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Stein Π-Importance Sampling

Lookup NU author(s): Congye Wang, Dr Heishiro Kanagawa, Professor Chris OatesORCiD

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Abstract

© 2023 Neural information processing systems foundation. All rights reserved.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.

Publication metadata

Author(s): Wang C, Chen WY, Kanagawa H, Oates CJ

Publication type: Conference Proceedings (inc. Abstract)

Publication status: Published

Conference Name: Advances in Neural Information Processing Systems

Year of Conference: 2023

Acceptance date: 13/09/2023

Publisher: Neural Information Processing Systems Foundation

URL: https://proceedings.neurips.cc/paper_files/paper/2023/hash/e389b15166cf98966ba058965a8c17e3-Abstract-Conference.html

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