Adaptive MCMC via Combining Local Samplers

TL;DR

This paper introduces an adaptive MCMC method that combines samples from multiple local chains prioritized by kernel Stein discrepancy, achieving faster convergence especially on multimodal distributions.

Contribution

The paper proposes a novel approach to MCMC by combining parallel local chains with a new weighting technique, improving sampling efficiency for complex distributions.

Findings

Significant speedups in sampling complex distributions.

Competitive performance with NUTS on unimodal distributions.

Outperforms existing methods on multimodal and real-world tasks.

Abstract

Markov chain Monte Carlo (MCMC) methods are widely used in machine learning. One of the major problems with MCMC is the question of how to design chains that mix fast over the whole state space; in particular, how to select the parameters of an MCMC algorithm. Here we take a different approach and, similarly to parallel MCMC methods, instead of trying to find a single chain that samples from the whole distribution, we combine samples from several chains run in parallel, each exploring only parts of the state space (e.g., a few modes only). The chains are prioritized based on kernel Stein discrepancy, which provides a good measure of performance locally. The samples from the independent chains are combined using a novel technique for estimating the probability of different regions of the sample space. Experimental results demonstrate that the proposed algorithm may provide significant speedups in different sampling problems. Most importantly, when combined with the state-of-the-art NUTS algorithm as the base MCMC sampler, our method remained competitive with NUTS on sampling from unimodal distributions, while significantly outperforming state-of-the-art competitors on synthetic multimodal problems as well as on a challenging sensor localization task.