplanations.jl: Developed a new tool for generating counterfactual explanations using causal information. This allows users to create smarter perturbations rather than random adjustments, ultimately providing more meaningful insights.

      2. +

    2. CausalInference.jl: Implemented a Structural Causal Model (SCM) structure that extracts information from data, laying the groundwork for the causal reasoning capabilities in CounterfactualExplanations.jl.

      3. +
    +

    This was an amazing experience, not just experience contribute to two repositories simultaneously, but also to work with the mantainers of these repos. I learned a lot about the Julia language and the Julia community. This was possible because of the mentorship of Patrick Altmeyer (CounterfactualExplanations) and Moritz Schauer (CausalInference), who guided me throughout the project and are amazing researchers.

    +
    +
    +

    The MINTGenerator

    +

    In this project, we developed the MINTGenerator, a counterfactual generator based on the Recourse through Minimal Intervention (MINT) method proposed by Karimi, Schölkopf, and Valera (2021).

    +
    +
    +

    Description

    +

    The MINTGenerator incorporates causal reeasoning in algorithm recourse to achieve minimal interventions when generating a counterfactual explanation. In this sense, the main ideia is that just perturbating a black box model without taking into account the causal relations in the data can guide to misleading recommendations. Here we now shift to a perspective where every action/pertubation is an intervetion in the causal graph of the problem, thus the change is not made just in the intervened upon variable, but also in its childs in the causal structure. The generator utilizes a Structural Causal Model(SCM) to encode the variables in a way that causal effects are propagated and uses a generic gradient-based generator to create the search path, that is, any gradient-base generator (ECCo, REVISE, Watcher, …) can be used with the MINT SCM encoder to generate counterfactual samples in latent space for minimal intervetions algorithm recourse.

    +

    The MINT algorithm minimizes a loss function that combines the causal constraints of the SCM and the distance between the generated counterfactual and the original input. Since we want a gradient-based generator, we need to pass the constrained optimizaiton problem into an unconstrained one and we do this by using the Lagrangian. Initially, as defined in (Karimi, Schölkopf, and Valera 2021), we aim to aim to find the minimal cost set of actions (in the form of structural interventions) that results in a counterfactual instance yielding the favorable output from ,

    +$$ + +

    $$

    +

    where is the original input, is the counterfactual instance, and is the black-box model. We use the terminology because the counterfactual is derived from the SCM,

    +

    +

    where is the set of intervened upon variables, is the function that generates the value of the variable given its parents, and and are the parents of the variable in the counterfactual and original instance, respectively. This closed formula for the decision variable is what makes possible to use a gradient-based generator, since with it the lagrangian is differentiable,

    +

    +

    or in simple terms and more standard, since is constant,

    +

    +

    where is clearly and is :

    +

    +
    +
    +

    Implementation

    +
    +

    CausalInference.jl

    +

    In terms of implementation, we need to capture the causal relations from the data, that’s where CausalInference.jl comes in. However, before the project, the package did not have a SCM structure, in the sense that the methods just captured the topological Directed Acyclic Graph (DAG) that showed the causality ruling the data, that is, no causal structural equations were provided,

    +
    +
    +Code +
    using CausalInference
+using Plots, GraphRecipes
+using Random
+Random.seed!(1)
+
+N = 2000 # number of data points
+
+x = randn(N)
+v = x + randn(N)*0.25
+w = x + randn(N)*0.25
+z = v + w + randn(N)*0.25
+s = z + randn(N)*0.25
+
+df = (x=x, v=v, w=w, z=z, s=s)
+
+est_g, score = ges(df; penalty=1.0, parallel=true)
+
+plt = graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)], size=(500,500), nodesize=0.3)
+savefig(plt, "www/intro.png")
+display(plt)
    +
    +
    +
    ┌ Warning: Only one thread available
+└ @ CausalInference ~/.julia/packages/CausalInference/ozcj8/src/ges.jl:52
    +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    +

    So, our goal was given the DAG provided by the ges method in the causal discovery (Chickering 2003), generate equations that rules each of these causal relations, represented in the DAG as directed edges. The SCM is the union of the DAG and these causal equations, that is, the SCM is a tuple , where is the DAG and is the set of functions that generates the value of each variable given its parents.

    +

    Our solution for constructing the structural causal equations was to assume that the data was generated by a linear model, ie, the causal relations were linear. For the DAG provided in the code example we derive

    +

    +

    +

    +

    +

    +

    and that’s the tricky thing, as we can see these causal equations are different than the ones that generated the data, but they are the ones that respect the causal system obtained from the obtained DAG. Here and are the intercept term and the coefficient obtained from the linear regression, respectively. To correctly solve the linear regression respecting the dependencies of the causal graph, we use topological_sort_by_dfs from Graphs.jl.

    +

    Now, with the SCM structure in hand, we see that the representation could be a struct containing the DAG and the coefficients/intercepts of the causal equations, this maps exactly the tuple that we defined. However, since we need these equations to be differentiable, we need to define a function that takes the SCM and returns the value of the variable given its parents and using just the coefficients and the DAG, lead to errors, because AutoDiff does not deal well with functions that are conditioned (if statements). So, we need to define a way to retrieve the system of causal equations in a smooth way and that’s where the causal_effects matrix comes to the rescue.

    +

    Let the factual vector of features be denoted as:

    +

    +

    Let the causal_effects matrix be:

    +

    +

    Here, represents the coefficient from the causal effect of on , and represents the intercept term for the variable .

    +

    The matrix multiplication of the causal_effects matrix with the factual vector (excluding the bias term) is given by:

    +

    +

    Finally, we add the bias term:

    +

    +

    In expanded form:

    +

    +

    This equation shows how each counterfactual variable is generated as a linear combination of the factual inputs based on the causal effects matrix, with an intercept term added for each variable.

    +

    One can note that the orphan nodes, that is, the nodes that do not have parents in the DAG, are going to be equal to the intercept term . The intuition behind this is that when we do the linear regression, variables that have no causal parents are just equal to the unconditional mean of the variable, i.e, we get . Because of this, in some cases a better understanding of the regression is needed, so the residuals are also part of the SCM structure,

    +
    +
    +Code +
    struct SCM
+    variables::Vector{String}
+    coefficients::Vector{Vector{Float64}}
+    residuals::Vector{Vector{Float64}}
+    dag::DiGraph
+    causal_effects::Matrix{Float64}
+end
    +
    +
    +
    +
    +

    CounterfactualExplanations.jl

    +
    +
    +
    +
    +

    Conclusion

    + +
    +
    + + + + + + +
    + +

    References

    +
    +Chickering, David Maxwell. 2003. “Optimal Structure Identification with Greedy Search.” J. Mach. Learn. Res. 3 (null): 507–54. https://doi.org/10.1162/153244303321897717. +
    +
    +Karimi, Amir-Hossein, Bernhard Schölkopf, and Isabel Valera. 2021. “Algorithmic Recourse: From Counterfactual Explanations to Interventions.” In Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency, 353–62. FAccT ’21. New York, NY, USA: Association for Computing Machinery. https://doi.org/10.1145/3442188.3445899. +
    +

    Citation

    BibTeX citation:
    @online{altmeyer2024,
+  author = {Altmeyer, Patrick and Luiz Franco, Jorge},
+  title = {When {Causality} Meets {Recourse}},
+  date = {2024-09-17},
+  url = {https://www.taija.org/blog/posts/causal-recourse/},
+  langid = {en}
+}
+
    For attribution, please cite this work as:
    +Altmeyer, Patrick, and Jorge Luiz Franco. 2024. “When Causality +Meets Recourse.” September 17, 2024. https://www.taija.org/blog/posts/causal-recourse/. +
    ]]> + counterfactuals + explainable AI + causality + Julia + https://www.taija.org/blog/posts/causal-recourse/ + Mon, 16 Sep 2024 22:00:00 GMT + + New Package for Energy-Based Sampling Patrick Altmeyer @@ -807,7 +1171,7 @@ Figure 2: The animation shows the last 250 draws from the marginal posterio
    1. UnconditionalSampler — samples from the unconditional distribution as in Grathwohl et al. (2020).
    2. ConditionalSampler — samples from the conditional distribution as in Grathwohl et al. (2020).
      3. -
    3. JointSampler — samples from the joint distribution as in Kelly, Zemel, and Grathwohl (2021).
      4. +
    4. JointSampler — samples from the joint distribution as in (kelly2021directly?).

    Example: Joint Energy-Based Model

    @@ -3683,9 +4047,6 @@ font-style: inherit;">plot(plt)
    Grathwohl, Will, Kuan-Chieh Wang, Joern-Henrik Jacobsen, David Duvenaud, Mohammad Norouzi, and Kevin Swersky. 2020. “Your Classifier Is Secretly an Energy Based Model and You Should Treat It Like One.” In International Conference on Learning Representations.
    -
    -Kelly, Jacob, Richard Zemel, and Will Grathwohl. 2021. “Directly Training Joint Energy-Based Models for Conditional Synthesis and Calibrated Prediction of Multi-Attribute Data.” https://arxiv.org/abs/2108.04227. -
    Murphy, Kevin P. 2023. Probabilistic Machine Learning: Advanced Topics. MIT press.
    @@ -8093,7 +8454,7 @@ Conformalized prediction sets for a
    simple Deep Image Classifier.

    🎯 The Task at Hand

    The task at hand is to predict the labels of handwritten images of digits using the famous MNIST dataset (LeCun 1998). Importing this popular machine learning dataset in Julia is made remarkably easy through MLDatasets.jl:

    -
    +
    Code 
    :N]

    Figure 1 below shows a few random samples from the training data:

    -
    +
    Code 
    ..., ncol=n_samples)
    -
    +
    - +
    Figure 1: Random samples from the MNIST dataset. @@ -8201,7 +8562,7 @@ Figure 1: Random samples from the MNIST dataset.

    🚧 Building the Network

    To model the mapping from image inputs to labels will rely on a simple Multi-Layer Perceptron (MLP). A great Julia library for Deep Learning is Flux.jl. But wait … doesn’t ConformalPrediction.jl work with models trained in MLJ.jl? That’s right, but fortunately there exists a Flux.jl interface to MLJ.jl, namely MLJFlux.jl. The interface is still in its early stages, but already very powerful and easily accessible for anyone (like myself) who is used to building Neural Networks in Flux.jl.

    In Flux.jl, you could build an MLP for this task as follows,

    -
    +
    Code 
    10)

    where (28,28) is just the input dimension (28x28 pixel images). Since we have ten digits, our output dimension is ten.1

    We can do the exact same thing in MLJFlux.jl as follows,

    -
    +
    Code 
    32, n_out)

    where here we rely on the @builder macro to make the transition from Flux.jl to MLJ.jl as seamless as possible. Finally, MLJFlux.jl already comes with a number of helper functions to define plain-vanilla networks. In this case, we will use the ImageClassifier with our custom builder and cross-entropy loss:

    -
    +
    Code 
    ImageClassifier =Flux.crossentropy

    The generated instance clf is a model (in the MLJ.jl sense) so from this point on we can rely on standard MLJ.jl workflows. For example, we can wrap our model in data to create a machine and then evaluate it on a holdout set as follows:

    -
    +
    Code 
    mach =[accuracy]
 
    
 
    🔥 Conformalizing the Network
    
 
    Since clf is a model, it is also compatible with our package: ConformalPrediction.jl. To conformalize our MLP, we therefore only need to call conformal_model(clf). Since the generated instance conf_model is also just a model, we can still rely on standard MLJ.jl workflows. Below we first wrap it in data and then fit it. Aaaand … we’re done! Let’s look at the results in the next section.
    
-
    
+
    
 
    
 Code
 
    fit!(mach)
    
 
    📊 Results
    
 
    Figure 2 below presents the results. Figure 2 (a) displays highly certain predictions, now defined in the rigorous sense of Conformal Prediction: in each case, the conformal set (just beneath the image) includes only one label.
    
 
    Figure 2 (b) and Figure 2 (c) display increasingly uncertain predictions of set size two and three, respectively. They demonstrate that CP is well equipped to deal with samples characterized by high aleatoric uncertainty: digits four (4), seven (7) and nine (9) share certain similarities. So do digits five (5) and six (6) as well as three (3) and eight (8). These may be hard to distinguish from each other even after seeing many examples (and even for a human). It is therefore unsurprising to see that these digits often end up together in conformal sets.
    
-
    
+
    
 
    
 
    
 
    
@@ -8386,30 +8747,27 @@ font-style: inherit;">fit!(mach)
    - + - + - + - + - + - + - - - - - - - - - + + + + + + + + + - + - + - + - +
    (a) Randomly selected prediction sets of size . @@ -8791,31 +9155,27 @@ RK5CYII= - + - + - + - + - + - + - - - - - - - - - +MQAAAEmCGAAAgCRBDAAAQJIgBgAAIEkQAwAAkCSIAQAASBLEAAAAJAliAAAAkgQxAAAASYIYAACA +JEEMAABAkiAGAAAgSRADAACQJIgBAABIEsQAAAAkCWIAAACSBDEAAABJghgAAIAkQQwAAECSIAYA +ACDpnzJKxgVH2LvBAAAAAElFTkSuQmCC +" transform="translate(118, 47)"> - + - - + + - + + + + + + + + + + - +
    (b) Randomly selected prediction sets of size . @@ -9193,152 +9565,158 @@ EAMAAJAkiAEAAEj6L+4aoBa2pyb3AAAAAElFTkSuQmCC - + - + - + - + - + - + - + - + - + - + - + - + - +
    (c) Randomly selected prediction sets of size . @@ -9610,7 +9969,7 @@ Figure 2: Conformalized predictions from an image classifier.

    To evaluate the performance of conformal models, specific performance measures can be used to assess if the model is correctly specified and well-calibrated (A. N. Angelopoulos and Bates 2022). We will look at this in some more detail in another post in the future. For now, just be aware that these measures are already available in ConformalPrediction.jl and we will briefly showcase them here.

    As for many other things, ConformalPrediction.jl taps into the existing functionality of MLJ.jl for model evaluation. In particular, we will see below how we can use the generic evaluate! method on our machine. To assess the correctness of our conformal predictor, we can compute the empirical coverage rate using the custom performance measure emp_coverage. With respect to model calibration we will look at the model’s conditional coverage. For adaptive, well-calibrated conformal models, conditional coverage is high. One general go-to measure for assessing conditional coverage is size-stratified coverage. The custom measure for this purpose is just called size_stratified_coverage, aliased by ssc.

