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稀疏化是由Riabiz等人（2022）提出的一种用于处理马尔可夫链蒙特卡洛（MCMC）输出后处理的具有前景的算法。其主要原理是贪心最小化核化Stein散度（KSD），该散度仅需对数目标分布的梯度，因此非常适用于贝叶斯推断。Stein稀疏化的主要优势包括自动去除燃烧期、修正近期MCMC算法引入的偏差，以及渐近收敛于目标分布的性质。然而，如文献所述，Stein稀疏化存在若干经验性病理问题，可能导致较差的近似效果。本文对这些病理现象进行理论分析，以明确其作用机制并提出改进策略。随后，我们引入正则化Stein稀疏化算法以缓解已识别的病理问题。最后，理论保证和大量实验证明了所提算法的高效性。