Markov Equivalence Classes for Maximal Ancestral Graphs

TL;DR

This paper introduces a new representation for Markov equivalence classes of ancestral graphs, simplifying model search in DAG models with latent variables by defining a join operation and extending separation criteria.

Contribution

It presents a novel join operation on ancestral graphs that uniquely represents Markov equivalence classes, extending separation criteria and proving the Markov property for these joined graphs.

Findings

Defined a join operation for ancestral graphs

Provided a new representation for Markov equivalence classes

Extended separation criteria for ancestral graphs

Abstract

Ancestral graphs are a class of graphs that encode conditional independence relations arising in DAG models with latent and selection variables, corresponding to marginalization and conditioning. However, for any ancestral graph, there may be several other graphs to which it is Markov equivalent. We introduce a simple representation of a Markov equivalence class of ancestral graphs, thereby facilitating model search. \ More specifically, we define a join operation on ancestral graphs which will associate a unique graph with a Markov equivalence class. We also extend the separation criterion for ancestral graphs (which is an extension of d-separation) and provide a proof of the pairwise Markov property for joined ancestral graphs.