    The code below implements the model evaluation using cross-validation. The Simple Inductive Classifier that we used above is not adaptive and hence the attained conditional coverage is low compared to the overall empirical coverage, which is close to , so in line with the desired coverage rate specified above.

    -
    +
    Code 
    _eval 3))")
    +
    +
    Evaluating over 6 folds:  33%[========>                ]  ETA: 0:00:05Evaluating over 6 folds:  50%[============>            ]  ETA: 0:00:03Evaluating over 6 folds:  67%[================>        ]  ETA: 0:00:02Evaluating over 6 folds:  83%[====================>    ]  ETA: 0:00:01Evaluating over 6 folds: 100%[=========================] Time: 0:00:05
+Empirical coverage: 0.959
+SSC: 0.791
    +
    -
    -
    PerformanceEvaluation object with these fields:
+
    PerformanceEvaluation object with these fields:
   measure, operation, measurement, per_fold,
   per_observation, fitted_params_per_fold,
   report_per_fold, train_test_rows
@@ -9679,23 +10042,17 @@ Extract:
 ┌──────────────────────────────────────────────┬───────────┬─────────────┬──────
 │ measure                                      │ operation │ measurement │ 1.9 ⋯
 ├──────────────────────────────────────────────┼───────────┼─────────────┼──────
-│ ConformalPrediction.emp_coverage             │ predict   │ 0.954       │ 0.0 ⋯
-│ ConformalPrediction.size_stratified_coverage │ predict   │ 0.661       │ 0.3 ⋯
+│ ConformalPrediction.emp_coverage             │ predict   │ 0.959       │ 0.0 ⋯
+│ ConformalPrediction.size_stratified_coverage │ predict   │ 0.791       │ 0.1 ⋯
 └──────────────────────────────────────────────┴───────────┴─────────────┴──────
-                                                               2 columns omitted
-
    
-
    -
    -
    -
    Empirical coverage: 0.954
-SSC: 0.661
    + 2 columns omitted

    We can attain higher adaptivity (SSC) when using adaptive prediction sets:

    -
    +
    Code -
    conf_model 
    conf_model = =.95)
-mach mach = machine(conf_model, X, y)
-fit!(mach)
-_eval _eval = evaluate!(
-    mach,
-    resampling    mach,
+    resampling=CV(),
-    operation    operation=predict,
-    measure    measure=[emp_coverage, ssc]
-)
-results[)
+results[:adaptive_inductive] = mach
-display(_eval)
-println(3))")
-println(3))")
    +
    +
    [ Info: Training machine(AdaptiveInductiveClassifier(model = ImageClassifier(builder = GenericBuilder(apply = #3), …), …), …).
+Optimising neural net:  18%[====>                    ]  ETA: 0:00:00Optimising neural net:  27%[======>                  ]  ETA: 0:00:01Optimising neural net:  36%[=========>               ]  ETA: 0:00:01Optimising neural net:  45%[===========>             ]  ETA: 0:00:00Optimising neural net:  55%[=============>           ]  ETA: 0:00:00Optimising neural net:  64%[===============>         ]  ETA: 0:00:00Optimising neural net:  73%[==================>      ]  ETA: 0:00:00Optimising neural net:  82%[====================>    ]  ETA: 0:00:00Optimising neural net:  91%[======================>  ]  ETA: 0:00:00Optimising neural net: 100%[=========================] Time: 0:00:00
+Evaluating over 6 folds:  33%[========>                ]  ETA: 0:00:03Evaluating over 6 folds:  50%[============>            ]  ETA: 0:00:02Evaluating over 6 folds:  67%[================>        ]  ETA: 0:00:02Evaluating over 6 folds:  83%[====================>    ]  ETA: 0:00:01Evaluating over 6 folds: 100%[=========================] Time: 0:00:05
+Empirical coverage: 0.996
+SSC: 0.983
    +
    -
    -
    PerformanceEvaluation object with these fields:
+
    PerformanceEvaluation object with these fields:
   measure, operation, measurement, per_fold,
   per_observation, fitted_params_per_fold,
   report_per_fold, train_test_rows
@@ -9785,33 +10148,27 @@ Extract:
 ┌──────────────────────────────────────────────┬───────────┬─────────────┬──────
 │ measure                                      │ operation │ measurement │ 1.9 ⋯
 ├──────────────────────────────────────────────┼───────────┼─────────────┼──────
-│ ConformalPrediction.emp_coverage             │ predict   │ 0.995       │ 0.0 ⋯
-│ ConformalPrediction.size_stratified_coverage │ predict   │ 0.981       │ 0.0 ⋯
+│ ConformalPrediction.emp_coverage             │ predict   │ 0.996       │ 0.0 ⋯
+│ ConformalPrediction.size_stratified_coverage │ predict   │ 0.983       │ 0.0 ⋯
 └──────────────────────────────────────────────┴───────────┴─────────────┴──────
-                                                               2 columns omitted
-
    
-
    -
    -
    -
    Empirical coverage: 0.995
-SSC: 0.981
    + 2 columns omitted

    We can also have a look at the resulting set size for both approaches using a custom Plots.jl recipe (fig-setsize). In line with the above, the spread is wider for the adaptive approach, which reflects that “the procedure is effectively distinguishing between easy and hard inputs” (A. N. Angelopoulos and Bates 2022).

    -
    +
    Code -
    plt_list 
    plt_list = []
-for (_mod, mach) in results
-        push!(plt_list, =String(_mod)))
-end
-plot(plt_list800,300))
-plot(plt_list300),bg_colour=:transparent)
    -
    +
    - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    @@ -10775,7 +11125,7 @@ Turning a 9 (nine) into a 4 (four).

    Black-box models

    The code below loads relevant packages along with the MNIST data and pre-trained models.

    -
    +
    Code 
    1))
  • Multiple dispatch: the package-internal functions logits and probs need to be extended through custom methods for the new model type.

    • The following code implements these two steps first for the MLP and then for the deep ensemble.

    -
    +
    Code 
    FittedEnsemble(ensemble)

    Next, we need to specify the counterfactual generators we want to use. The package currently ships with two default generators that both need gradient access: firstly, the generic generator introduced by Wachter, Mittelstadt, and Russell (2017) and, secondly, a greedy generator introduced by Schut et al. (2021).

    The greedy generator is designed to be used with models that incorporate uncertainty in their predictions such as the deep ensemble introduced above. It works for probabilistic (Bayesian) models, because they only produce high-confidence predictions in regions of the feature domain that are populated by training samples. As long as the model is expressive enough and well-specified, counterfactuals in these regions will always be realistic and unambiguous since by construction they should look very similar to training samples. Other popular approaches to counterfactual explanations like REVISE (Joshi et al. 2019) and CLUE (Antorán et al. 2020) also play with this simple idea.

    The following code instantiates the two generators for the problem at hand.

    -
    +
    Code 
    generic =:logitcrossentropy)

    Explanations

    Once the model and counterfactual generator are specified, running counterfactual search is very easy using the package. For a given factual (x), target class (target) and data set (counterfactual_data), simply running

    -
    +
    generate_counterfactual(x, target, counterfactual_data, M, generic)
    @@ -11059,7 +11409,7 @@ Figure 1: Counterfactual explanations for MNIST: turning a nine (9) into a

    Explaining a torch model

    We will consider a simple MLP trained for a binary classification task. As before we first need to adapt this custom model for use with our package. The code below the two necessary steps - sub-typing and method extension. Logits are returned by the torch model and copied from the R environment into the Julia scope. Probabilities are then computed inside the Julia scope by passing the logits through the sigmoid function.

    -
    +
    Code 
    
+
    
 
    
 Code
 
    Counterfact
 
    
 
    Black-box models
    
 
    The code below loads relevant packages along with the MNIST data and pre-trained models.
    
-
    
+
    
 
    
 Code
 
    # Load package, models and data:
@@ -327,7 +327,7 @@ 
    Black-box models
    
 
  • Multiple dispatch: the package-internal functions logits and probs need to be extended through custom methods for the new model type.
    • 
 
 
    The following code implements these two steps first for the MLP and then for the deep ensemble.
    
-
    
+
    
 
    
 Code
 
    using CounterfactualExplanations.Models
@@ -361,7 +361,7 @@ 
    Counterfactual g
 
    Next, we need to specify the counterfactual generators we want to use. The package currently ships with two default generators that both need gradient access: firstly, the generic generator introduced by Wachter, Mittelstadt, and Russell (2017) and, secondly, a greedy generator introduced by Schut et al. (2021).
    
 
    The greedy generator is designed to be used with models that incorporate uncertainty in their predictions such as the deep ensemble introduced above. It works for probabilistic (Bayesian) models, because they only produce high-confidence predictions in regions of the feature domain that are populated by training samples. As long as the model is expressive enough and well-specified, counterfactuals in these regions will always be realistic and unambiguous since by construction they should look very similar to training samples. Other popular approaches to counterfactual explanations like REVISE (Joshi et al. 2019) and CLUE (Antorán et al. 2020) also play with this simple idea.
    
 
    The following code instantiates the two generators for the problem at hand.
    
-
    
+
    
 
    
 Code
 
    generic = GenericGenerator(;loss=:logitcrossentropy)
@@ -372,7 +372,7 @@ 
    Counterfactual g
 
    
 
    Explanations
    
 
    Once the model and counterfactual generator are specified, running counterfactual search is very easy using the package. For a given factual (x), target class (target) and data set (counterfactual_data), simply running
    
-
    
+
    
 
    generate_counterfactual(x, target, counterfactual_data, M, generic)
    
 
    
 
    will generate the results, in this case using the generic generator (generic) for the MLP (M). Since we have specified two different black-box models and two different counterfactual generators, we have four combinations of a model and a generator in total. For each of these combinations I have used the generate_counterfactual function to produce the results in Figure 1.
    
@@ -395,7 +395,7 @@ 
    Language interop
 
    
 
    Explaining a torch model
    
 
    We will consider a simple MLP trained for a binary classification task. As before we first need to adapt this custom model for use with our package. The code below the two necessary steps - sub-typing and method extension. Logits are returned by the torch model and copied from the R environment into the Julia scope. Probabilities are then computed inside the Julia scope by passing the logits through the sigmoid function.
    
-
    
+
    
 
    
 Code
 
    using Flux
@@ -434,7 +434,7 @@ 
    Explaining a You may have stumbled across the term respecify above: does it really seem like a good idea to just replace an existing function from our package? Surely not! There are certainly better ways to go about this, which we will consider when adding native support for Python and R models in future package releases. Which brings us to our final section …
    
 
    
 
    
-
    
+
    
 
    
 Code
 
    import CounterfactualExplanations.Generators: ∂ℓ
@@ -1031,374 +1031,373 @@ 
    Further reading 📚
    
