Parallel sampling of decomposable graphs using Markov chain on junction trees

TL;DR

This paper introduces a parallel MCMC sampler for decomposable graphs that improves sampling efficiency and accuracy by leveraging new conditions for edge perturbations and graph decomposability, facilitating Bayesian inference.

Contribution

It provides necessary and sufficient conditions for edge perturbations that preserve decomposability and proposes a parallel non-reversible MCMC sampler for junction tree representations.

Findings

Parallel sampler shows better mixing than single-move methods.

Outperforms existing methods in accuracy and efficiency.

Implementation available in Python package parallelDG.

Abstract

Bayesian inference for undirected graphical models is mostly restricted to the class of decomposable graphs, as they enjoy a rich set of properties making them amenable to high-dimensional problems. While parameter inference is straightforward in this setup, inferring the underlying graph is a challenge driven by the computational difficulty in exploring the space of decomposable graphs. This work makes two contributions to address this problem. First, we provide sufficient and necessary conditions for when multi-edge perturbations maintain decomposability of the graph. Using these, we characterize a simple class of partitions that efficiently classify all edge perturbations by whether they maintain decomposability. Second, we propose a novel parallel non-reversible Markov chain Monte Carlo sampler for distributions over junction tree representations of the graph. At every step, the parallel sampler executes simultaneously all edge perturbations within a partition. Through simulations, we demonstrate the efficiency of our new edge perturbation conditions and class of partitions. We find that our parallel sampler yields improved mixing properties in comparison to the single-move variate, and outperforms current state-of-the-arts methods in terms of accuracy and computational efficiency. The implementation of our work is available in the Python package parallelDG.