  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.