 execute:
   eval: false
   echo: true
-draft: false
----
-
-```{julia}
-#| echo: false
-www_path = "posts/a-new-tool-for-explainable-ai/www"
-```
-
-<div class="intro-gif">
-  <figure>
-    <img src="www/intro.gif">
-    <figcaption>Turning a 9 (nine) into a 4 (four).</figcaption>
-  </figure>
-</div>
-
-<!-- Intro -->
-
-Counterfactual explanations, which I introduced in one of my previous posts^[See: [[TDS](https://towardsdatascience.com/individual-recourse-for-black-box-models-5e9ed1e4b4cc)], [[blog](https://www.patalt.org/blog/posts/individual-recourse-for-black-box-models/)]], offer a simple and intuitive way to explain black-box models without opening them. Still, as of today there exists only one open-source library that provides a unifying approach to generate and benchmark counterfactual explanations for models built and trained in Python [@pawelczyk2021carla]. This is great, but of limited use to users of other programming languages 🥲. 
-
-Enter [`CounterfactualExplanations.jl`](https://www.patalt.org/CounterfactualExplanations.jl/stable/): a Julia package that can be used to explain machine learning algorithms developed and trained in Julia, Python and R. Counterfactual explanations fall into the broader category of explainable artificial intelligence (XAI). 
-
-Explainable AI typically involves models that are not inherently interpretable but require additional tools to be explainable to humans. Examples of the latter include ensembles, support vector machines and deep neural networks. This is not to be confused with interpretable AI, which involves models that are inherently interpretable and transparent such as general additive models (GAM), decision trees and rule-based models. 
-
-Some would argue that we best avoid explaining black-box models altogether [@rudin2019stop] and instead focus solely on interpretable AI. While I agree that initial efforts should always be geared towards interpretable models, stopping there would entail missed opportunities and anyway is probably not very realistic in times of [DALL$\cdot$E](https://openai.com/blog/dall-e/) and Co.
-
-> Even though [...] interpretability is of great importance and should be pursued, explanations can, in principle, be offered without opening the “black box.”
->
-> --- @wachter2017counterfactual
-
-<!-- Nut paragraph -->
-
-This post introduces the main functionality of the new Julia package. Following a motivating example using a model trained in Julia, we will see how easy the package can be adapted to work with models trained in Python and R. Since the motivation for this post is also to hopefully attract contributors, the final section outlines some of the exciting developments we have planned. 
-
-## Counterfactuals for image data 🖼
-
-To introduce counterfactual explanations I used a simple binary classification problem in my previous [post](https://towardsdatascience.com/individual-recourse-for-black-box-models-5e9ed1e4b4cc). It involved a linear classifier and a linearly separable, synthetic data set with just two features. This time we are going to step it up a notch: we will generate counterfactual explanations MNIST data. The MNIST dataset contains 60,000 training samples of handwritten digits in the form of 28x28 pixel grey-scale images [@lecun1998mnist]. Each image is associated with a label indicating the digit (0-9) that the image represents. 
-
-The [`CounterfactualExplanations.jl`](https://www.patalt.org/CounterfactualExplanations.jl/stable/) package ships with two black-box models that were trained to predict labels for this data: firstly, a simple multi-layer perceptron (MLP) and, secondly, a corresponding deep ensemble. Originally proposed by @lakshminarayanan2016simple, deep ensembles are really just ensembles of deep neural networks. They are still among the most popular approaches to Bayesian deep learning.^[For more information on Bayesian deep learning see my previous post: [[TDS](https://towardsdatascience.com/go-deep-but-also-go-bayesian-ab25efa6f7b)], [[blog](https://www.patalt.org/blog/posts/effortsless-bayesian-dl/)].] 
-
-### Black-box models
-
-The code below loads relevant packages along with the MNIST data and pre-trained models. 
-
-```{julia}
-# Load package, models and data:
-using CounterfactualExplanations, Flux
-using CounterfactualExplanations.Data: mnist_data, mnist_model, mnist_ensemble
-data, X, ys = mnist_data()
-model = mnist_model()
-ensemble = mnist_ensemble()
-counterfactual_data = CounterfactualData(X,ys;domain=(0,1))
-```
-
-While the package can currently handle a few simple classification models natively, it is designed to be easily extensible through users and contributors. Extending the package to deal with custom models typically involves only two simple steps:
-
-1. **Subtyping**: the custom model needs to be declared as a subtype of the package-internal type `AbstractFittedModel`.
-2. **Multiple dispatch**: the package-internal functions `logits` and `probs` need to be extended through custom methods for the new model type.
-
-The following code implements these two steps first for the MLP and then for the deep ensemble.
-
-```{julia}
-using CounterfactualExplanations.Models
-import CounterfactualExplanations.Models: logits, probs
-# MLP:
-# Step 1)
-struct NeuralNetwork <: Models.AbstractFittedModel
-    model::Any
-end
-# Step 2)
-logits(M::NeuralNetwork, X::AbstractArray) = M.model(X)
-probs(M::NeuralNetwork, X::AbstractArray)= softmax(logits(M, X))
-M = NeuralNetwork(model)
-
-# Deep ensemble:
-using Flux: stack
-# Step 1)
-struct FittedEnsemble <: Models.AbstractFittedModel
-    ensemble::AbstractArray
-end
-# Step 2)
-using Statistics
-logits(M::FittedEnsemble, X::AbstractArray) = mean(stack([m(X) for m in M.ensemble],3),dims=3)
-probs(M::FittedEnsemble, X::AbstractArray) = mean(stack([softmax(m(X)) for m in M.ensemble],3),dims=3)
-M_ensemble = FittedEnsemble(ensemble)
-```
-
-### Counterfactual generators
-
-Next, we need to specify the counterfactual generators we want to use. The package currently ships with two default generators that both need gradient access: firstly, the generic generator introduced by @wachter2017counterfactual and, secondly, a greedy generator introduced by @schut2021generating. 
-
-The greedy generator is designed to be used with models that incorporate uncertainty in their predictions such as the deep ensemble introduced above. It works for probabilistic (Bayesian) models, because they only produce high-confidence predictions in regions of the feature domain that are populated by training samples. As long as the model is expressive enough and well-specified, counterfactuals in these regions will always be realistic and unambiguous since by construction they should look very similar to training samples. Other popular approaches to counterfactual explanations like REVISE [@joshi2019realistic] and CLUE [@antoran2020getting] also play with this simple idea. 
-
-The following code instantiates the two generators for the problem at hand. 
-
-```{julia}
-generic = GenericGenerator(;loss=:logitcrossentropy)
-greedy = GreedyGenerator(;loss=:logitcrossentropy)
-```
-
-### Explanations
-
-```{julia}
-#| echo: false
-# Randomly selected factual:
-using Random
-Random.seed!(1234)
-x = Flux.unsqueeze(select_factual(counterfactual_data, rand(1:size(X)[2])),2)
-target = 5
-γ = 0.80
-```
-
-Once the model and counterfactual generator are specified, running counterfactual search is very easy using the package. For a given factual (`x`), target class (`target`) and data set (`counterfactual_data`), simply running 
-
-```{julia}
-#| code-fold: false
-generate_counterfactual(x, target, counterfactual_data, M, generic)
-``` 
-
-will generate the results, in this case using the generic generator (`generic`) for the MLP (`M`). Since we have specified two different black-box models and two different counterfactual generators, we have four combinations of a model and a generator in total. For each of these combinations I have used the `generate_counterfactual` function to produce the results in @fig-mnist-9to4. 
-
-In every case the desired label switch is in fact achieved, but arguably from a human perspective only the counterfactuals for the deep ensemble look like a four. The generic generator produces mild perturbations in regions that seem irrelevant from a human perspective, but nonetheless yields a counterfactual that can pass as a four. The greedy approach clearly targets pixels at the top of the handwritten nine and yields the best result overall. For the non-Bayesian MLP, both the generic and the greedy approach generate counterfactuals that look much like adversarial examples: they perturb pixels in seemingly random regions on the image.
-
-```{julia}
-#| echo: false
-generators = Dict(
-    "Wachter" => generic,
-    "Greedy" => greedy
-)
-models = Dict("MLP" => M, "Ensemble" => M_ensemble)
-
-# Plotting utilities:
-using Images
-using MLDatasets.MNIST: convert2image
-
-input_dim = size(X)[1]
-
-using Flux: onecold
-
-# Specific image:
-function from_digit_to_digit(from::AbstractArray, to::Number, generator, model; γ=γ, x=X, y=ys, seed=1234, T=1000)
-    
-    x = from
-    target = to + 1
-    counterfactuals = Dict()
-
-    for (k_gen,v_gen) ∈ generators
-        for (k_mod,v_mod) ∈ models 
-            k = k_mod * " - " * k_gen
-            counterfactuals[k] = generate_counterfactual(x, target, counterfactual_data, v_mod, v_gen; T=T, γ=γ)
-        end
-    end
-
-    return counterfactuals
-
-end
-
-# Specific digit:
-function from_digit_to_digit(from::Number, to::Number, generator::Dict, model::Dict; γ=γ, x=X, y=ys, seed=1234, T=1000)
-
-    Random.seed!(seed)
-
-    candidates = findall(onecold(y,0:9).==from)
-    x = Flux.unsqueeze(x[:,rand(candidates)],2)
-    target = to + 1
-    counterfactuals = Dict()
-
-    for (k_gen,v_gen) ∈ generators
-        for (k_mod,v_mod) ∈ models 
-            k = k_mod * " - " * k_gen
-            counterfactuals[k] = generate_counterfactual(x, target, counterfactual_data, v_mod, v_gen; T=T, γ=γ)
-        end
-    end
-
-    return counterfactuals
-end
-```
-
-```{julia}
-#| echo: false
-using Plots
-to = 4
-counterfactuals = from_digit_to_digit(x,to,generators,models)
-plts =  first(values(counterfactuals)).x |> x -> plot(convert2image(reshape(x,Int(√(input_dim)),Int(√(input_dim)))),title="Original")
-plts = vcat(plts, [plot(convert2image(reshape(v.x′,Int(√(input_dim)),Int(√(input_dim)))),title=k) for (k,v) in counterfactuals])
-plt = plot(plts...,layout=(1,length(plts)),axis=nothing, size=(1200,300))
-savefig(plt, joinpath(www_path, "mnist_9_to_4.png"))
-```
-
-![Counterfactual explanations for MNIST: turning a nine (9) into a four (4).](www/mnist_9_to_4.png){#fig-mnist-9to4}
-
-```{julia}
-#| echo: false
-X = counterfactuals["Ensemble - Greedy"].search[:path]
-anim = @animate for t in 1:length(X)
-    plot(convert2image(reshape(X[t],Int(√(input_dim)),Int(√(input_dim)))),axis=nothing,size=(300,300))
-end every 10
-gif(anim, joinpath(www_path, "intro.gif"))
-```
-
-## Language interoperability 👥
-
-The Julia language offers unique support for programming language interoperability. For example, calling R or Python is made remarkably easy through `RCall.jl` and `PyCall.jl`, respectively. This functionality can be leveraged to use `CounterfactualExplanations.jl` to generate explanations for models that were developed in other programming languages. At this time there is no native support for foreign programming languages, but the following example involving a `torch` neural network trained in `R` demonstrates how versatile the package is.^[The corresponding example involving `PyTorch` is analogous and therefore not included here. You may find it [here](https://www.patalt.org/CounterfactualExplanations.jl/dev/tutorials/interop/).]
-
-### Explaining a `torch` model 
-
-```{julia}
-#| echo: false
-using Random
-# Some random data:
-Random.seed!(1234)
-N = 100
-using CounterfactualExplanations
-using CounterfactualExplanations.Data
-xs, ys = Data.toy_data_non_linear(N)
-X = hcat(xs...)
-counterfactual_data = CounterfactualData(X,ys')
-```
-
-```{julia}
-#| echo: false
-using RCall
-R"""
-# Data
-library(torch)
-X <- torch_tensor(t($X))
-ys <- torch_tensor($ys)
-
-# Model:
-mlp <- nn_module(
-  initialize = function() {
-    self$layer1 <- nn_linear(2, 32)
-    self$layer2 <- nn_linear(32, 1)
-  },
-  forward = function(input) {
-    input <- self$layer1(input)
-    input <- nnf_sigmoid(input)
-    input <- self$layer2(input)
-    input
-  }
-)
-model <- mlp()
-optimizer <- optim_adam(model$parameters, lr = 0.1)
-loss_fun <- nnf_binary_cross_entropy_with_logits
-
-for (epoch in 1:100) {
-
-  model$train()
-  train_losses <- c()  
-
-  optimizer$zero_grad()
-  output <- model(X)
-  loss <- loss_fun(output[,1], ys)
-  loss$backward()
-  optimizer$step()
-  train_losses <- c(train_losses, loss$item())
-  
-  cat(sprintf("Loss at epoch %d: %3f\n", epoch, mean(train_losses)))
-}
-"""
-```
-
-We will consider a simple MLP trained for a binary classification task. As before we first need to adapt this custom model for use with our package. The code below the two necessary steps - sub-typing and method extension. Logits are returned by the `torch` model and copied from the R environment into the Julia scope. Probabilities are then computed inside the Julia scope by passing the logits through the sigmoid function.
-
-```{julia}
-using Flux
-using CounterfactualExplanations, CounterfactualExplanations.Models
-import CounterfactualExplanations.Models: logits, probs # import functions in order to extend
-
-# Step 1)
-struct TorchNetwork <: Models.AbstractFittedModel
-    nn::Any
-end
-
-# Step 2)
-function logits(M::TorchNetwork, X::AbstractArray)
-  nn = M.nn
-  y = rcopy(R"as_array($nn(torch_tensor(t($X))))")
-  y = isa(y, AbstractArray) ? y : [y]
-  return y'
-end
-function probs(M::TorchNetwork, X::AbstractArray)
-  return σ.(logits(M, X))
-end
-M = TorchNetwork(R"model")
-```
-
-Compared to models trained in Julia, we need to do a little more work at this point. Since our counterfactual generators need gradient access, we essentially need to allow our package to communicate with the R `torch` library. While this may sound daunting, it turns out to be quite manageable: all we have to do is respecify the function that computes the gradient with respect to the counterfactual loss function so that it can deal with the `TorchNetwork` type we defined above. That is all the adjustment needed to use `CounterfactualExplanations.jl` for our custom R model. @fig-torch shows a counterfactual path for a randomly chosen sample with respect to the MLP trained in R.
-
-:::{.callout-caution}
-## Experimental functionality
-
-You may have stumbled across the term *respecify* above: does it really seem like a good idea to just replace an existing function from our package? Surely not! There are certainly better ways to go about this, which we will consider when adding native support for Python and R models in future package releases. Which brings us to our final section ...
-:::
-
-```{julia}
-import CounterfactualExplanations.Generators: ∂ℓ
-using LinearAlgebra
-
-# Countefactual loss:
-function ∂ℓ(
-    generator::AbstractGradientBasedGenerator, 
-    counterfactual_state::CounterfactualState) 
-  M = counterfactual_state.M
-  nn = M.nn
-  x′ = counterfactual_state.x′
-  t = counterfactual_state.target_encoded
-  R"""
-  x <- torch_tensor($x′, requires_grad=TRUE)
-  output <- $nn(x)
-  loss_fun <- nnf_binary_cross_entropy_with_logits
-  obj_loss <- loss_fun(output,$t)
-  obj_loss$backward()
-  """
-  grad = rcopy(R"as_array(x$grad)")
-  return grad
-end
-```
-
-```{julia}
-#| echo: false
-# Randomly selected factual:
-Random.seed!(123)
-x = select_factual(counterfactual_data, rand(1:length(xs))) 
-y = round(probs(M, x)[1])
-target = ifelse(y==1.0,0.0,1.0) # opposite label as target
-# Define generator:
-generator = GenericGenerator()
-# Generate recourse:
-counterfactual = generate_counterfactual(x, target, counterfactual_data, M, generator)
-```
-
-```{julia}
-#| echo: false
-using Plots
-T = size(path(counterfactual))[1]
-X_path = reduce(hcat,path(counterfactual))
-plt = plot_contour(X',ys,M)
-[scatter!(plt, [path(counterfactual)[t][1]], [path(counterfactual)[t][2]], ms=7.5, color=Int(y), label="") for t in 1:T]
-savefig(plt, joinpath(www_path,"interop_r.png"))
-```
-
-![Counterfactual path using the generic counterfactual generator for a model trained in R.](www/interop_r.gif){#fig-torch}
-
-<!-- kicker -->
-
-## We need you! 🫵
-
-The ambition for `CounterfactualExplanations.jl` is to provide a go-to place for counterfactual explanations to the Julia community and beyond. This is a grand ambition, especially for a package that has so far been built by a single developer who has little prior experience with Julia. We would therefore very much like to invite community contributions. If you have an interest in trustworthy AI, the open-source community and Julia, please do get involved! This package is still in its early stages of development, so any kind of contribution is welcome: advice on the core package architecture, pull requests, issues, discussions and even just comments below would be much appreciated. 
-
-To give you a flavor of what type of future developments we envision, here is a non-exhaustive list:
-
-1. Native support for additional counterfactual generators and predictive models including those built and trained in Python or R.
-2. Additional datasets for testing, evaluation and benchmarking.
-3. Improved preprocessing including native support for categorical features.
-4. Support for regression models.
-
-Finally, if you like this project but don't have much time, then simply sharing this article or starring the [repo](https://github.com/juliatrustworthyai/CounterfactualExplanations.jl) on GitHub would also go a long way.
-
-## Further reading 📚
-
-If you're interested in learning more about this development, feel free to check out the following resources:
-
-- Package docs: [[stable]](https://juliatrustworthyai.github.io/CounterfactualExplanations.jl/stable), [[dev]](https://juliatrustworthyai.github.io/CounterfactualExplanations.jl/dev).
-- [Contributor's guide](https://www.patalt.org/CounterfactualExplanations.jl/stable/contributing/).
-- [GitHub repo](https://github.com/juliatrustworthyai/CounterfactualExplanations.jl).
