Sampling by Divergence Minimization

TL;DR

This paper presents an adaptive MCMC method that minimizes divergence to efficiently sample from complex, irregular target distributions by focusing adaptation on local geometry, improving sampling accuracy.

Contribution

The paper introduces a regional divergence minimization approach for adaptive MCMC, enabling rapid local adaptation without extensive pre-sampling.

Findings

Effective sampling from irregularly shaped distributions

Rapid local adaptation to target geometry

Improved convergence over traditional methods

Abstract

We introduce a Markov Chain Monte Carlo (MCMC) method that is designed to sample from target distributions with irregular geometry using an adaptive scheme. In cases where targets exhibit non-Gaussian behaviour, we propose that adaption should be regional rather than global. Our algorithm minimizes the information projection component of the Kullback-Leibler (KL) divergence between the proposal and target distributions to encourage proposals that are distributed similarly to the regional geometry of the target. Unlike traditional adaptive MCMC, this procedure rapidly adapts to the geometry of the target's current position as it explores the surrounding space without the need for many preexisting samples. The divergence minimization algorithms are tested on target distributions with irregularly shaped modes and we provide results demonstrating the effectiveness of our methods.