Polynomial-Time Algorithms for Counting and Sampling Markov Equivalent DAGs with Applications

Abstract

Counting and sampling directed acyclic graphs from a Markov equivalence class are fundamental tasks in graphical causal analysis. In this paper we show that these tasks can be performed in polynomial time, solving a long-standing open problem in this area. Our algorithms are effective and easily implementable. As we show in experiments, these breakthroughs make thought-to-be-infeasible strategies in active learning of causal structures and causal effect identification with regard to a Markov equivalence class practically applicable.

Practical Algorithms for Orientations of Partially Directed Graphical Models

“…Finally, in more structured cases, the maximal orientation task may be performed in linear-time O(n+m). This occurs in the setting of active learning using single-target interventions (that is, only single variables can be manipulated at a time) and is shown in Wienöbst et al (2022) (Theorem 5).…”