The Global Markov Property for a Mixture of DAGs

2019/09/12 by Eric V. Strobl, Strobl, Eric V. · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1909.05418

openalex publication_date 2019/09/12 · arxiv created 2019/09/13 · arxiv updated 2019/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Real causal processes may contain feedback loops and change over time. In this paper, we model cycles and non-stationary distributions using a mixture of directed acyclic graphs (DAGs). We then study the conditional independence (CI) relations induced by a density that factorizes according to a mixture of DAGs in two steps. First, we generalize d-separation for a single DAG to mixture d-separation for a mixture of DAGs. We then utilize the mixture d-separation criterion to derive a global Markov property that allows us to read off the CI relations induced by a mixture of DAGs using a particular summary graph. This result has potentially far reaching applications in algorithm design for causal discovery.

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