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arXiv · 2201.07130

Online, Informative MCMC Thinning with Kernelized Stein Discrepancy

Cole Hawkins·Alec Koppel·Zheng Zhang
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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.

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Cole Hawkins, Alec Koppel, Zheng Zhang. 2022-01-18. Online, Informative MCMC Thinning with Kernelized Stein Discrepancy. https://arxiv.org/abs/2201.07130

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