Generating Markov Equivalent Maximal Ancestral Graphs by Single Edge Replacement

TL;DR

This paper studies how to transform maximal ancestral graphs (MAGs) by reversing or swapping edges to generate all Markov equivalent graphs, aiding understanding of their structure with hidden variables.

Contribution

It provides conditions for edge reversal and interchange in MAGs without undirected edges to produce Markov equivalent graphs.

Findings

Identifies conditions for arrow reversal in MAGs.

Establishes when edges can be interchanged with bi-directed edges.

Enhances understanding of MAG equivalence transformations.

Abstract

Maximal ancestral graphs (MAGs) are used to encode conditional independence relations in DAG models with hidden variables. Different MAGs may represent the same set of conditional independences and are called Markov equivalent. This paper considers MAGs without undirected edges and shows conditions under which an arrow in a MAG can be reversed or interchanged with a bi-directed edge so as to yield a Markov equivalent MAG.