Partition MCMC for inference on acyclic digraphs

TL;DR

This paper introduces a novel Partition MCMC algorithm for Bayesian network structure learning that leverages DAG combinatorial structure to improve convergence while maintaining unbiased sampling.

Contribution

The paper presents a new grouping strategy for DAGs in MCMC that enhances convergence speed and can be combined with edge reversal moves for further improvements.

Findings

Improved convergence over traditional structure MCMC.

Maintains unbiased sampling of DAGs.

Compatible with edge reversal moves for enhanced performance.

Abstract

Acyclic digraphs are the underlying representation of Bayesian networks, a widely used class of probabilistic graphical models. Learning the underlying graph from data is a way of gaining insights about the structural properties of a domain. Structure learning forms one of the inference challenges of statistical graphical models. MCMC methods, notably structure MCMC, to sample graphs from the posterior distribution given the data are probably the only viable option for Bayesian model averaging. Score modularity and restrictions on the number of parents of each node allow the graphs to be grouped into larger collections, which can be scored as a whole to improve the chain's convergence. Current examples of algorithms taking advantage of grouping are the biased order MCMC, which acts on the alternative space of permuted triangular matrices, and non ergodic edge reversal moves. Here we propose a novel algorithm, which employs the underlying combinatorial structure of DAGs to define a new grouping. As a result convergence is improved compared to structure MCMC, while still retaining the property of producing an unbiased sample. Finally the method can be combined with edge reversal moves to improve the sampler further.