A0352
Title: Stein pi-importance sampling
Authors: Congye Wang - Newcastle University (United Kingdom)
Heishiro Kanagawa - Newcastle University (United Kingdom)
Chris Oates - Newcastle University (United Kingdom)
Wilson Chen - The University of Sydney (Australia) [presenting]
Abstract: 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. Stein importance sampling is studied, in which weights are assigned to the states visited by a Pi-invariant Markov chain to obtain a consistent approximation of P, the intended target. Surprisingly, the optimal choice of Pi is not identical to the target P; an explicit construction for Pi is therefore proposed based on a novel variational argument. Explicit conditions for convergence of Stein pi-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.
