2023/05/17 by Congye Wang, Wilson Chen, Wang, Congye +5 · 2 citations
Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Random Matrices and Applications #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2305.10068
Stein discrepancies have emerged as a powerful tool for retrospective improvement of Markov chain Monte Carlo output. However, the question of how to design Markov chains that are well-suited to such post-processing has yet to be addressed. This paper studies Stein importance sampling, in which weights are assigned to the states visited by a Π-invariant Markov chain to obtain a consistent approximation of P, the intended target. Surprisingly, the optimal choice of Π is not identical to the target P; we therefore propose an explicit construction for Π based on a novel variational argument. Explicit conditions for convergence of Stein Π-Importance Sampling are established. For ≈ 70% of tasks in the PosteriorDB benchmark, a significant improvement over the analogous post-processing of P-invariant Markov chains is reported.