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Spotlight Poster

Stein $\Pi$-Importance Sampling

Congye Wang · Ye Chen · Heishiro Kanagawa · Chris Oates

Great Hall & Hall B1+B2 (level 1) #1400
[ ]
[ Paper [ Poster [ OpenReview
Thu 14 Dec 3 p.m. PST — 5 p.m. PST

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. This paper studies Stein importance sampling, 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 $P$; we therefore propose an explicit construction for $\Pi$ based on a novel variational argument. Explicit conditions for convergence of Stein $\Pi$-Importance Sampling are established. For $\approx 70$% of tasks in the PosteriorDB benchmark, a significant improvement over the analogous post-processing of $P$-invariant Markov chains is reported.

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