Differentiable Causal Discovery Under Unmeasured Confounding

Rohit Bhattacharya, Tushar Nagarajan, Daniel Malinsky, Ilya Shpitser
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:2314-2322, 2021.

Abstract

The data drawn from biological, economic, and social systems are often confounded due to the presence of unmeasured variables. Prior work in causal discovery has focused on discrete search procedures for selecting acyclic directed mixed graphs (ADMGs), specifically ancestral ADMGs, that encode ordinary conditional independence constraints among the observed variables of the system. However, confounded systems also exhibit more general equality restrictions that cannot be represented via these graphs, placing a limit on the kinds of structures that can be learned using ancestral ADMGs. In this work, we derive differentiable algebraic constraints that fully characterize the space of ancestral ADMGs, as well as more general classes of ADMGs, arid ADMGs and bow-free ADMGs, that capture all equality restrictions on the observed variables. We use these constraints to cast causal discovery as a continuous optimization problem and design differentiable procedures to find the best fitting ADMG when the data comes from a confounded linear system of equations with correlated errors. We demonstrate the efficacy of our method through simulations and application to a protein expression dataset. Code implementing our methods is open-source and publicly available at https://gitlab.com/rbhatta8/dcd and will be incorporated into the Ananke package.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-bhattacharya21a, title = { Differentiable Causal Discovery Under Unmeasured Confounding }, author = {Bhattacharya, Rohit and Nagarajan, Tushar and Malinsky, Daniel and Shpitser, Ilya}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {2314--2322}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/bhattacharya21a/bhattacharya21a.pdf}, url = {https://proceedings.mlr.press/v130/bhattacharya21a.html}, abstract = { The data drawn from biological, economic, and social systems are often confounded due to the presence of unmeasured variables. Prior work in causal discovery has focused on discrete search procedures for selecting acyclic directed mixed graphs (ADMGs), specifically ancestral ADMGs, that encode ordinary conditional independence constraints among the observed variables of the system. However, confounded systems also exhibit more general equality restrictions that cannot be represented via these graphs, placing a limit on the kinds of structures that can be learned using ancestral ADMGs. In this work, we derive differentiable algebraic constraints that fully characterize the space of ancestral ADMGs, as well as more general classes of ADMGs, arid ADMGs and bow-free ADMGs, that capture all equality restrictions on the observed variables. We use these constraints to cast causal discovery as a continuous optimization problem and design differentiable procedures to find the best fitting ADMG when the data comes from a confounded linear system of equations with correlated errors. We demonstrate the efficacy of our method through simulations and application to a protein expression dataset. Code implementing our methods is open-source and publicly available at https://gitlab.com/rbhatta8/dcd and will be incorporated into the Ananke package. } }
Endnote
%0 Conference Paper %T Differentiable Causal Discovery Under Unmeasured Confounding %A Rohit Bhattacharya %A Tushar Nagarajan %A Daniel Malinsky %A Ilya Shpitser %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-bhattacharya21a %I PMLR %P 2314--2322 %U https://proceedings.mlr.press/v130/bhattacharya21a.html %V 130 %X The data drawn from biological, economic, and social systems are often confounded due to the presence of unmeasured variables. Prior work in causal discovery has focused on discrete search procedures for selecting acyclic directed mixed graphs (ADMGs), specifically ancestral ADMGs, that encode ordinary conditional independence constraints among the observed variables of the system. However, confounded systems also exhibit more general equality restrictions that cannot be represented via these graphs, placing a limit on the kinds of structures that can be learned using ancestral ADMGs. In this work, we derive differentiable algebraic constraints that fully characterize the space of ancestral ADMGs, as well as more general classes of ADMGs, arid ADMGs and bow-free ADMGs, that capture all equality restrictions on the observed variables. We use these constraints to cast causal discovery as a continuous optimization problem and design differentiable procedures to find the best fitting ADMG when the data comes from a confounded linear system of equations with correlated errors. We demonstrate the efficacy of our method through simulations and application to a protein expression dataset. Code implementing our methods is open-source and publicly available at https://gitlab.com/rbhatta8/dcd and will be incorporated into the Ananke package.
APA
Bhattacharya, R., Nagarajan, T., Malinsky, D. & Shpitser, I.. (2021). Differentiable Causal Discovery Under Unmeasured Confounding . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:2314-2322 Available from https://proceedings.mlr.press/v130/bhattacharya21a.html.

Related Material