Structure Learning in Bayesian Networks of Moderate Size by Efficient Sampling

TL;DR

This paper introduces an efficient sampling algorithm for Bayesian network structures, enabling accurate Bayesian model averaging and superior estimators for network features, with strong theoretical and empirical validation.

Contribution

The paper presents the first efficient algorithm for exact sampling of DAGs from the structure posterior, improving Bayesian network structure learning.

Findings

Samples enable better estimators for network features.

Estimators outperform previous state-of-the-art methods.

Theoretical properties are rigorously proven.

Abstract

We study the Bayesian model averaging approach to learning Bayesian network structures (DAGs) from data. We develop new algorithms including the first algorithm that is able to efficiently sample DAGs according to the exact structure posterior. The DAG samples can then be used to construct estimators for the posterior of any feature. We theoretically prove good properties of our estimators and empirically show that our estimators considerably outperform the estimators from the previous state-of-the-art methods.