Asynchronous Gibbs Sampling

TL;DR

This paper introduces a theoretical framework for asynchronous Gibbs sampling, analyzing its convergence properties, and provides heuristics for its effective application in parallel Bayesian inference.

Contribution

It develops a convergence theory for asynchronous Gibbs sampling, including modifications for correctness, and evaluates its performance across different models.

Findings

Asynchronous Gibbs can converge under certain conditions.

The paper identifies scenarios where asynchronous Gibbs fails.

Heuristics are proposed to guide effective use of the method.

Abstract

Gibbs sampling is a Markov Chain Monte Carlo (MCMC) method often used in Bayesian learning. MCMC methods can be difficult to deploy on parallel and distributed systems due to their inherently sequential nature. We study asynchronous Gibbs sampling, which achieves parallelism by simply ignoring sequential requirements. This method has been shown to produce good empirical results for some hierarchical models, and is popular in the topic modeling community, but was also shown to diverge for other targets. We introduce a theoretical framework for analyzing asynchronous Gibbs sampling and other extensions of MCMC that do not possess the Markov property. We prove that asynchronous Gibbs can be modified so that it converges under appropriate regularity conditions -- we call this the exact asynchronous Gibbs algorithm. We study asynchronous Gibbs on a set of examples by comparing the exact and approximate algorithms, including two where it works well, and one where it fails dramatically. We conclude with a set of heuristics to describe settings where the algorithm can be effectively used.