An efficient algorithm for computing interventional distributions in latent variable causal models

Ilya Shpitser, Thomas S. Richardson, James M. Robins

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publicationProceedings of the 27th Conference on Uncertainty in Artificial Intelligence, UAI 2011
PublisherAUAI Press
Pages661-670
Number of pages10
StatePublished - 2011

Publication series

NameProceedings of the 27th Conference on Uncertainty in Artificial Intelligence, UAI 2011

ASJC Scopus subject areas

  • Artificial Intelligence
  • Applied Mathematics

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