Causal Inference Despite Limited Global Confounding via Mixture Models

Spencer L. Gordon, Bijan Mazaheri, Yuval Rabani, Leonard Schulman
Proceedings of the Second Conference on Causal Learning and Reasoning, PMLR 213:574-601, 2023.

Abstract

A Bayesian Network is a directed acyclic graph (DAG) on a set of $n$ random variables (the vertices); a Bayesian Network Distribution (BND) is a probability distribution on the random variables that is Markovian on the graph. A finite $k$-mixture of such models is graphically represented by a larger graph which has an additional “hidden” (or “latent”) random variable $U$, ranging in $\{1,\ldots,k\}$, and a directed edge from $U$ to every other vertex. Models of this type are fundamental to causal inference, where $U$ models an unobserved confounding effect of multiple populations, obscuring the causal relationships in the observable DAG. By solving the mixture problem and recovering the joint probability distribution with $U$, traditionally unidentifiable causal relationships become identifiable. Using a reduction to the more well-studied “product” case on empty graphs, we give the first algorithm to learn mixtures of non-empty DAGs.

Cite this Paper

BibTeX
@InProceedings{pmlr-v213-gordon23a, title = {Causal Inference Despite Limited Global Confounding via Mixture Models}, author = {Gordon, Spencer L. and Mazaheri, Bijan and Rabani, Yuval and Schulman, Leonard}, booktitle = {Proceedings of the Second Conference on Causal Learning and Reasoning}, pages = {574--601}, year = {2023}, editor = {van der Schaar, Mihaela and Zhang, Cheng and Janzing, Dominik}, volume = {213}, series = {Proceedings of Machine Learning Research}, month = {11--14 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v213/gordon23a/gordon23a.pdf}, url = {https://proceedings.mlr.press/v213/gordon23a.html}, abstract = {A Bayesian Network is a directed acyclic graph (DAG) on a set of $n$ random variables (the vertices); a Bayesian Network Distribution (BND) is a probability distribution on the random variables that is Markovian on the graph. A finite $k$-mixture of such models is graphically represented by a larger graph which has an additional “hidden” (or “latent”) random variable $U$, ranging in $\{1,\ldots,k\}$, and a directed edge from $U$ to every other vertex. Models of this type are fundamental to causal inference, where $U$ models an unobserved confounding effect of multiple populations, obscuring the causal relationships in the observable DAG. By solving the mixture problem and recovering the joint probability distribution with $U$, traditionally unidentifiable causal relationships become identifiable. Using a reduction to the more well-studied “product” case on empty graphs, we give the first algorithm to learn mixtures of non-empty DAGs. } }
Endnote
%0 Conference Paper %T Causal Inference Despite Limited Global Confounding via Mixture Models %A Spencer L. Gordon %A Bijan Mazaheri %A Yuval Rabani %A Leonard Schulman %B Proceedings of the Second Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2023 %E Mihaela van der Schaar %E Cheng Zhang %E Dominik Janzing %F pmlr-v213-gordon23a %I PMLR %P 574--601 %U https://proceedings.mlr.press/v213/gordon23a.html %V 213 %X A Bayesian Network is a directed acyclic graph (DAG) on a set of $n$ random variables (the vertices); a Bayesian Network Distribution (BND) is a probability distribution on the random variables that is Markovian on the graph. A finite $k$-mixture of such models is graphically represented by a larger graph which has an additional “hidden” (or “latent”) random variable $U$, ranging in $\{1,\ldots,k\}$, and a directed edge from $U$ to every other vertex. Models of this type are fundamental to causal inference, where $U$ models an unobserved confounding effect of multiple populations, obscuring the causal relationships in the observable DAG. By solving the mixture problem and recovering the joint probability distribution with $U$, traditionally unidentifiable causal relationships become identifiable. Using a reduction to the more well-studied “product” case on empty graphs, we give the first algorithm to learn mixtures of non-empty DAGs.
APA
Gordon, S.L., Mazaheri, B., Rabani, Y. & Schulman, L.. (2023). Causal Inference Despite Limited Global Confounding via Mixture Models. Proceedings of the Second Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 213:574-601 Available from https://proceedings.mlr.press/v213/gordon23a.html.

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