Polynomial-Time Algorithms for Counting and Sampling Markov Equivalent DAGs

TL;DR

This paper presents polynomial-time algorithms for counting and sampling DAGs within Markov equivalence classes, advancing causal graph analysis with practical, efficient solutions that outperform existing methods.

Contribution

It introduces the first polynomial-time algorithms for counting and sampling Markov equivalent DAGs, solving a long-standing open problem.

Findings

Algorithms are effective and easily implementable.

Experimental results show significant performance improvements.

Algorithms outperform state-of-the-art methods.

Abstract

Counting and uniform sampling of directed acyclic graphs (DAGs) 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. Experimental results show that the algorithms significantly outperform state-of-the-art methods.