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Stein thinning is a promising algorithm proposed by (Riabiz et al., 2022) forpost-processing outputs of Markov chain Monte Carlo (MCMC). The main principleis to greedily minimize the kernelized Stein discrepancy (KSD), which onlyrequires the gradient of the log-target distribution, and is thus well-suitedfor Bayesian inference. The main advantages of Stein thinning are the automaticremove of the burn-in period, the correction of the bias introduced by recentMCMC algorithms, and the asymptotic properties of convergence towards thetarget distribution. Nevertheless, Stein thinning suffers from severalempirical pathologies, which may result in poor approximations, as observed inthe literature. In this article, we conduct a theoretical analysis of thesepathologies, to clearly identify the mechanisms at stake, and suggest improvedstrategies. Then, we introduce the regularized Stein thinning algorithm toalleviate the identified pathologies. Finally, theoretical guarantees andextensive experiments show the high efficiency of the proposed algorithm. Animplementation of regularized Stein thinning as the kernax library in pythonand JAX is available at https://gitlab.com/drti/kernax.

Kernel Stein Discrepancy thinning: a theoretical perspective of pathologies and a practical fix with regularization