On sampling graphical Markov models

TL;DR

This paper studies sampling methods for Markov equivalence classes of DAGs, proposing a Markov chain approach with conditions for efficient mixing and analyzing the ratio of classes to DAGs.

Contribution

It introduces a Markov chain for uniform sampling within Markov equivalence classes and identifies conditions for polynomial-time mixing.

Findings

Markov chain mixing can be exponentially slow in worst case

A condition for polynomial-time mixing is identified

Analyzes the ratio of Markov equivalence classes to DAGs

Abstract

We consider sampling and enumeration problems for Markov equivalence classes. We create and analyze a Markov chain for uniform random sampling on the DAGs inside a Markov equivalence class. Though the worst case is exponentially slow mixing, we find a condition on the Markov equivalence class for polynomial time mixing. We also investigate the ratio of Markov equivalence classes to DAGs and a Markov chain of He, Jia, and Yu for random sampling of sparse Markov equivalence classes.