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

The Global Markov Property for a Mixture of DAGs