+---
+
+```{julia}
+#| echo: false
+www_path = "posts/a-new-tool-for-explainable-ai/www"
+```
+
+<div class="intro-gif">
+  <figure>
+    <img src="www/intro.gif">
+    <figcaption>Turning a 9 (nine) into a 4 (four).</figcaption>
+  </figure>
+</div>
+
+<!-- Intro -->
+
+Counterfactual explanations, which I introduced in one of my previous posts^[See: [[TDS](https://towardsdatascience.com/individual-recourse-for-black-box-models-5e9ed1e4b4cc)], [[blog](https://www.patalt.org/blog/posts/individual-recourse-for-black-box-models/)]], offer a simple and intuitive way to explain black-box models without opening them. Still, as of today there exists only one open-source library that provides a unifying approach to generate and benchmark counterfactual explanations for models built and trained in Python [@pawelczyk2021carla]. This is great, but of limited use to users of other programming languages 🥲. 
+
+Enter [`CounterfactualExplanations.jl`](https://www.patalt.org/CounterfactualExplanations.jl/stable/): a Julia package that can be used to explain machine learning algorithms developed and trained in Julia, Python and R. Counterfactual explanations fall into the broader category of explainable artificial intelligence (XAI). 
+
+Explainable AI typically involves models that are not inherently interpretable but require additional tools to be explainable to humans. Examples of the latter include ensembles, support vector machines and deep neural networks. This is not to be confused with interpretable AI, which involves models that are inherently interpretable and transparent such as general additive models (GAM), decision trees and rule-based models. 
+
+Some would argue that we best avoid explaining black-box models altogether [@rudin2019stop] and instead focus solely on interpretable AI. While I agree that initial efforts should always be geared towards interpretable models, stopping there would entail missed opportunities and anyway is probably not very realistic in times of [DALL$\cdot$E](https://openai.com/blog/dall-e/) and Co.
+
+> Even though [...] interpretability is of great importance and should be pursued, explanations can, in principle, be offered without opening the “black box.”
+>
+> --- @wachter2017counterfactual
+
+<!-- Nut paragraph -->
+
+This post introduces the main functionality of the new Julia package. Following a motivating example using a model trained in Julia, we will see how easy the package can be adapted to work with models trained in Python and R. Since the motivation for this post is also to hopefully attract contributors, the final section outlines some of the exciting developments we have planned. 
+
+## Counterfactuals for image data 🖼
+
+To introduce counterfactual explanations I used a simple binary classification problem in my previous [post](https://towardsdatascience.com/individual-recourse-for-black-box-models-5e9ed1e4b4cc). It involved a linear classifier and a linearly separable, synthetic data set with just two features. This time we are going to step it up a notch: we will generate counterfactual explanations MNIST data. The MNIST dataset contains 60,000 training samples of handwritten digits in the form of 28x28 pixel grey-scale images [@lecun1998mnist]. Each image is associated with a label indicating the digit (0-9) that the image represents. 
+
+The [`CounterfactualExplanations.jl`](https://www.patalt.org/CounterfactualExplanations.jl/stable/) package ships with two black-box models that were trained to predict labels for this data: firstly, a simple multi-layer perceptron (MLP) and, secondly, a corresponding deep ensemble. Originally proposed by @lakshminarayanan2016simple, deep ensembles are really just ensembles of deep neural networks. They are still among the most popular approaches to Bayesian deep learning.^[For more information on Bayesian deep learning see my previous post: [[TDS](https://towardsdatascience.com/go-deep-but-also-go-bayesian-ab25efa6f7b)], [[blog](https://www.patalt.org/blog/posts/effortsless-bayesian-dl/)].] 
+
+### Black-box models
+
+The code below loads relevant packages along with the MNIST data and pre-trained models. 
+
+```{julia}
+# Load package, models and data:
+using CounterfactualExplanations, Flux
+using CounterfactualExplanations.Data: mnist_data, mnist_model, mnist_ensemble
+data, X, ys = mnist_data()
+model = mnist_model()
+ensemble = mnist_ensemble()
+counterfactual_data = CounterfactualData(X,ys;domain=(0,1))
+```
+
+While the package can currently handle a few simple classification models natively, it is designed to be easily extensible through users and contributors. Extending the package to deal with custom models typically involves only two simple steps:
+
+1. **Subtyping**: the custom model needs to be declared as a subtype of the package-internal type `AbstractFittedModel`.
+2. **Multiple dispatch**: the package-internal functions `logits` and `probs` need to be extended through custom methods for the new model type.
+
+The following code implements these two steps first for the MLP and then for the deep ensemble.
+
+```{julia}
+using CounterfactualExplanations.Models
+import CounterfactualExplanations.Models: logits, probs
+# MLP:
+# Step 1)
+struct NeuralNetwork <: Models.AbstractFittedModel
+    model::Any
+end
+# Step 2)
+logits(M::NeuralNetwork, X::AbstractArray) = M.model(X)
+probs(M::NeuralNetwork, X::AbstractArray)= softmax(logits(M, X))
+M = NeuralNetwork(model)
+
+# Deep ensemble:
+using Flux: stack
+# Step 1)
+struct FittedEnsemble <: Models.AbstractFittedModel
+    ensemble::AbstractArray
+end
+# Step 2)
+using Statistics
+logits(M::FittedEnsemble, X::AbstractArray) = mean(stack([m(X) for m in M.ensemble],3),dims=3)
+probs(M::FittedEnsemble, X::AbstractArray) = mean(stack([softmax(m(X)) for m in M.ensemble],3),dims=3)
+M_ensemble = FittedEnsemble(ensemble)
+```
+
+### Counterfactual generators
+
+Next, we need to specify the counterfactual generators we want to use. The package currently ships with two default generators that both need gradient access: firstly, the generic generator introduced by @wachter2017counterfactual and, secondly, a greedy generator introduced by @schut2021generating. 
+
+The greedy generator is designed to be used with models that incorporate uncertainty in their predictions such as the deep ensemble introduced above. It works for probabilistic (Bayesian) models, because they only produce high-confidence predictions in regions of the feature domain that are populated by training samples. As long as the model is expressive enough and well-specified, counterfactuals in these regions will always be realistic and unambiguous since by construction they should look very similar to training samples. Other popular approaches to counterfactual explanations like REVISE [@joshi2019realistic] and CLUE [@antoran2020getting] also play with this simple idea. 
+
+The following code instantiates the two generators for the problem at hand. 
+
+```{julia}
+generic = GenericGenerator(;loss=:logitcrossentropy)
+greedy = GreedyGenerator(;loss=:logitcrossentropy)
+```
+
+### Explanations
+
+```{julia}
+#| echo: false
+# Randomly selected factual:
+using Random
+Random.seed!(1234)
+x = Flux.unsqueeze(select_factual(counterfactual_data, rand(1:size(X)[2])),2)
+target = 5
+γ = 0.80
+```
+
+Once the model and counterfactual generator are specified, running counterfactual search is very easy using the package. For a given factual (`x`), target class (`target`) and data set (`counterfactual_data`), simply running 
+
+```{julia}
+#| code-fold: false
+generate_counterfactual(x, target, counterfactual_data, M, generic)
+``` 
+
+will generate the results, in this case using the generic generator (`generic`) for the MLP (`M`). Since we have specified two different black-box models and two different counterfactual generators, we have four combinations of a model and a generator in total. For each of these combinations I have used the `generate_counterfactual` function to produce the results in @fig-mnist-9to4. 
+
+In every case the desired label switch is in fact achieved, but arguably from a human perspective only the counterfactuals for the deep ensemble look like a four. The generic generator produces mild perturbations in regions that seem irrelevant from a human perspective, but nonetheless yields a counterfactual that can pass as a four. The greedy approach clearly targets pixels at the top of the handwritten nine and yields the best result overall. For the non-Bayesian MLP, both the generic and the greedy approach generate counterfactuals that look much like adversarial examples: they perturb pixels in seemingly random regions on the image.
+
+```{julia}
+#| echo: false
+generators = Dict(
+    "Wachter" => generic,
+    "Greedy" => greedy
+)
+models = Dict("MLP" => M, "Ensemble" => M_ensemble)
+
+# Plotting utilities:
+using Images
+using MLDatasets.MNIST: convert2image
+
+input_dim = size(X)[1]
+
+using Flux: onecold
+
+# Specific image:
+function from_digit_to_digit(from::AbstractArray, to::Number, generator, model; γ=γ, x=X, y=ys, seed=1234, T=1000)
+    
+    x = from
+    target = to + 1
+    counterfactuals = Dict()
+
+    for (k_gen,v_gen) ∈ generators
+        for (k_mod,v_mod) ∈ models 
+            k = k_mod * " - " * k_gen
+            counterfactuals[k] = generate_counterfactual(x, target, counterfactual_data, v_mod, v_gen; T=T, γ=γ)
+        end
+    end
+
+    return counterfactuals
+
+end
+
+# Specific digit:
+function from_digit_to_digit(from::Number, to::Number, generator::Dict, model::Dict; γ=γ, x=X, y=ys, seed=1234, T=1000)
+
+    Random.seed!(seed)
+
+    candidates = findall(onecold(y,0:9).==from)
+    x = Flux.unsqueeze(x[:,rand(candidates)],2)
+    target = to + 1
+    counterfactuals = Dict()
+
+    for (k_gen,v_gen) ∈ generators
+        for (k_mod,v_mod) ∈ models 
+            k = k_mod * " - " * k_gen
+            counterfactuals[k] = generate_counterfactual(x, target, counterfactual_data, v_mod, v_gen; T=T, γ=γ)
+        end
+    end
+
+    return counterfactuals
+end
+```
+
+```{julia}
+#| echo: false
+using Plots
+to = 4
+counterfactuals = from_digit_to_digit(x,to,generators,models)
+plts =  first(values(counterfactuals)).x |> x -> plot(convert2image(reshape(x,Int(√(input_dim)),Int(√(input_dim)))),title="Original")
+plts = vcat(plts, [plot(convert2image(reshape(v.x′,Int(√(input_dim)),Int(√(input_dim)))),title=k) for (k,v) in counterfactuals])
+plt = plot(plts...,layout=(1,length(plts)),axis=nothing, size=(1200,300))
+savefig(plt, joinpath(www_path, "mnist_9_to_4.png"))
+```
+
+![Counterfactual explanations for MNIST: turning a nine (9) into a four (4).](www/mnist_9_to_4.png){#fig-mnist-9to4}
+
+```{julia}
+#| echo: false
+X = counterfactuals["Ensemble - Greedy"].search[:path]
+anim = @animate for t in 1:length(X)
+    plot(convert2image(reshape(X[t],Int(√(input_dim)),Int(√(input_dim)))),axis=nothing,size=(300,300))
+end every 10
+gif(anim, joinpath(www_path, "intro.gif"))
+```
+
+## Language interoperability 👥
+
+The Julia language offers unique support for programming language interoperability. For example, calling R or Python is made remarkably easy through `RCall.jl` and `PyCall.jl`, respectively. This functionality can be leveraged to use `CounterfactualExplanations.jl` to generate explanations for models that were developed in other programming languages. At this time there is no native support for foreign programming languages, but the following example involving a `torch` neural network trained in `R` demonstrates how versatile the package is.^[The corresponding example involving `PyTorch` is analogous and therefore not included here. You may find it [here](https://www.patalt.org/CounterfactualExplanations.jl/dev/tutorials/interop/).]
+
+### Explaining a `torch` model 
+
+```{julia}
+#| echo: false
+using Random
+# Some random data:
+Random.seed!(1234)
+N = 100
+using CounterfactualExplanations
+using CounterfactualExplanations.Data
+xs, ys = Data.toy_data_non_linear(N)
+X = hcat(xs...)
+counterfactual_data = CounterfactualData(X,ys')
+```
+
+```{julia}
+#| echo: false
+using RCall
+R"""
+# Data
+library(torch)
+X <- torch_tensor(t($X))
+ys <- torch_tensor($ys)
+
+# Model:
+mlp <- nn_module(
+  initialize = function() {
+    self$layer1 <- nn_linear(2, 32)
+    self$layer2 <- nn_linear(32, 1)
+  },
+  forward = function(input) {
+    input <- self$layer1(input)
+    input <- nnf_sigmoid(input)
+    input <- self$layer2(input)
+    input
+  }
+)
+model <- mlp()
+optimizer <- optim_adam(model$parameters, lr = 0.1)
+loss_fun <- nnf_binary_cross_entropy_with_logits
+
+for (epoch in 1:100) {
+
+  model$train()
+  train_losses <- c()  
+
+  optimizer$zero_grad()
+  output <- model(X)
+  loss <- loss_fun(output[,1], ys)
+  loss$backward()
+  optimizer$step()
+  train_losses <- c(train_losses, loss$item())
+  
+  cat(sprintf("Loss at epoch %d: %3f\n", epoch, mean(train_losses)))
+}
+"""
+```
+
+We will consider a simple MLP trained for a binary classification task. As before we first need to adapt this custom model for use with our package. The code below the two necessary steps - sub-typing and method extension. Logits are returned by the `torch` model and copied from the R environment into the Julia scope. Probabilities are then computed inside the Julia scope by passing the logits through the sigmoid function.
+
+```{julia}
+using Flux
+using CounterfactualExplanations, CounterfactualExplanations.Models
+import CounterfactualExplanations.Models: logits, probs # import functions in order to extend
+
+# Step 1)
+struct TorchNetwork <: Models.AbstractFittedModel
+    nn::Any
+end
+
+# Step 2)
+function logits(M::TorchNetwork, X::AbstractArray)
+  nn = M.nn
+  y = rcopy(R"as_array($nn(torch_tensor(t($X))))")
+  y = isa(y, AbstractArray) ? y : [y]
+  return y'
+end
+function probs(M::TorchNetwork, X::AbstractArray)
+  return σ.(logits(M, X))
+end
+M = TorchNetwork(R"model")
+```
+
+Compared to models trained in Julia, we need to do a little more work at this point. Since our counterfactual generators need gradient access, we essentially need to allow our package to communicate with the R `torch` library. While this may sound daunting, it turns out to be quite manageable: all we have to do is respecify the function that computes the gradient with respect to the counterfactual loss function so that it can deal with the `TorchNetwork` type we defined above. That is all the adjustment needed to use `CounterfactualExplanations.jl` for our custom R model. @fig-torch shows a counterfactual path for a randomly chosen sample with respect to the MLP trained in R.
+
+:::{.callout-caution}
+## Experimental functionality
+
+You may have stumbled across the term *respecify* above: does it really seem like a good idea to just replace an existing function from our package? Surely not! There are certainly better ways to go about this, which we will consider when adding native support for Python and R models in future package releases. Which brings us to our final section ...
+:::
+
+```{julia}
+import CounterfactualExplanations.Generators: ∂ℓ
+using LinearAlgebra
+
+# Countefactual loss:
+function ∂ℓ(
+    generator::AbstractGradientBasedGenerator, 
+    counterfactual_state::CounterfactualState) 
+  M = counterfactual_state.M
+  nn = M.nn
+  x′ = counterfactual_state.x′
+  t = counterfactual_state.target_encoded
+  R"""
+  x <- torch_tensor($x′, requires_grad=TRUE)
+  output <- $nn(x)
+  loss_fun <- nnf_binary_cross_entropy_with_logits
+  obj_loss <- loss_fun(output,$t)
+  obj_loss$backward()
+  """
+  grad = rcopy(R"as_array(x$grad)")
+  return grad
+end
+```
+
+```{julia}
+#| echo: false
+# Randomly selected factual:
+Random.seed!(123)
+x = select_factual(counterfactual_data, rand(1:length(xs))) 
+y = round(probs(M, x)[1])
+target = ifelse(y==1.0,0.0,1.0) # opposite label as target
+# Define generator:
+generator = GenericGenerator()
+# Generate recourse:
+counterfactual = generate_counterfactual(x, target, counterfactual_data, M, generator)
+```
+
+```{julia}
+#| echo: false
+using Plots
+T = size(path(counterfactual))[1]
+X_path = reduce(hcat,path(counterfactual))
+plt = plot_contour(X',ys,M)
+[scatter!(plt, [path(counterfactual)[t][1]], [path(counterfactual)[t][2]], ms=7.5, color=Int(y), label="") for t in 1:T]
+savefig(plt, joinpath(www_path,"interop_r.png"))
+```
+
+![Counterfactual path using the generic counterfactual generator for a model trained in R.](www/interop_r.gif){#fig-torch}
+
+<!-- kicker -->
+
+## We need you! 🫵
+
+The ambition for `CounterfactualExplanations.jl` is to provide a go-to place for counterfactual explanations to the Julia community and beyond. This is a grand ambition, especially for a package that has so far been built by a single developer who has little prior experience with Julia. We would therefore very much like to invite community contributions. If you have an interest in trustworthy AI, the open-source community and Julia, please do get involved! This package is still in its early stages of development, so any kind of contribution is welcome: advice on the core package architecture, pull requests, issues, discussions and even just comments below would be much appreciated. 
+
+To give you a flavor of what type of future developments we envision, here is a non-exhaustive list:
+
+1. Native support for additional counterfactual generators and predictive models including those built and trained in Python or R.
+2. Additional datasets for testing, evaluation and benchmarking.
+3. Improved preprocessing including native support for categorical features.
+4. Support for regression models.
+
+Finally, if you like this project but don't have much time, then simply sharing this article or starring the [repo](https://github.com/juliatrustworthyai/CounterfactualExplanations.jl) on GitHub would also go a long way.
+
+## Further reading 📚
+
+If you're interested in learning more about this development, feel free to check out the following resources:
+
+- Package docs: [[stable]](https://juliatrustworthyai.github.io/CounterfactualExplanations.jl/stable), [[dev]](https://juliatrustworthyai.github.io/CounterfactualExplanations.jl/dev).
+- [Contributor's guide](https://www.patalt.org/CounterfactualExplanations.jl/stable/contributing/).
+- [GitHub repo](https://github.com/juliatrustworthyai/CounterfactualExplanations.jl).
+
 
