Parallel Markov Chain Monte Carlo via Spectral Clustering

TL;DR

This paper introduces a spectral clustering-based parallelization scheme for MCMC methods that accelerates sampling for complex distributions, outperforming naive approaches and providing practical tuning guidance.

Contribution

It generalizes previous state space partitioning methods, enabling more efficient parallel MCMC, with theoretical convergence guarantees and empirical validation.

Findings

Speeds up MCMC sampling for multimodal distributions

Can be more efficient than naive parallelization in flat distributions

Provides practical guidance on tuning parameters

Abstract

As it has become common to use many computer cores in routine applications, finding good ways to parallelize popular algorithms has become increasingly important. In this paper, we present a parallelization scheme for Markov chain Monte Carlo (MCMC) methods based on spectral clustering of the underlying state space, generalizing earlier work on parallelization of MCMC methods by state space partitioning. We show empirically that this approach speeds up MCMC sampling for multimodal distributions and that it can be usefully applied in greater generality than several related algorithms. Our algorithm converges under reasonable conditions to an `optimal' MCMC algorithm. We also show that our approach can be asymptotically far more efficient than naive parallelization, even in situations such as completely flat target distributions where no unique optimal algorithm exists. Finally, we combine theoretical and empirical bounds to provide practical guidance on the choice of tuning parameters.