Establishing Markov Equivalence in Cyclic Directed Graphs
This work addresses a theoretical bottleneck in causal discovery for cyclic models, potentially enabling more robust methods in the presence of latent confounders, though it appears incremental as it builds on prior foundational results.
The paper tackles the problem of efficiently establishing Markov equivalence between directed graphs that may contain cycles under the d-separation criterion, resulting in a procedure that reduces algorithmic complexity by eliminating the need for d-separation tests.
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.