 
-
 
    
 
    
 
     
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+When Causality meets Recourse – Taija
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+
    When Causality meets Recourse
    
+
    Counterfactual Explanations through Structural Causal Models
    
+  
    
+    
    counterfactuals
    
+    
    explainable AI
    
+    
    causality
    
+    
    Julia
    
+  
    
+  
    
+
+
    
+  
    
+    
    This post introduces a new tool in CounterfactualExplanations.jl, enhancing the package with causal reasoning to generate counterfactual explanations.
    
+  
    
+
    
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+
    
+
+    
    
+    
    Author
    
+    
    
+             
    Jorge Luiz Franco 
    
+          
    
+  
    
+    
+    
    
+    
    Published
    
+    
    
+      
    September 17, 2024
    
+    
    
+  
    
+  
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+
    
+
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+
    
+
    Introduction
    
+
    In recent years, the need for interpretable and explainable AI has surged, particularly in high-stakes domains. Counterfactual explanations provide a means to understand how changes to input features could alter the outcomes of machine learning models. This blog post presents a new tool in the CounterfactualExplanations.jl package, developed during my JSoC (Julia Summer of Code) project, which incorporates causal reasoning into counterfactual generation.
    
+
    
+
    
+
    Project Overview
    
+
    This project aimed to enhance the CounterfactualExplanations.jl package by infusing it with a robust mathematical foundation for minimal algorithmic recourse, based on the principles of causal reasoning (Karimi, Schölkopf, and Valera 2021).
    
+
    
+
    Key Contributions
    
+
    During the project, I contributed to two key repositories:
    
+
      
+
    1. CounterfactualExplanations.jl: Developed a new tool for generating counterfactual explanations using causal information. This allows users to create smarter perturbations rather than random adjustments, ultimately providing more meaningful insights.
      2. 
+
    2. CausalInference.jl: Implemented a Structural Causal Model (SCM) structure that extracts information from data, laying the groundwork for the causal reasoning capabilities in CounterfactualExplanations.jl.
      3. 
+
    
+
    This was an amazing experience, not just experience contribute to two repositories simultaneously, but also to work with the mantainers of these repos. I learned a lot about the Julia language and the Julia community. This was possible because of the mentorship of Patrick Altmeyer (CounterfactualExplanations) and Moritz Schauer (CausalInference), who guided me throughout the project and are amazing researchers.
    
+
    
+
    
+
    The MINTGenerator
    
+
    In this project, we developed the MINTGenerator, a counterfactual generator based on the Recourse through Minimal Intervention (MINT) method proposed by Karimi, Schölkopf, and Valera (2021).
    
+
    
+
    
+
    Description
    
+
    The MINTGenerator incorporates causal reeasoning in algorithm recourse to achieve minimal interventions when generating a counterfactual explanation. In this sense, the main ideia is that just perturbating a black box model without taking into account the causal relations in the data can guide to misleading recommendations. Here we now shift to a perspective where every action/pertubation is an intervetion in the causal graph of the problem, thus the change is not made just in the intervened upon variable, but also in its childs in the causal structure. The generator utilizes a Structural Causal Model(SCM) to encode the variables in a way that causal effects are propagated and uses a generic gradient-based generator to create the search path, that is, any gradient-base generator (ECCo, REVISE, Watcher, …) can be used with the MINT SCM encoder to generate counterfactual samples in latent space for minimal intervetions algorithm recourse.
    
+
    The MINT algorithm minimizes a loss function that combines the causal constraints of the SCM and the distance between the generated counterfactual and the original input. Since we want a gradient-based generator, we need to pass the constrained optimizaiton problem into an unconstrained one and we do this by using the Lagrangian. Initially, as defined in (Karimi, Schölkopf, and Valera 2021), we aim to aim to find the minimal cost set of actions \(A\) (in the form of structural interventions) that results in a counterfactual instance yielding the favorable output from \(h\),
    
+$$
+\[\begin{aligned}
+
+A^* \in \arg\min_A \text{cost}(A; \mathbf{x}_F)\\
+\textrm{s.t.} \quad  h(\mathbf{x}_{SCF}) \neq h(\mathbf{x}_F) \; \; \text{,}\\
+
+\end{aligned}\]
+
    $$
    
+
    where \(\mathbf{x}_F\) is the original input, \(\mathbf{x}_{SCF}\) is the counterfactual instance, and \(h\) is the black-box model. We use the \(\mathbf{x}_{SCF}\) terminology because the counterfactual is derived from the SCM,
    
+
    \[
+x_{SCF_i} =
+\begin{cases}
+x_{F_i} + \delta_i, & \text{if } i \in I \\
+x_{F_i} + f_i(\text{pa}_{SCF_i}) - f_i(\text{pa}_{F_i}), & \text{if } i \notin I  \; \; \text{,}
+\end{cases}
+\]
    
+
    where \(I\) is the set of intervened upon variables, \(f_i\) is the function that generates the value of the variable \(i\) given its parents, and \(\text{pa}_{SCF_i}\) and \(\text{pa}_{F_i}\) are the parents of the variable \(i\) in the counterfactual and original instance, respectively. This closed formula for the decision variable \(\mathbf{x}_{SCF}\) is what makes possible to use a gradient-based generator, since with it the lagrangian is differentiable,
    
+
    \[
+\mathcal{L}(A ; \lambda) = \text{cost}(A; \mathbf{x}_F) + \lambda \left(h(\mathbf{x}_{SCF}) - h(\mathbf{x}_F) \right) \; \; \text{,}
+\]
    
+
    or in simple terms and more standard, since \(\lambda\) is constant,
    
+
    \[
+\mathcal{L_{\texttt{MINT}}}(\mathbf{x}_{SCF}) = \lambda \text{cost}(\mathbf{x}_{SCF}; \mathbf{x}_F) + \text{yloss}(\mathbf{x}_{SCF},y^*) \; \; \text{,}
+\]
    
+
    where \(y^*\) is clearly \(h(x_F)\) and \(\text{yloss}\) is :
    
+
    \[
+\text{yloss}(\mathbf{x}_{SCF}, y^*) = h \left(\left\{ x_{F_i} + \delta_i [i \in I] + \left(f_i(\text{pa}_{SCF_i}) - f_i(\text{pa}_{F_i}) \right) [i \notin I] \right\}_{i=1}^n \right) - y^* \; \; \text{.}
+\]
    
+
    
+
    
+
    Implementation
    
+
    
+
    CausalInference.jl
    
+
    In terms of implementation, we need to capture the causal relations from the data, that’s where CausalInference.jl comes in. However, before the project, the package did not have a SCM structure, in the sense that the methods just captured the topological Directed Acyclic Graph (DAG) that showed the causality ruling the data, that is, no causal structural equations were provided,
    
+
    
+
    
+Code
+
    using CausalInference
+using Plots, GraphRecipes
+using Random
+Random.seed!(1)
+
+N = 2000 # number of data points
+
+x = randn(N)
+v = x + randn(N)*0.25
+w = x + randn(N)*0.25
+z = v + w + randn(N)*0.25
+s = z + randn(N)*0.25
+
+df = (x=x, v=v, w=w, z=z, s=s)
+
+est_g, score = ges(df; penalty=1.0, parallel=true)
+
+plt = graphplot(pdag2dag!(est_g), names= [String(k) for k in keys(df)], size=(500,500), nodesize=0.3)
+savefig(plt, "www/intro.png")
+display(plt)
    
+
    
+
    
+
    ┌ Warning: Only one thread available
+└ @ CausalInference ~/.julia/packages/CausalInference/ozcj8/src/ges.jl:52
    
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    So, our goal was given the DAG provided by the ges method in the causal discovery (Chickering 2003), generate equations that rules each of these causal relations, represented in the DAG as directed edges. The SCM is the union of the DAG and these causal equations, that is, the SCM is a tuple \((G, \mathbf{f})\), where \(G\) is the DAG and \(\mathbf{f}\) is the set of functions that generates the value of each variable given its parents.
    
+
    Our solution for constructing the structural causal equations was to assume that the data was generated by a linear model, ie, the causal relations were linear. For the DAG provided in the code example we derive
    
+
    \[ v = \mathcal{b}_v \]
    
+
    \[ x = \mathcal{a}_{v \to x} v + \mathcal{b}_x \]
    
+
    \[ w = \mathcal{a}_{x \to w} x + \mathcal{b}_w \]
    
+
    \[ z = \mathcal{a}_{v \to z} v+ \mathcal{a}_{w \to z} w + \mathcal{b}_z \]
    
+
    \[ s = \mathcal{a}_{z \to s} z + \mathcal{b}_s \]
    
+
    and that’s the tricky thing, as we can see these causal equations are different than the ones that generated the data, but they are the ones that respect the causal system obtained from the obtained DAG. Here \(\mathcal{b}_i\) and \(\mathcal{a}_{i \to j}\) are the intercept term and the coefficient obtained from the linear regression, respectively. To correctly solve the linear regression respecting the dependencies of the causal graph, we use topological_sort_by_dfs from Graphs.jl.
    
+
    Now, with the SCM structure in hand, we see that the representation could be a struct containing the DAG and the coefficients/intercepts of the causal equations, this maps exactly the tuple \((G, \mathbf{f})\) that we defined. However, since we need these equations to be differentiable, we need to define a function that takes the SCM and returns the value of the variable given its parents and using just the coefficients and the DAG, lead to errors, because AutoDiff does not deal well with functions that are conditioned (if statements). So, we need to define a way to retrieve the system of causal equations in a smooth way and that’s where the causal_effects matrix comes to the rescue.
    
+
    Let the factual vector of features be denoted as:
    
+
    \[
+\mathbf{x}_F =
+\begin{bmatrix}
+x_{F_1} \\
+x_{F_2} \\
+x_{F_3} \\
+\vdots \\
+x_{F_n}
+\end{bmatrix}
+\]
    
+
    Let the causal_effects matrix be:
    
+
    \[
+\mathbf{C} =
+\begin{bmatrix}
+a_{11} & a_{12} & \cdots & a_{1n} & b_1 \\
+a_{21} & a_{22} & \cdots & a_{2n} & b_2 \\
+a_{31} & a_{32} & \cdots & a_{3n} & b_3 \\
+\vdots & \vdots & \ddots & \vdots & \vdots \\
+a_{n1} & a_{n2} & \cdots & a_{nn} & b_n \\
+\end{bmatrix}
+\]
    
+
    Here, \(a_{ij}\) represents the coefficient from the causal effect of \(x_{F_j}\) on \(x_{F_i}\), and \(b_i\) represents the intercept term for the variable \(x_{F_i}\).
    
