The Global Markov Property for a Mixture of DAGs

TL;DR

This paper extends the global Markov property to mixtures of DAGs, enabling the modeling of complex causal processes with feedback and non-stationarity, and provides a criterion for reading off CI relations from such mixtures.

Contribution

It introduces mixture d-separation and a global Markov property for mixtures of DAGs, advancing causal discovery methods for dynamic and feedback-rich systems.

Findings

Generalizes d-separation to mixture d-separation for multiple DAGs

Derives a global Markov property for mixtures of DAGs

Provides a summary graph to read off CI relations in complex models

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.