An Efficient Algorithm for Computing Interventional Distributions in Latent Variable Causal Models

TL;DR

This paper introduces an efficient recursive algorithm for computing interventional distributions in latent variable causal models represented by acyclic directed mixed graphs, extending variable elimination techniques.

Contribution

It presents a novel algorithm that generalizes variable elimination to ADMGs, enabling efficient inference in complex causal models with latent variables.

Findings

Algorithm is exponential in the mixed graph treewidth.

Generalizes Markov factorization for DAGs to ADMGs.

Provides a recursive approach for interventional distribution computation.

Abstract

Probabilistic inference in graphical models is the task of computing marginal and conditional densities of interest from a factorized representation of a joint probability distribution. Inference algorithms such as variable elimination and belief propagation take advantage of constraints embedded in this factorization to compute such densities efficiently. In this paper, we propose an algorithm which computes interventional distributions in latent variable causal models represented by acyclic directed mixed graphs(ADMGs). To compute these distributions efficiently, we take advantage of a recursive factorization which generalizes the usual Markov factorization for DAGs and the more recent factorization for ADMGs. Our algorithm can be viewed as a generalization of variable elimination to the mixed graph case. We show our algorithm is exponential in the mixed graph generalization of treewidth.