+
    The matrix multiplication of the causal_effects matrix with the factual vector (excluding the bias term) is given by:
    
+
    \[
+\mathbf{C}_{:, 1:n} \cdot \mathbf{x}_F =
+\begin{bmatrix}
+a_{11} & a_{12} & \cdots & a_{1n} \\
+a_{21} & a_{22} & \cdots & a_{2n} \\
+a_{31} & a_{32} & \cdots & a_{3n} \\
+\vdots & \vdots & \ddots & \vdots \\
+a_{n1} & a_{n2} & \cdots & a_{nn}
+\end{bmatrix}
+\begin{bmatrix}
+x_{F_1} \\
+x_{F_2} \\
+x_{F_3} \\
+\vdots \\
+x_{F_n}
+\end{bmatrix}
+\]
    
+
    Finally, we add the bias term:
    
+
    \[
+\mathbf{x}_{SCF} = \mathbf{C}_{:, 1:n} \cdot \mathbf{x}_F +
+\begin{bmatrix}
+b_1 \\
+b_2 \\
+b_3 \\
+\vdots \\
+b_n
+\end{bmatrix}
+\]
    
+
    In expanded form:
    
+
    \[
+\mathbf{x}_{SCF_i} = a_{i1} x_{F_1} + a_{i2} x_{F_2} + \cdots + a_{in} x_{F_n} + b_i, \quad \forall i = 1, 2, \dots, n
+\]
    
+
    This equation shows how each counterfactual variable \(x_{SCF_i}\) is generated as a linear combination of the factual inputs \(x_{F_j}\) based on the causal effects matrix, with an intercept term \(b_i\) added for each variable.
    
+
    One can note that the orphan nodes, that is, the nodes that do not have parents in the DAG, are going to be equal to the intercept term \(\mathcal{b}_\hat{o}\). The intuition behind this is that when we do the linear regression, variables that have no causal parents are just equal to the unconditional mean of the variable, i.e, we get \(x_{SCF_\hat{o}} = \mathbb{E}(x_\hat{o})\). Because of this, in some cases a better understanding of the regression is needed, so the residuals are also part of the SCM structure,
    
+
    
+
    
+Code
+
    struct SCM
+    variables::Vector{String}
+    coefficients::Vector{Vector{Float64}}
+    residuals::Vector{Vector{Float64}}
+    dag::DiGraph
+    causal_effects::Matrix{Float64}
+end
    
+
    
+
    
+
    
+
    
+
    CounterfactualExplanations.jl
    
+
    
+
    
+
    
+
    
+
    Conclusion
    
+
+
    
+
    
+
+
+
+
+
+
+
    
+
+
    References
    
+
    
+Chickering, David Maxwell. 2003. “Optimal Structure Identification with Greedy Search.” J. Mach. Learn. Res. 3 (null): 507–54. https://doi.org/10.1162/153244303321897717.
+
    
+
    
+Karimi, Amir-Hossein, Bernhard Schölkopf, and Isabel Valera. 2021. “Algorithmic Recourse: From Counterfactual Explanations to Interventions.” In Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency, 353–62. FAccT ’21. New York, NY, USA: Association for Computing Machinery. https://doi.org/10.1145/3442188.3445899.
+
    
+
    Citation
    BibTeX citation:
    @online{altmeyer2024,
+  author = {Altmeyer, Patrick and Luiz Franco, Jorge},
+  title = {When {Causality} Meets {Recourse}},
+  date = {2024-09-17},
+  url = {https://www.taija.org/blog/posts/causal-recourse/},
+  langid = {en}
+}
+
    For attribution, please cite this work as:
    
+Altmeyer, Patrick, and Jorge Luiz Franco. 2024. “When Causality
+Meets Recourse.” September 17, 2024. https://www.taija.org/blog/posts/causal-recourse/.
+
     
+
+
+
     
+
+
+
+
+
+
\ No newline at end of file
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zoT>$|e%3KE5;gc?`cQe|bb5^jDe!8k7C`Fg8n>Cvil+Mj++yWtbOn this page
    
 
    
 
    🎯 The Task at Hand
    
 
    The task at hand is to predict the labels of handwritten images of digits using the famous MNIST dataset (LeCun 1998). Importing this popular machine learning dataset in Julia is made remarkably easy through MLDatasets.jl:
    
-
    
+
    
 
    
 Code
 
    using MLDatasets
@@ -306,7 +306,7 @@ 
    🎯 The Task at Hand
    
 
    
 
    Figure 1 below shows a few random samples from the training data:
    
-
    
+
    
 
    
 Code
 
    using MLJ
@@ -317,10 +317,10 @@ 
    🎯 The Task at Hand
    n_samples = 10
 mosaic(rand(X, n_samples)..., ncol=n_samples)
    
 
    
-
    
+
    
 
    
 
    
-
+
 
    
 
    
 Figure 1: Random samples from the MNIST dataset.
@@ -333,7 +333,7 @@ 
    🎯 The Task at Hand
    🚧 Building the Network

     + + + + + + + +📊 Results EAMAAJAkiAEAAEgSxAAAACQJYgAAAJIEMQAAAEmCGAAAgCRBDAAAQJIgBgAAIEkQAwAAkCSIAQAA SBLEAAAAJAliAAAAkgQxAAAASYIYAACAJEEMAABAkiAGAAAgSRADAACQJIgBAABIEsQAAAAkCWIA AACSBDEAAABJghgAAIAkQQwAAECSIAYAACBJEAMAAJAkiAEAAEgSxAAAACQJYgAAAJIEMQAAAEmC -GAAAgCRBDAAAQJIgBgAAIEkQAwAAkCSIAQAASBLEAAAAJAliAAAAkv4A3XR5beO14yUAAAAASUVO -RK5CYII= +GAAAgCRBDAAAQJIgBgAAIEkQAwAAkCSIAQAASBLEAAAAJAliAAAAkgQxAAAASYIYAACAJEEMAABA +kiAGAAAgSRADAACQJIgBAABIEsQAAAAkCWIAAACSBDEAAABJghgAAIAkQQwAAECSIAYAACBJEAMA +AJAkiAEAAEgSxAAAACQJYgAAAJIEMQAAAEmCGAAAgCRBDAAAQJIgBgAAIEkQAwAAkCSIAQAASBLE +AAAAJAliAAAAkgQxAAAASYIYAACAJEEMAABAkiAGAAAg6Tg9AABgj7bX1+kJAFyYCzEAAABJghgA +AIAkQQwAAECSIAYAACBJEAMAAJAkiAEAAEgSxAAAACQJYgAAAJIEMQAAAEmCGAAAgCRBDAAAQJIg +BgAAIEkQAwAAkCSIAQAASBLEAAAAJAliAAAAkgQxAAAASYIYAACAJEEMAABAkiAGAAAgSRADAACQ +JIgBAABIEsQAAAAkCWIAAACSBDEAAABJghgAAIAkQQwAAECSIAYAACBJEAMAAJAkiAEAAEgSxAAA +ACQJYgAAAJKO0wMAAHbp8XF6AQAX5kIMAABAkiAGAAAgSRADAACQJIgBAABIEsQAAAAkCWIAAACS +BDEAAABJghgAAIAkQQwAAECSIAYAACBJEAMAAJAkiAEAAEgSxAAAACQJYgAAAJIEMQAAAEmCGAAA +gCRBDAAAQJIgBgAAIEkQAwAAkCSIAQAASBLEAAAAJAliAAAAkgQxAAAASYIYAACAJEEMAABAkiAG +AAAgSRADAACQJIgBAABIEsQAAAAkCWIAAACSBDEAAABJghgAAIAkQQwAAEDScXoAALATNzfTC/bl +5WV6AQAX5kIMAABAkiAGAAAgSRADAACQJIgBAABIEsQAAAAkCWIAAACSBDEAAABJghgAAIAkQQwA +AECSIAYAACBJEAMAAJAkiAEAAEgSxAAAACQJYgAAAJIEMQAAAEmCGAAAgCRBDAAAQJIgBgAAIEkQ +AwAAkCSIAQAASBLEAAAAJAliAAAAkgQxAAAASYIYAACAJEEMAABAkiAGAAAgSRADAACQJIgBAABI +EsQAAAAkCWIAAACSBDEAAABJghgAAIAkQQwAAECSIAYAACBJEAMAAJAkiAEAAEgSxAAAACQJYgAA +AJIEMQAAAEmCGAAAgCRBDAAAQJIgBgAAIEkQAwAAkCSIAQAASBLEAAAAJAliAAAAkgQxAAAASYIY +AACAJEEMAABAkiAGAAAgSRADAACQJIgBAABIEsQAAAAkCWIAAACSBDEAAABJghgAAIAkQQwAAECS +IAYAACBJEAMAAJAkiAEAAEgSxAAAACQJYgAAAJIEMQAAAEmCGAAAgCRBDAAAQJIgBgAAIEkQAwAA +kCSIAQAASBLEAAAAJB2nBwAAO3F1Nb1gX56ephcAcGEuxAAAACQJYgAAAJIEMQAAAEmCGAAAgCRB +DAAAQJIgBgAAIEkQAwAAkCSIAQAASBLEAAAAJAliAAAAkgQxAAAASYIYAACAJEEMAABAkiAGAAAg +SRADAACQJIgBAABIEsQAAAAkCWIAAACSBDEAAABJghgAAIAkQQwAAECSIAYAACBJEAMAAJAkiAEA +AEgSxAAAACQJYgAAAJIEMQAAAEmCGAAAgCRBDAAAQJIgBgAAIEkQAwAAkCSIAQAASBLEAAAAJB2n +BwAAO3E6TS/Yl9fX6QUAXJgLMQAAAEmCGAAAgCRBDAAAQJIgBgAAIEkQAwAAkCSIAQAASBLEAAAA +JAliAAAAkgQxAAAASYIYAACAJEEMAABAkiAGAAAgSRADAACQJIgBAABIEsQAAAAkCWIAAACSBDEA +AABJghgAAIAkQQwAAECSIAYAACBJEAMAAJAkiAEAAEgSxAAAACQJYgAAAJIEMQAAAEmCGAAAgCRB +DAAAQJIgBgAAIEkQAwAAkCSIAQAASBLEAAAAJAliAAAAkgQxAAAASYIYAACApOP0AABgHw6fPk1P +AIDfyoUYAACAJEEMAABAkiAGAAAgSRADAACQJIgBAABIEsQAAAAkCWIAAACSBDEAAABJghgAAIAk +QQwAAECSIAYAACBJEAMAAJAkiAEAAEgSxAAAACQJYgAAAJIEMQAAAEmCGAAAgCRBDAAAQJIgBgAA +IEkQAwAAkCSIAQAASBLEAAAAJAliAAAAkgQxAAAASYIYAACAJEEMAABAkiAGAAAgSRADAACQJIgB +AABIEsQAAAAkCWIAAACSBDEAAABJghgAAIAkQQwAAECSIAYAACBJEAMAAJAkiAEAAEgSxAAAACQJ +YgAAAJIEMQAAAEmCGAAAgCRBDAAAQJIgBgAAIEkQAwAAkCSIAQAASBLEAAAAJAliAAAAkgQxAAAA +SYIYAACAJEEMAABAkiAGAAAgSRADAACQJIgBAABIEsQAAAAkCWIAAACSBDEAAABJghgAAIAkQQwA +AECSIAYAACBJEAMAAJAkiAEAAEgSxAAAACQJYgAAAJIEMQAAAEmCGAAAgCRBDAAAQJIgBgAAIEkQ +AwAAkCSIAQAASBLEAAAAJAliAAAAkgQxAAAASYIYAACAJEEMAABAkiAGAAAgSRADAACQJIgBAABI +EsQAAAAkCWIAAACSBDEAAABJghgAAIAkQQwAAECSIAYAACBJEAMAAJAkiAEAAEgSxAAAACQJYgAA +AJIEMQAAAEmCGAAAgCRBDAAAQJIgBgAAIEkQAwAAkCSIAQAASBLEAAAAJAliAAAAkgQxAAAASYIY +AACAJEEMAABAkiAGAAAgSRADAACQJIgBAABIEsQAAAAkCWIAAACSBDEAAABJghgAAIAkQQwAAECS +IAYAACBJEAMAAJAkiAEAAEgSxAAAACQJYgAAAJIEMQAAAEmCGAAAgCRBDAAAQJIgBgAAIEkQAwAA +kCSIAQAASBLEAAAAJAliAAAAkgQxAAAASYIYAACAJEEMAABAkiAGAAAgSRADAACQJIgBAABIEsQA +AAAkCWIAAACSBDEAAABJghgAAIAkQQwAAECSIAYAACBJEAMAAJAkiAEAAEgSxAAAACQJYgAAAJIE +MQAAAEnH6QEAwD5sDw/TE95dX08vACDAhRgAAIAkQQwAAECSIAYAACBJEAMAAJAkiAEAAEgSxAAA +ACQJYgAAAJIEMQAAAEmCGAAAgCRBDAAAQJIgBgAAIEkQAwAAkCSIAQAASBLEAAAAJAliAAAAkgQx +AAAASYIYAACAJEEMAABAkiAGAAAgSRADAACQJIgBAABIEsQAAAAkCWIAAACSBDEAAABJghgAAIAk +QQwAAECSIAYAACBJEAMAAJAkiAEAAEgSxAAAACQJYgAAAJIEMQAAAEmCGAAAgCRBDAAAQNJhrbVN +jwAAAIDfzYUYAACAJEEMAABAkiAGAAAgSRADAACQJIgBAABIEsQAAAAkCWIAAACSBDEAAABJghgA +AIAkQQwAAECSIAYAACBJEAMAAJAkiAEAAEgSxAAAACQJYgAAAJIEMQAAAEmCGAAAgCRBDAAAQJIg +BgAAIEkQAwAAkCSIAQAASBLEAAAAJAliAAAAkgQxAAAASYIYAACAJEEMAABAkiAGAAAgSRADAACQ +JIgBAABIEsQAAAAkCWIAAACSBDEAAABJghgAAICkvwC9q1EMapSI2AAAAABJRU5ErkJggg== " transform="translate(2518, 47)"> - +
    (b) Randomly selected prediction sets of size \(|C|=2\). @@ -1234,129 +1230,131 @@

    📊 Results

    - + - + - + - + - + - + 📊 Results kiAGAAAgSRADAACQJIgBAABIEsQAAAAkCWIAAACSBDEAAABJghgAAIAkQQwAAECSIAYAACBJEAMA AJAkiAEAAEgSxAAAACQJYgAAAJIEMQAAAEmCGAAAgCRBDAAAQJIgBgAAIEkQAwAAkCSIAQAASBLE AAAAJAliAAAAkgQxAAAASYIYAACAJEEMAABAkiAGAAAgSRADAACQJIgBAABIEsQAAAAkCWIAAACS -BDEAAABJghgAAIAkQQwAAECSIAYAACBJEAMAAJAkiAEAAEj6J4oRmcX5+jYWAAAAAElFTkSuQmCC +BDEAAABJghgAAIAkQQwAAECSIAYAACBJEAMAAJAkiAEAAEgSxAAAACQJYgAAAJIEMQAAAEmCGAAA +gKR/A7WApcwpJeXaAAAAAElFTkSuQmCC " transform="translate(118, 47)"> - + - + - + 📊 Results JEEMAABAkiAGAAAgSRADAACQJIgBAABIEsQAAAAkCWIAAACSBDEAAABJghgAAIAkQQwAAECSIAYA ACBJEAMAAJAkiAEAAEgSxAAAACQJYgAAAJIEMQAAAEmCGAAAgCRBDAAAQJIgBgAAIEkQAwAAkCSI AQAASBLEAAAAJAliAAAAkgQxAAAASYIYAACAJEEMAABAkiAGAAAgSRADAACQJIgBAABIEsQAAAAk -CWIAAACS9tMDAAB4TJycTC/YXLo0vYD/5u7d6QWb77+fXsBjwIUYAACAJEEMAABAkiAGAAAgSRAD -AACQJIgBAABIEsQAAAAkCWIAAACSBDEAAABJghgAAIAkQQwAAECSIAYAACBJEAMAAJAkiAEAAEgS -xAAAACQJYgAAAJIEMQAAAEmCGAAAgCRBDAAAQJIgBgAAIEkQAwAAkCSIAQAASBLEAAAAJAliAAAA 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    (c) Randomly selected prediction sets of size \(|C|=3\). @@ -1639,7 +1642,7 @@

    🧐 Evaluation

    As for many other things, ConformalPrediction.jl taps into the existing functionality of MLJ.jl for model evaluation. In particular, we will see below how we can use the generic evaluate! method on our machine. To assess the correctness of our conformal predictor, we can compute the empirical coverage rate using the custom performance measure emp_coverage. With respect to model calibration we will look at the model’s conditional coverage. For adaptive, well-calibrated conformal models, conditional coverage is high. One general go-to measure for assessing conditional coverage is size-stratified coverage. The custom measure for this purpose is just called size_stratified_coverage, aliased by ssc.

