  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.
