Online, Informative MCMC Thinning with Kernelized Stein Discrepancy

TL;DR

This paper introduces KSD Thinning, an online MCMC method that selectively retains samples exceeding a kernelized Stein discrepancy threshold, improving efficiency in Bayesian posterior representation.

Contribution

It proposes a novel online MCMC thinning technique based on KSD, with theoretical convergence analysis and superior empirical performance over existing methods.

Findings

KSD Thinning achieves better complexity-accuracy tradeoffs.

The method converges under specified conditions.

Experimental results show improved posterior approximation efficiency.

Abstract

A fundamental challenge in Bayesian inference is efficient representation of a target distribution. Many non-parametric approaches do so by sampling a large number of points using variants of Markov Chain Monte Carlo (MCMC). We propose an MCMC variant that retains only those posterior samples which exceed a KSD threshold, which we call KSD Thinning. We establish the convergence and complexity tradeoffs for several settings of KSD Thinning as a function of the KSD threshold parameter, sample size, and other problem parameters. Finally, we provide experimental comparisons against other online nonparametric Bayesian methods that generate low-complexity posterior representations, and observe superior consistency/complexity tradeoffs. Code is available at github.com/colehawkins/KSD-Thinning.