    The code below implements the model evaluation using cross-validation. The Simple Inductive Classifier that we used above is not adaptive and hence the attained conditional coverage is low compared to the overall empirical coverage, which is close to \(0.95\), so in line with the desired coverage rate specified above.

    -
    +
    Code 
    _eval = evaluate!(
     mach,
@@ -1653,8 +1656,8 @@ 
    🧐 Evaluation
    
 
    Evaluating over 6 folds:  33%[========>                ]  ETA: 0:00:05Evaluating over 6 folds:  50%[============>            ]  ETA: 0:00:03Evaluating over 6 folds:  67%[================>        ]  ETA: 0:00:02Evaluating over 6 folds:  83%[====================>    ]  ETA: 0:00:01Evaluating over 6 folds: 100%[=========================] Time: 0:00:05
-Empirical coverage: 0.959
-SSC: 0.791
    +Empirical coverage: 0.958 +SSC: 0.828     
    PerformanceEvaluation object with these fields:
@@ -1665,15 +1668,15 @@ 
    🧐 Evaluation
    
 ┌──────────────────────────────────────────────┬───────────┬─────────────┬──────
 │ measure                                      │ operation │ measurement │ 1.9 ⋯
 ├──────────────────────────────────────────────┼───────────┼─────────────┼──────
-│ ConformalPrediction.emp_coverage             │ predict   │ 0.959       │ 0.0 ⋯
-│ ConformalPrediction.size_stratified_coverage │ predict   │ 0.791       │ 0.1 ⋯
+│ ConformalPrediction.emp_coverage             │ predict   │ 0.958       │ 0.0 ⋯
+│ ConformalPrediction.size_stratified_coverage │ predict   │ 0.828       │ 0.0 ⋯
 └──────────────────────────────────────────────┴───────────┴─────────────┴──────
                                                                2 columns omitted

    We can attain higher adaptivity (SSC) when using adaptive prediction sets:

    -
    +
    Code 
    conf_model = conformal_model(clf; method=:adaptive_inductive, coverage=.95)
 mach = machine(conf_model, X, y)
@@ -1691,10 +1694,10 @@ 
    🧐 Evaluation
    
 
    [ Info: Training machine(AdaptiveInductiveClassifier(model = ImageClassifier(builder = GenericBuilder(apply = #3), …), …), …).
-Optimising neural net:  18%[====>                    ]  ETA: 0:00:00Optimising neural net:  27%[======>                  ]  ETA: 0:00:01Optimising neural net:  36%[=========>               ]  ETA: 0:00:01Optimising neural net:  45%[===========>             ]  ETA: 0:00:00Optimising neural net:  55%[=============>           ]  ETA: 0:00:00Optimising neural net:  64%[===============>         ]  ETA: 0:00:00Optimising neural net:  73%[==================>      ]  ETA: 0:00:00Optimising neural net:  82%[====================>    ]  ETA: 0:00:00Optimising neural net:  91%[======================>  ]  ETA: 0:00:00Optimising neural net: 100%[=========================] Time: 0:00:00
-Evaluating over 6 folds:  33%[========>                ]  ETA: 0:00:03Evaluating over 6 folds:  50%[============>            ]  ETA: 0:00:02Evaluating over 6 folds:  67%[================>        ]  ETA: 0:00:02Evaluating over 6 folds:  83%[====================>    ]  ETA: 0:00:01Evaluating over 6 folds: 100%[=========================] Time: 0:00:05
-Empirical coverage: 0.996
-SSC: 0.983
    +Optimising neural net: 18%[====> ] ETA: 0:00:01Optimising neural net: 27%[======> ] ETA: 0:00:01Optimising neural net: 36%[=========> ] ETA: 0:00:01Optimising neural net: 45%[===========> ] ETA: 0:00:00Optimising neural net: 55%[=============> ] ETA: 0:00:00Optimising neural net: 64%[===============> ] ETA: 0:00:00Optimising neural net: 73%[==================> ] ETA: 0:00:00Optimising neural net: 82%[====================> ] ETA: 0:00:00Optimising neural net: 91%[======================> ] ETA: 0:00:00Optimising neural net: 100%[=========================] Time: 0:00:00 +Evaluating over 6 folds: 33%[========> ] ETA: 0:00:04Evaluating over 6 folds: 50%[============> ] ETA: 0:00:03Evaluating over 6 folds: 67%[================> ] ETA: 0:00:02Evaluating over 6 folds: 83%[====================> ] ETA: 0:00:01Evaluating over 6 folds: 100%[=========================] Time: 0:00:04 +Empirical coverage: 0.998 +SSC: 0.99     
    PerformanceEvaluation object with these fields:
@@ -1705,15 +1708,15 @@ 
    🧐 Evaluation
    
 ┌──────────────────────────────────────────────┬───────────┬─────────────┬──────
 │ measure                                      │ operation │ measurement │ 1.9 ⋯
 ├──────────────────────────────────────────────┼───────────┼─────────────┼──────
-│ ConformalPrediction.emp_coverage             │ predict   │ 0.996       │ 0.0 ⋯
-│ ConformalPrediction.size_stratified_coverage │ predict   │ 0.983       │ 0.0 ⋯
+│ ConformalPrediction.emp_coverage             │ predict   │ 0.998       │ 0.0 ⋯
+│ ConformalPrediction.size_stratified_coverage │ predict   │ 0.99        │ 0.0 ⋯
 └──────────────────────────────────────────────┴───────────┴─────────────┴──────
                                                                2 columns omitted

    We can also have a look at the resulting set size for both approaches using a custom Plots.jl recipe (fig-setsize). In line with the above, the spread is wider for the adaptive approach, which reflects that “the procedure is effectively distinguishing between easy and hard inputs” (A. N. Angelopoulos and Bates 2022).

    -
    +
    Code 
    plt_list = []
 for (_mod, mach) in results
@@ -1728,98 +1731,105 @@ 
    🧐 Evaluation
    
 
 
 
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    🔁 Recap

    } }); -
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zY`TxNKWg)as(CCMTMW)+HeMJsH=7gK+6{U6%m&q?vQg`x4^_jrrs|Pm8Kgp4i!

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    Paving the Way Towards Low-Overhead Uncertainty Calibration

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    An Accessible Intro to Laplace Approximations in Julia for Bayesian Deep Learning

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    bayesian deep learning
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    laplace approximation
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    guest post
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    Julia
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    + A guest blog post by a team of students from TU Delft, who have contributed multiple improvements to LaplaceRedux.jl. +
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    Authors
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    Severin Bratus

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    Mark Ardman

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    Adelina Cazacu

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    Andrei Ionescu

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    Ivan Makarov

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    Patrick Altmeyer

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    Published
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    July 4, 2023

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    +Guest Blog Post +
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    This blog post was originally written by Severin Bratus and colleagues from TU Delft and published on Medium. This version of the post includes only minor edits. If you would like to contribute a guest blog post, please get in touch.

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    This post summarizes a quarter-long second-year BSc coursework project at TU Delft. Our team of five students has made multiple improvements to LaplaceRedux.jl, due to Patrick Altmeyer. Inspired by its Pythonic counterpart, laplacet-torch, this Julia library aims to provide low-overhead Bayesian uncertainty calibration to deep neural networks via Laplace Approximations [@daxberger2021laplace].

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    A nice image to attract your attention. The exact inverse Fisher information matrix for a MNIST classifier network (left), its block-diagonal and tri-block-diagonal approximations (middle), and the absolute error (right). Source: Martens & Grosse (2015)
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    We will begin by demystifying the technical terms in the last sentence, in order to explain our contributions to the library and highlight some impressions from the experience. Note that our team has begun working on this PhD-tier subject only having had some introductory courses on probability and statistics, machine learning, and computational intelligence, without any prior exposure to Julia.

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    Bayesian Learning

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    Uncertainty calibration remains a crucial issue in safety-critical applications of modern AI, as, for instance, in autonomous driving. You would want your car autopilot not only to make accurate predictions but also to indicate when a model prediction is uncertain, to give control back to the human driver.

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    A model is well-calibrated if the confidence of a prediction matches its true error rate. Note that you can have well-fit models that are badly calibrated, and vice versa (just like in life, you meet smart people, yet annoyingly arrogant).

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    The standard deep learning training process of gradient descent converges at a weight configuration that minimizes the loss function. The model obtained may be great, yet it is only a point estimate of what the weight parameters should look like.

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    However, with the sheer immensity of the weight space, neural networks are probably underspecified by the data (or, overfit). As neural networks can approximate highly complex functions, many weight configurations would yield roughly the same training loss, yet with varying abilities to generalize outside the training dataset. This is why there are so many regularization methods out there, to keep the models simpler. One radical, yet effective approach is described by @lecun1989optimal:

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    … it is possible to take a perfectly reasonable network, delete half (or more) of the weights and wind up with a network that works just as well, or better.

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    +Figure 1: The loss landscape. One can imagine gradient descent as a particle, let’s say a ball, or a grain of sand, rolling to the bottom of a pit. Then for Bayesian Learning, we have as if a pile of sand poured around at that bottom point, with the pile being thicker where loss is lower. This proverbial sand pile would represent the posterior parameter distribution. Figure due to @amini2019spatial +
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    The way gradient is usually illustrated is with a picture like the one shown in Figure 1 above a curved terrain of the loss function across the parameter space. Each point of the horizontal plane corresponds to some configuration of parameters. Gradient descent seeks the point at the bottom of this terrain, as the point with the lowest loss, however as the loss-curvature is highly non-convex and high-dimensional there are many directions in which we could move and still maintain a low loss. Thus instead of a singular point we would like to specify a probability distribution around that optimal point. Bayesian methods, and in particular Laplace Approximations, allow us to do this!

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    Firstly, the Bayesian approach to neural network uncertainty calibration is that of modelling the posterior using Bayes’ Theorem:

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    \[ +p(\theta \mid \mathcal{D}) = \tfrac{1}{Z} \,p(\mathcal{D} \mid \theta) \, p(\theta), \qquad Z:= p(\mathcal{D}) = \textstyle\int p(\mathcal{D} \mid \theta) \, p(\theta) \,d\theta +\]

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    Here \(p(\mathcal{D} \mid \theta)\) is the likelihood of the data given by the parameters \(\theta\). The prior distribution \(p(\theta)\) specifies our beliefs about what the model parameters would be prior to observing the data. Finally, the intractable constant \(Z\) is called the evidence: it characterizes the probability of observing \(\mathcal{D}\) as a whole, across all possible parameter settings (see here for details).

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    For models returning a probability distribution (e.g. classifiers), the loss is commonly defined as the negative log-likelihood. Thus if gradient descent minimizes loss, it maximizes the likelihood, producing the maximum likelihood estimate (MLE), which (assuming a uniform prior) also maximizes the posterior. This is why we call this point the maximum a posteriori, or the MAP. It makes sense to model this point as the mode of the posterior distribution, which could, for example, be a normal Gaussian distribution (see also the introductory post on this blog).

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    Laplace Approximations

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    We do this by a simple-yet-smart trick introduced back in the late 18th century by Pierre-Simon Laplace, the self-proclaimed “greatest French mathematician of his time”. In general, the Laplace Approximation (LA) aims to find a Gaussian approximation to a probability density (in our case, the posterior) defined over a set of continuous variables (in our case, the weights) [@bishop2006pattern]. We can then estimate the loss (negative log-likelihood) as its second-order Taylor expansion:

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    \[ +\mathcal{L}(\mathcal{D}; \theta) \approx \mathcal{L}(\mathcal{D}; \theta_\text{MAP}) + \tfrac{1}{2} (\theta - \theta_\text{MAP})^\intercal \left( \nabla^2 _\theta \mathcal{L}(\mathcal{D}; \theta) \vert_{\theta_\text{MAP}} \right)(\theta - \theta_\text{MAP}) +\]

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    Note that the first-order Taylor term vanishes at the MAP since it contains the gradient, and the gradient is zero at MAP, since MAP is a maximum, by definition. What remains is the constant (zeroth-order) term, and the second-order term, containing the Hessian, which is a matrix of partial second-order derivatives.

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    Then from this approximation, we can derive the long-sought multivariate normal distribution with the MAP as the mean, and the inverted Hessian as the covariance:

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    \[ +p(\theta \mid \mathcal{D}) \approx N(\theta; \theta_\text{MAP}, \varSigma) \qquad\text{with}\qquad \varSigma := \left( \nabla^2_\theta \mathcal{L}(\mathcal{D};\theta) \vert_{\theta_\text{MAP}} \right)^{-1} +\]

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    The evidence \(Z\) is now also tractably approximated in closed form, allowing us to apply the Bayes’ theorem, to obtain the posterior distribution \(p(\theta \mid \mathcal{D})\). We can then express the posterior predictive distribution, for an input \(x_*\), prediction \(f(x_*)\), to obtain the probability for an output \(y\).

