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math.ST updates on arXiv.org

What is Learnable in Valiant's Theory of the Learnable? 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The Global Markov Property for a Mixture of DAGs
Eric V. Strobl · 2019-09-12 · via math.ST updates on arXiv.org

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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