Partial Order MCMC for Structure Discovery in Bayesian Networks

TL;DR

This paper introduces a novel MCMC method that samples from partial orders to estimate Bayesian network structures, providing more accurate posterior probabilities than previous graph or linear order sampling techniques.

Contribution

The paper proposes a new Markov chain Monte Carlo approach that samples partial orders for Bayesian network structure discovery, improving estimation accuracy.

Findings

Analytical results show the method's theoretical advantages.

Empirical experiments demonstrate superior performance over previous methods.

Exact computation of conditional probabilities enhances accuracy.

Abstract

We present a new Markov chain Monte Carlo method for estimating posterior probabilities of structural features in Bayesian networks. The method draws samples from the posterior distribution of partial orders on the nodes; for each sampled partial order, the conditional probabilities of interest are computed exactly. We give both analytical and empirical results that suggest the superiority of the new method compared to previous methods, which sample either directed acyclic graphs or linear orders on the nodes.