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    The evidence \(Z\) is now also tractably approximated in closed form, allowing us to apply the Bayes’ theorem, to obtain the posterior distribution \(p(\theta \mid \mathcal{D})\). We can then express the posterior predictive distribution, to obtain the probability for an output \(y\), given a prediction \(f(x_*)\) for an input \(x_*\).

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    \[ +p(y \mid f(x_*), \mathcal{D}) = \int p(y \mid f_\theta(x_*)) \, p(\theta \mid \mathcal{D}) \,d\theta +\]

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    This is what we are really after, after all — instead of giving one singular point-estimate prediction \(\widehat{y} = f(x_*)\), we make the neural network give a distribution over \(y\).

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    However, since the Hessian, a square matrix, defines the covariance between all model parameters (upon inversion), of which there may be millions or billions, the computation and storage of the Hessian (not to speak of inversion!) become intractable, as its size scales quadratically with the number of parameters involved. Thus to apply Laplace approximations to large models, we must make some simplifications — which brings us to…

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    Hessian approximations

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    Multiple techniques to approximate the Hessian have arisen from a field adjacent, yet distinct from Bayesian learning — that of second-order optimization, where Hessians are used to accelerate gradient descent convergence.

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    One such approximation is the Fisher information matrix, or simply the Fisher:

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    \[ +F := \textstyle\sum_{n=1}^N \mathbb{E}_{\widehat{y} \sim p(y \mid f_\theta(x_n))} \left[ gg^\intercal \right] \quad\text{with}\quad g = \nabla_\theta \log p(\widehat{y} \mid f_\theta(x_n)) \large\vert_{\theta_\text{MAP}} +\]

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    Note that if instead of sampling the prediction \(\widehat{y} ~ p(y \mid f(x_n))\) from the model-defined distribution, we take the actual training-set label \(y_n\), the resulting matrix is called the empirical Fisher, which is distinct from the Fisher, yet aligns with it under some conditions, and does not generally capture second-order information. See Kunstner et al. (2019) for an excellent discussion on the distinction.

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    Instead of the Fisher, one can use the Generalized Gauss-Newton (GGN):

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    \[ +G := \textstyle\sum_{n=1}^N J(x_n) \left( \nabla^2_{f} \log p(y_n \mid f) \Large\vert_{f=f_{\theta_\text{map}}(x_n)} \right) J(x_n)^\intercal +\text{with}\qquad J(x_n) := \nabla_\theta f_\theta(x_n) \vert_{\theta_\text{map}} +\]

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    Here \(J(x_n)\) represents the Jacobian of the model output w.r.t. the parameters. The middle factor \(\nabla^2 …\) is a Hessian of log-likelihood of \(y_n\) w.r.t. model output. Note that the model does not necessarily output ready target probabilities — for instance, classifiers output logits, values that define a probability distribution only after the application of the soft-max.

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    Unlike the Fisher, GGN does not require the network to define a probabilistic model on its output [@botev2017practical]. For models defining an exponential family distribution over the output, the two coincide [@kunstner2020limitations]. This applies to classifiers since they define a categorical distribution over the output, but not to simple regression models.

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    These matrices are quadratically large, it is infeasible to store them in full. The simplest estimation is to model the matrix as a diagonal — however one can easily contemplate how crude this approximation can be: for 100 parameters, only 1% of the full Hessian is captured.

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    A more sophisticated approach, due to Martens and Grosse (2015), is inspired by the observation that in practice the covariance matrices (i.e. inverted Hessians) for neural networks are block-diagonal-dominant. Thus we can effectively model the covariance matrix (and hence the Fisher) as a block-diagonal matrix, where blocks correspond to parameters grouped by layers. Additionally, each block is decomposed into two Kronecker factors, reducing the size of data stored several magnitudes more, at a cost of another assumption.

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    Lastly, a novel approach is to sketch a low-rank approximation of the Fisher [@sharma2021sketching]. Figure 2 shows four Hessian approximation structures:

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    +Figure 2: (a) Hessian in full, intractable for large networks. (b) Low-rank. (c) Kronecker-factored Approximate Curvature, a block-diagonal method. (d) Diagonal. Source: @daxberger2021laplace +
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    It is also possible to cut the costs by treating only a subset of the model parameters, i.e. a subnetwork, probabilistically, fixing the remaining parameters at their MAP-estimated values. One special case of subnetwork Laplace that was found to perform well in practice is last-layer Laplace, where the selected subnetwork contains only the weights and biases of the last layer.

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    Our contributions to LaplaceRedux.jl

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    In the scope of the project we have added support for: - multi-class classification, in addition to regression and binary classification; - GGN, in addition to empirical Fisher; - hardware-parallelized batched computation of both the empirical Fisher and the GGN; - subnetwork and last-layer Laplace; - KFAC for multi-class classification with Fisher; and - interfacing with MLJ, a common machine learning framework for Julia.

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    We have also made quality assurance / quality-of-life additions to the repository, adding: - a formatting check in the CI/CD pipeline; - an extensive test suite comparing the results of LaplaceRedux.jl against those of its Python counter-part package laplace-torch; and - a benchmark pipeline tracking possible downturns in performance.

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    Methodology

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    We adhered to the Agile/Scrum practices, with two-week-long sprints, and weekly meetings with our formal client, Patrick Altmeyer. We have prioritized the expected requirements by the Moscow method into must-, could-, should-, and won’t-haves. This is all fairly standard for BSc software projects at TU Delft. By the end of the project, we have completed all of our self-assigned must-haves and should-haves.

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    Pain Points

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    Here we list some obstacles we have encountered along the way: - Julia is slow to compile and load dependencies on less powerful machines. - Stack traces are sometimes rather obscure, though it seems to be the price to pay for macros. - Zygote.jl, the automatic differentiation library, is not self-autodifferentiable – it cannot differentiate its own functions. We would want this since we apply Zygote.jacobians when making predictions with the LA. - There is no accessible tool reporting branch coverage on tests – only line coverage is available. - Limited LSP and Unicode support for Jupyter Lab. - Conversion between Flux and ONNX is not yet implemented. - There is no extension library for Zygote equivalent to BackPACK or ASDL for second-order information.

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    • Zygote.jl, the automatic differentiation library, is not self-autodifferentiable: issue. We would want this since we apply Zygote.jacobians when making predictions with the LA.
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    • There is no accessible tool reporting branch coverage on tests – only line coverage is available.
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    • Limited LSP and Unicode support for Jupyter Lab.
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    • No conversion between Flux and ONNX is implemented yet ONNX.jl
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    • There is no extension library for Zygote equivalent to BackPACK or ASDL for second-order information.
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    Highlights

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    And here is what we found refreshing: - Metaprogramming and first-class support for macros are something completely different for students who are used to Java & Python. - The Julia standard API, and Flux/Zygote, are fairly straightforward to use, and well-thought-out for numerical computing and machine learning.

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    Conclusions

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    We have covered some elements of the theory behind Laplace Approximations, laid down our additions to the LaplaceRedux.jl package, and brought out some difficulties we, as complete newcomers to Julia, came across. Hope you have enjoyed the tour, and hopefully it has intrigued you enough to look deeper into Bayesian learning and/or Julia since both are developing at a lively pace. You can check out LaplaceRedux on the JuliaTrustworthyAI GitHub page here. Contributions and comments are welcome!

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    Acknowedgements

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    Our team members are Mark Ardman, Severin Bratus, Adelina Cazacu, Andrei Ionescu, and Ivan Makarov. We would like to thank Patrick Altmeyer for the opportunity to work on this unique project and for the continuous guidance throughout the development process. We are also grateful to Sebastijan Dumančić, our coach, Sven van der Voort, our TA mentor, and Antony Bartlett, our supporting advisor.

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    References

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    When Causal meets Recourse

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    Counterfactual Explanations through Structural Causal Models

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    counterfactuals
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    explainable AI
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    causality
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    Julia
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    This post introduces a new tool in CounterfactualExplanations.jl, enhancing the package with causal reasoning to generate counterfactual explanations. The functionality can be used to explain machine learning algorithms developed in Julia and other popular programming languages like Python and R. Unlike traditional counterfactual generators, this approach utilizes causal information to perturb features intelligently.

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    Published
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    September 3, 2024

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    Introduction

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    In recent years, the need for interpretable and explainable AI has surged, particularly in high-stakes domains. Counterfactual explanations provide a means to understand how changes to input features could alter the outcomes of machine learning models. This blog post presents a new tool in the CounterfactualExplanations.jl package, developed during my JSoC (Julia Summer of Code) project, which incorporates causal reasoning into counterfactual generation.

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    Project Overview

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    This project aimed to enhance the CounterfactualExplanations.jl package by infusing it with a robust mathematical foundation for minimal algorithmic recourse, based on the principles of causal reasoning @karimi2021.

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    Key Contributions

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    During the project, I contributed to two key repositories:

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    1. CounterfactualExplanations.jl: Developed a new tool for generating counterfactual explanations using causal information. This allows users to create smarter perturbations rather than random adjustments, ultimately providing more meaningful insights.

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    2. CausalInference.jl: Implemented a Structural Causal Model (SCM) structure that extracts information from data, laying the groundwork for the causal reasoning capabilities in CounterfactualExplanations.jl.

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    This was an amazing experience, not just experience contribute to two repositories simultaneously, but also to work with the mantainers of these repos. I learned a lot about the Julia language and the Julia community. This was possible because of the mentorship of Patrick Altmeyer(CounterfactualExplanations) and Moritz Schauer (CausalInference), who guided me throughout the project and are amazing researchers.

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    The MINTGenerator

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    In this project, we developed the MINTGenerator, a counterfactual generator based on the Recourse through Minimal Intervention (MINT) method proposed by @karimi2021.

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    Description

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    The MINTGenerator incorporates causal reeasoning in algorithm recourse to achieve minimal interventions when generating a counterfactual explanation. In this sense, the main ideia is that just perturbating a black box model without taking into account the causal relations in the data can guide to misleading recommendations. Here we now shift to a perspective where every action/pertubation is an intervetion in the causal graph of the problem, thus the change is not made just in the intervened upon variable, but also in its childs in the causal structure. The generator utilizes a Structural Causal Model(SCM) to encode the variables in a way that causal effects are propagated and uses a generic gradient-based generator to create the search path, that is, any gradient-base generator (ECCo, REVISE, Watcher, …) can be used with the MINT SCM encoder to generate counterfactual samples in latent space for minimal intervetions algorithm recourse.

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    The MINT algorithm minimizes a loss function that combines the causal constraints of the SCM and the distance between the generated counterfactual and the original input. Since we want a gradient-based generator, we need to pass the constrained optimizaiton problem into an unconstrained one and we do this by using the Lagrangian. Initially, as defined in [@karimi2021], we aim to aim to find the minimal cost set of actions \(A\) (in the form of structural interventions) that results in a counterfactual instance yielding the favorable output from \(h\),

    +\[\begin{aligned} + +A^* \in \arg\min_A \text{cost}(A; \mathbf{x}_F)\\ +\textrm{s.t.} \quad h(\mathbf{x}_{SCF}) \neq h(\mathbf{x}_F) \; \; \text{,}\\ + +\end{aligned}\] +

    where \(\mathbf{x}_F\) is the original input, \(\mathbf{x}_{SCF}\) is the counterfactual instance, and \(h\) is the black-box model. We use the \(\mathbf{x}_{SCF}\) terminology because the counterfactual is derived from the SCM,

    +

    \[\begin{equation} + +x_{SCF_i} = +\begin{cases} +x_{F_i} + \delta_i, & \text{if } i \in I \\ +x_{F_i} + f_i(\text{pa}_{SCF_i}) - f_i(\text{pa}_{F_i}), & \text{if } i \notin I \; \; \text{,} +\end{cases} + +\end{equation}\]

    +

    where \(I\) is the set of intervened upon variables, \(f_i\) is the function that generates the value of the variable \(i\) given its parents, and \(\text{pa}_{SCF_i}\) and \(\text{pa}_{F_i}\) are the parents of the variable \(i\) in the counterfactual and original instance, respectively. This closed formula for the decision variable \(\mathbf{x}_{SCF}\) is what makes possible to use a gradient-based generator, since with it the lagrangian is differentiable,

    +

    \[\begin{equation} +\mathcal{L}(A ; \lambda) = \text{cost}(A; \mathbf{x}_F) + \lambda \left(h(\mathbf{x}_{SCF}) - h(\mathbf{x}_F) \right) \; \; \text{,} +\end{equation}\]

    +

    or in simple terms and more standard, since \(\lambda\) is constant,

    +

    \[\begin{equation} +\mathcal{L_{\texttt{MINT}}}(\mathbf{x}_{SCF}) = \lambda \text{cost}(\mathbf{x}_{SCF}; \mathbf{x}_F) + \text{yloss}(\mathbf{x}_{SCF},y^*) \; \; \text{,} +\end{equation}\]

    +

    where \(y^*\) is clearly \(h(x_F)\) and \(\text{yloss}\) is :

    +

    \[\begin{equation} +\text{yloss}(\mathbf{x}_{SCF}, y^*) = h \left(\left\{ x_{F_i} + \delta_i [i \in I] + \left(f_i(\text{pa}_{SCF_i}) - f_i(\text{pa}_{F_i}) \right) [i \notin I] \right\}_{i=1}^n \right) - y^* \; \; \text{.} +\end{equation}\]

    +
    +
    +

    Implementation

    +

    In terms of implementation, we need to capture the causal relations from the data, that’s where CausalInference.jl comes in. However, before the project, the package did not have a SCM structure, in the sense that the methods just captured the topological Directed Acyclic Graph (DAG) that generated the data, that is, no causal structural equations were provided,

    +
    +
    using CausalInference
+using Plots, GraphRecipes
+using Random
+Random.seed!(1)
+
+N = 2000 # number of data points
+
+x = randn(N)
+v = x + randn(N)*0.25
+w = x + randn(N)*0.25
+z = v + w + randn(N)*0.25
+s = z + randn(N)*0.25
+
+df = (x=x, v=v, w=w, z=z, s=s)
+
+est_g, score = ges(df; penalty=1.0, parallel=true)
+
+graphplot(est_g, names= [String(k) for k in keys(df)])
    +
    +
    +
    +
    +

    Conclusion

    +

    In conclusion, this project has successfully integrated causal reasoning into the CounterfactualExplanations.jl package, providing a valuable tool for generating counterfactual explanations that are not only interpretable but also actionable.

    +
    +
    +

    References

    +
    + +
    + + +