The Global Markov Property for a Mixture of DAGs
Statistics Theory
2019-09-16 v2 Statistics Theory
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.
Keywords
Cite
@article{arxiv.1909.05418,
title = {The Global Markov Property for a Mixture of DAGs},
author = {Eric V. Strobl},
journal= {arXiv preprint arXiv:1909.05418},
year = {2019}
}