Causal Inference Despite Limited Global Confounding via Mixture Models

• URL: http://arxiv.org/abs/2112.11602v5
• Date: Wed, 31 May 2023 08:12:37 GMT
• Title: Causal Inference Despite Limited Global Confounding via Mixture Models
• Authors: Spencer L. Gordon, Bijan Mazaheri, Yuval Rabani, Leonard J. Schulman
• Abstract summary: A finite $k$-mixture of such models is graphically represented by a larger graph. We give the first algorithm to learn mixtures of non-empty DAGs.
• Score: 4.721845865189578
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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