Graphical Instrumental Variables Estimation and Testing

This repository contains an implementation of the following paper

• Discovery and inference of a causal network with hidden confounding. Journal of the American Statistical Association.

The method is named Graphical Instrumental Variables Estimation and Testing (GrIVET).

Contents

• ./grivet/: contains an R package for algorithm implementations.

• ./real_data/: contains analysis of ADNI data with GrIVET.

• ./simulations/*.R: contains R scripts for simulations and summaries.

• ./simulations/primary_results: stores simulation results.

• ./simulations/summary_results: stores summaries of simulation results.

Package Installations

For R, the testing version is 4.1.0. To install the package, run the following Bash script to build and install the R package.

R CMD build grivet
R CMD install grivet_1.0.tar.gz

Note: replace "grivet_1.0.tar.gz" by the file built if applicable.

The following packages are used.

pkg <- c(
    "stats", "cvTools", " mnormt", # for R package
    "ggcorrplot", # for real data analysis
    "doParallel", "mvtnorm", "MASS", "lrpsadmm", "bnlearn","pcalg","clusterGeneration",
    "ggplot2", "cowplot", "gridExtra" # for simulations
)
install.packages(pkg)

NOTE: some packages have dependencies unavailable from CRAN. The user may need to install them manually.

Simulation Reproductions

To reproduce the simulation results in the paper, change the working directory using the following Bash script.

cd simulations

System information

The simulations are tested with a request of 2 nodes and 60 GB memory on a server with specs of each node:

System Version:             Linux cn0203 3.10.0-1160.83.1.el7.x86_64
Model name:                 Intel(R) Xeon(R) CPU E5-2680 v3 @ 2.50GHz
CPU(s):                     24

No GPU is required.

Table 1

To reproduce Table 1, run the following bash script(Approximately 34 hours).

Rscript comparison1_setting1_simu.R
Rscript summary_part1_setting1.R

The simulation results will be stored in ./simulations/primary_results/part1/setting1/ and the summary will be printed and stored in ./simulations/summary_results/part1/setting1/.

Table 2

To reproduce Table 2, run the following bash script(Approximately 21.5 hours).

Rscript comparison2_setting1_simu.R
Rscript summary_part2_setting1.R

The simulation results will be stored in ./simulations/primary_results/part2/setting1/ and the summary will be printed and stored in ./simulations/summary_results/part2/setting1/.

Table 3

To reproduce Hub Graph part of Table 3, run the following bash script(Approximately 24 hours).

Rscript infer_setting1_hub.R
Rscript summary_infer_setting1_hub.R

The simulation results will be stored in ./simulations/primary_results/part3/setting1/ and the summary will be printed and stored in ./simulations/summary_results/part3/setting1/. In addition, the statistics distribution figures will be stored in ./simulations/summary_results/part3/setting1/figures/.

To reproduce Random Graph part of Table 3, run the following bash script(Approximately 31 hours).

Rscript infer_setting1_random.R
Rscript summary_infer_setting1_random.R

The simulation results will be stored in ./simulations/primary_results/part3/setting1/ and the summary will be printed and stored in ./simulations/summary_results/part3/setting1/. In addition, the statistics distribution figures will be stored in ./simulations/summary_results/part3/setting1/figures/.

Figure 2

To reproduce Figure 2, run the following bash script(Approximately 17.5 hours).

Rscript infer_part5.R
Rscript summary_part5.R

The simulation results will be stored in ./simulations/primary_results/part5/ and the boxplots will be stored in ./simulations/summary_results/part5/.

Figure 1 (Supplementary Materials)

To reproduce Figure 1(Supplementary Materials), run the following bash script(Approximately 20 hours).

Rscript comparison4_discovery.R
Rscript comparison4_estimation.R
Rscript summary_part4.R

The simulation results will be stored in ./simulations/primary_results/part4/discovery/ and ./simulations/primary_results/part4/estimation/ and the summary of performance of structure learning will be printed and the figures will be stored in ./simulations/summary_results/part4/.

Table 1 (Supplementary Materials)

To reproduce Table 1(Supplementary Materials), run the following bash script(Approximately 12.5 hours).

Rscript comparison1_setting2_simu.R
Rscript summary_part1_setting2.R

The simulation results will be stored in ./simulations/primary_results/part1/setting2/ and the summary will be printed and stored in ./simulations/summary_results/part1/setting2/.

Table 2 (Supplementary Materials)

To reproduce Table 2(Supplementary Materials), run the following bash script(Approximately 3.5 hours).

Rscript comparison2_setting2_simu.R
Rscript summary_part2_setting2.R

The simulation results will be stored in ./simulations/primary_results/part2/setting2/ and the summary will be printed and stored in ./simulations/summary_results/part2/setting2/.

Table 3 (Supplementary Materials)

To reproduce Table 3(Supplementary Materials), run the following bash script(Approximately 3.5 hours).

Rscript comparison2_setting3_simu.R
Rscript summary_part2_setting3.R

The simulation results will be stored in ./simulations/primary_results/part2/setting3/ and the summary will be printed and stored in ./simulations/summary_results/part2/setting3/.

Table 4 (Supplementary Materials)

To reproduce Hub Graph part of Table 4(Supplementary Materials), run the following bash script(Approximately 2.5 hours).

Rscript infer_setting2_hub.R
Rscript summary_infer_setting2_hub.R

The simulation results will be stored in ./simulations/primary_results/part3/setting2/ and the summary will be printed and stored in ./simulations/summary_results/part3/setting2/. In addition, the statistics distribution figures will be stored in ./simulations/summary_results/part3/setting2/figures/.

To reproduce Random Graph part of Table 3(Supplementary Materials), run the following bash script(Approximately 5.5 hours).

Rscript infer_setting2_random.R
Rscript summary_infer_setting2_random.R

The simulation results will be stored in ./simulations/primary_results/part3/setting2/ and the summary will be printed and stored in ./simulations/summary_results/part3/setting2/. In addition, the statistics distribution figures will be stored in ./simulations/summary_results/part3/setting2/figures/.

Real Data Reproductions

Note: Due to license restrictions, we cannot directly share the ADNI data. Instead, we provide a pseudo-data along with a Rmd file to process the data, so that readers can reproduce the results obtained on the pseudo-data, which is similar but not exactly the same with the real data.

Contents

• pseudo_gene_expr_data.RData: simulated pseudo-data.
• real_data_analysis.Rmd: contains code reproducing the real data analysis with pseudo-data.
• real_data_analysis.pdf: results for edges testing and normality check with pseudo-data.
• resi_ad.pdf, resi_cn.pdf: residual correlation matrices with pseudo-data.

References

[1] Frot, B., Nandy, P., & Maathuis, M. H. (2019). Robust causal structure learning with some hidden variables, JRSSB. Open-sourced softwares: LRpS+GES is implemented by lrpsadmm and pcalg.

[2] Colombo, D., Maathuis, M. H., Kalisch, M., & Richardson, T. S. (2012). Learning high-dimensional directed acyclic graphs with latent and selection variables, AOS. Open-sourced software: RFCI is implemented by pcalg.

[3] Kalisch, M., Mächler, M., Colombo, D., Maathuis, M. H., & Bühlmann, P. (2012). Causal Inference Using Graphical Models with the R Package pcalg, JSS. Open-sourced software: pcalg.

In addition, part of the simulation code is adapted from Frot's code.

We would like to thank the authors of above open-sourced software.