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Move whole setup example to backup
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matthewfeickert committed Jan 28, 2024
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.bold.center[Having access to the gradients can make the fit orders of magnitude faster than finite difference]

---
# Moving towards differentiable workflows

.kol-1-3[
<p style="text-align:center;">
<img src="figures/signal_background_stacked.png"; width=100%>
</p>
* Counting experiment for presence of signal process
* Place discriminate selection ("cut") on observable $x$ to maximize significance $S(x)$
* Step along cut values in $x$ and calculate significance
]
.kol-1-3[
<p style="text-align:center;">
<img src="figures/significance_scan_compare.png"; width=100%>
</p>
* Need differentiable analogue to non-differentiable cut
* Weight events using activation function of sigmoid

.center[$w=\left(1 + e^{-\alpha(x-c)}\right)^{-1}$]

* Event far .italic[below] cut: $w \to 0$
* Event far .italic[above] cut: $w \to 1$
]
.kol-1-3[
<p style="text-align:center;">
<img src="figures/automated_optimization.png"; width=95%>
</p>
* With a simple gradient descent algorithm can easily automate the significance optimization
* Allows for the "cut" to become a parameter that can be differentiated through for the larger analysis
]

---
# New Art: Analysis as a Differentiable Program

Expand Down Expand Up @@ -1089,7 +1058,7 @@ Serve on Formation Task Force for the Coordinating Panel for Software and Comput
]
.kol-1-3[
<p style="text-align:center;">
<img src="figures/MLE_grad_map_full.png"; width=75%>
<img src="figures/MLE_grad_map.png"; width=75%>
</p>
]

Expand Down Expand Up @@ -1245,7 +1214,6 @@ Mathematical grammar for a simultaneous fit with multiple disjoint _channels_ (o
.center[Example: .bold[Each bin] is separate (1-bin) _channel_,<br> each .bold[histogram] (color) is a _sample_ and share<br> a .bold[normalization systematic] uncertainty]
]


---
# HistFactory Template: systematic uncertainties

Expand All @@ -1267,6 +1235,37 @@ Mathematical grammar for a simultaneous fit with multiple disjoint _channels_ (o
.center[Image credit: [Alex Held](https://indico.cern.ch/event/1076231/contributions/4560405/)]
]

---
# Moving towards differentiable workflows

.kol-1-3[
<p style="text-align:center;">
<img src="figures/signal_background_stacked.png"; width=100%>
</p>
* Counting experiment for presence of signal process
* Place discriminate selection ("cut") on observable $x$ to maximize significance $S(x)$
* Step along cut values in $x$ and calculate significance
]
.kol-1-3[
<p style="text-align:center;">
<img src="figures/significance_scan_compare.png"; width=100%>
</p>
* Need differentiable analogue to non-differentiable cut
* Weight events using activation function of sigmoid

.center[$w=\left(1 + e^{-\alpha(x-c)}\right)^{-1}$]

* Event far .italic[below] cut: $w \to 0$
* Event far .italic[above] cut: $w \to 1$
]
.kol-1-3[
<p style="text-align:center;">
<img src="figures/automated_optimization.png"; width=95%>
</p>
* With a simple gradient descent algorithm can easily automate the significance optimization
* Allows for the "cut" to become a parameter that can be differentiated through for the larger analysis
]

---
# Discriminate Signal and Background
<!-- -->
Expand Down

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