{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/stein-pi-importance-sampling","title":"Stein $\\Pi$-Importance Sampling","arxiv_id":null,"date":"2023-09-21","proceeding":"NeurIPS 2023 11","authors":[],"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.","url_abs":"https://openreview.net/forum?id=wiidCRA3at","url_pdf":"https://openreview.net/pdf?id=wiidCRA3at","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"stein-pi-importance-sampling","repo_url":"https://github.com/congyewang/stein-pi-importance-sampling","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"jax","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}