Markov equivalence for ancestral graphs

TL;DR

This paper extends the understanding of Markov equivalence in ancestral graphs, providing conditions and an efficient algorithm to determine when two such graphs encode the same conditional independencies.

Contribution

It establishes new conditions for Markov equivalence in ancestral graphs and introduces a polynomial-time algorithm for checking equivalence.

Findings

Conditions for Markov equivalence in ancestral graphs

An algorithm for testing Markov equivalence that runs in polynomial time

Extension of DAG Markov equivalence results to ancestral graphs

Abstract

Ancestral graphs can encode conditional independence relations that arise in directed acyclic graph (DAG) models with latent and selection variables. However, for any ancestral graph, there may be several other graphs to which it is Markov equivalent. We state and prove conditions under which two maximal ancestral graphs are Markov equivalent to each other, thereby extending analogous results for DAGs given by other authors. These conditions lead to an algorithm for determining Markov equivalence that runs in time that is polynomial in the number of vertices in the graph.