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

Online, Informative MCMC Thinning with Kernelized Stein Discrepancy