intdag: An R Package For Interventional DAG Estimation and Inference

This repository contains an implementation of the paper

• Li, C., Shen, X., & Pan, W. (2023). Inference for a large directed acyclic graph with unspecified interventions. Journal of Machine Learning Research. (A previous version was given the Student Paper Award, Conference on Statistical Learning and Data Science, ASA, May 2020)

Installation

R Packages

First, install the package glmtlp which implements the DC projection algorithm in the paper.

devtools::install_github("chunlinli/glmtlp")

Then install the package intdag which offers the peeling causal discovery method and data-perturbation/asymptotic inference.

devtools::install_github("chunlinli/intdag/intdag")

R Scripts of utilities

Before proceeding, source the following R scripts for utility functions required in the following illustration.

Assume the working directory is the cloned repository https://github.com/chunlinli/intdag.

source("utility.R")
set.seed(1110)

A Quick Example

First, we generate a random graph with p=10 and q=20.

p <- 10
q <- 20
graph <- graph_generation(p = p, q = q, graph_type = "random", iv_sufficient = FALSE)

Note that we use the option iv_sufficient = FALSE, which means a crucial assumption in the paper -- Assumption 1C is violated. Let's print the $U$ matrix.

graph$u

This is a p by p adjacency matrix of the DAG that we want to recover and/or make inference. Note that $U_{jk} \neq 0$ means an edge from $Y_{j}$ to $Y_{k}$.

Then print the $W$ matrix.

graph$w

This is a q by p matrix, indicating the interventional relations of an intervention varibale $X_{l}$ and a primary variable $Y_{j}$, where $W_{lj} \neq 0$ means $X_{l}$ directly intervenes on $Y_{j}$. In above, w corresponds to the simulation Setup B in the paper.

Next, generate a random sample of size n=200 based on the graph. According to the analysis in the paper, the distribution of intervention variables $X$ does not matter too much. Here we generate $X$ so that they have an AR(1) correlation structure.

n <- 200
x <- matrix(rnorm(n * q), nrow = n, ncol = q)
rho <- 0.5
if (rho != 0) {
    for (j in 2:q) {
        x[, j] <- sqrt(1 - rho^2) * x[, j] + rho * x[, j - 1]
    }
}

Note that x is an n by q matrix.

Then we generate the $Y$ variables, the ones of primary interest.

y <- (x %*% graph$w + rmvnorm(n, sigma = diag(seq(from = 0.5, to = 1, length.out = p), p, p))) %*% solve(diag(p) - graph$u)

Here y is an n by p matrix.

Now fit the model using intdag. Note that intdag calls glmtlp for solving multi-response regression in its first step.

v_out <- v_estimation(y = y, x = x, model_selection = "bic")

Second, use peeling algorithm to recover the topological layers.

top_out <- topological_order(v_out$v)
an_mat <- top_out$an_mat
in_mat <- top_out$in_mat

Third, refit to estimate $U$ and $W$.

discovery_out <- causal_discovery(y = y, x = x, an_mat = an_mat, in_mat = in_mat)

The final estimate for $U$ is:

discovery_out$u

We compare the final estimate with the true graph in the structural Hamming distance.

sum(abs((abs(discovery_out$u) > 0.05) - (graph$u != 0)))

Here we use a truncation threshold 0.05 to screen the small (noisy) coefficients.

Contents

The R package is placed in directory ./intdag/.

The extensive simulation code is placed in directory ./simulation/.

Citing information

If you find the code useful, please consider citing

@article{li2023inference,
    author = {Chunlin Li, Xiaotong Shen, Wei Pan},
    title = {Inference for a large directed acyclic graph with unspecified interventions},
    journal = {Journal of Machine Learning Research},
    year = {2023}
}

Implementing these algorithms is error-prone and this code project is still in development. Please file an issue if you encounter any error when using the code. I will be grateful to be informed.