Establishing Markov Equivalence in Cyclic Directed Graphs

TL;DR

This paper introduces an efficient method for determining Markov equivalence in cyclic directed graphs, simplifying the process and reducing computational complexity by leveraging a rephrased Cyclic Equivalence Theorem from an ancestral perspective.

Contribution

It presents a novel, simplified characterization and procedure for establishing Markov equivalence in cyclic graphs without d-separation tests, improving algorithmic efficiency.

Findings

Reduced complexity in establishing Markov equivalence

New characterization based on the Cyclic Equivalence Theorem

Potential to advance cyclic discovery research

Abstract

We present a new, efficient procedure to establish Markov equivalence between directed graphs that may or may not contain cycles under the \textit{d}-separation criterion. It is based on the Cyclic Equivalence Theorem (CET) in the seminal works on cyclic models by Thomas Richardson in the mid '90s, but now rephrased from an ancestral perspective. The resulting characterization leads to a procedure for establishing Markov equivalence between graphs that no longer requires tests for d-separation, leading to a significantly reduced algorithmic complexity. The conceptually simplified characterization may help to reinvigorate theoretical research towards sound and complete cyclic discovery in the presence of latent confounders. This version includes a correction to rule (iv) in Theorem 1, and the subsequent adjustment in part 2 of Algorithm 2.