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.

翻译：Bayesian推论中的一项根本挑战是目标分布的有效表示方式,许多非参数方法采用Markov 链条蒙特卡洛(MCMC)的变体对大量点进行取样,我们建议采用MCMC变体,只保留超过KSD临界值(我们称之为KSD Thinning)的后方样本。我们为KSD Thinning的若干设置设定了趋同和复杂权衡法,作为 KSD临界参数、样本大小和其他问题参数的函数。最后,我们提供了与其他产生低复度后方代表的在线非参数巴伊西亚方法的实验性比较,并遵守了高度一致性/复度权衡法。在 Github.com/Colexawkins/KSD-Tinning中可以找到守则。