Stein thinning is a promising algorithm proposed by (Riabiz et al., 2022) for post-processing outputs of Markov chain Monte Carlo (MCMC). The main principle is to greedily minimize the kernelized Stein discrepancy (KSD), which only requires the gradient of the log-target distribution, and is thus well-suited for Bayesian inference. The main advantages of Stein thinning are the automatic remove of the burn-in period, the correction of the bias introduced by recent MCMC algorithms, and the asymptotic properties of convergence towards the target distribution. Nevertheless, Stein thinning suffers from several empirical pathologies, which may result in poor approximations, as observed in the literature. In this article, we conduct a theoretical analysis of these pathologies, to clearly identify the mechanisms at stake, and suggest improved strategies. Then, we introduce the regularized Stein thinning algorithm to alleviate the identified pathologies. Finally, theoretical guarantees and extensive experiments show the high efficiency of the proposed algorithm.

翻译：Stein thinning是由Riabiz等人（2022）提出的一种用于后处理马尔可夫链蒙特卡洛（MCMC）输出结果的创新性算法。该算法的核心原理是通过贪心算法最小化核化Stein散度（KSD），其仅需目标分布的对数梯度，因此特别适用于贝叶斯推断。Stein thinning的主要优势包括：自动消除预烧期、校正现代MCMC算法引入的偏差，以及保证收敛至目标分布的渐近特性。然而，该算法存在若干经验性病理问题，可能导致文献中报道的近似效果不佳。本文通过理论分析厘清这些病理现象的作用机制，提出改进策略，进而引入正则化Stein thinning算法以缓解已识别的病理问题。最终，理论保证与大量实验证明了所提算法的高效性。