An efficient algorithm for counting Markov equivalent DAGs

Abstract

We consider the problem of counting the number of DAGs which are Markov equivalent, i.e., which encode the same conditional independencies between random variables. The problem has been studied, among others, in the context of causal discovery, and it is known that it reduces to counting the number of so-called moral acyclic orientations of certain undirected graphs, notably chordal graphs. Our main empirical contribution is a new algorithm which outperforms previously known exact algorithms for the considered problem by a significant margin. On the theoretical side, we show that our algorithm is guaranteed to run in polynomial time on a broad cubic-time recognisable class of chordal graphs, including interval graphs.