Establishing Markov Equivalence in Cyclic Directed Graphs

Tom Claassen, Joris Mooij

Keywords: Causality, Graphical models

TL;DR: A new ancestral perspective on the Cyclic Equivalence Theorem leads to a simplified and much faster procedure to decide on Markov equivalence between directed cyclic graphs.

Abstract:

We present a new, efficient procedure to establish Markov equivalence between directed graphs that may or may not contain cycles.
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 explicit 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.