ArXiv Preprint
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.
Clément Bénard, Brian Staber, Sébastien Da Veiga
2023-01-31
