A new constructive criterion for Markov equivalence of MAGs.

Ancestral graphs are an important tool for encoding causal knowledge as they represent uncertainty about the presence of latent confounding and selection bias, and they can be inferred from data. As for other graphical models, several maximal ancestral graphs (MAGs) may encode the same statistical information in the form of conditional independencies. Such MAGs are said to be Markov equivalent. This work concerns graphical characterizations and computational aspects of Markov equivalence between MAGs. These issues have been studied in past years leading to several criteria and methods to test Markov equivalence. The state-of-the-art algorithm, provided by Hu and Evans [UAI 2020], runs in time $O(n^5)$ for instances with $n$ vertices. We propose a new constructive graphical criterion for the Markov equivalence of MAGs, which allows us to develop a practically effective equivalence test with worst-case runtime $O(n^3)$. Additionally, our criterion is expressed in terms of natural graphical concepts, which is of independent value.