{"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/sequential-monte-carlo-approximations-of","title":"Sequential Monte Carlo approximations of Wasserstein--Fisher--Rao gradient flows","arxiv_id":"2506.05905","date":"2025-06-06","proceeding":null,"authors":["Francesca R. Crucinio","Sahani Pathiraja"],"abstract":"We consider the problem of sampling from a probability distribution $\\pi$. It is well known that this can be written as an optimisation problem over the space of probability distribution in which we aim to minimise the Kullback--Leibler divergence from $\\pi$. We consider several partial differential equations (PDEs) whose solution is a minimiser of the Kullback--Leibler divergence from $\\pi$ and connect them to well-known Monte Carlo algorithms. We focus in particular on PDEs obtained by considering the Wasserstein--Fisher--Rao geometry over the space of probabilities and show that these lead to a natural implementation using importance sampling and sequential Monte Carlo. We propose a novel algorithm to approximate the Wasserstein--Fisher--Rao flow of the Kullback--Leibler divergence which empirically outperforms the current state-of-the-art. We study tempered versions of these PDEs obtained by replacing the target distribution with a geometric mixture of initial and target distribution and show that these do not lead to a convergence speed up.","url_abs":"https://arxiv.org/abs/2506.05905v1","url_pdf":"https://arxiv.org/pdf/2506.05905v1.pdf","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":"sequential-monte-carlo-approximations-of","repo_url":"https://github.com/FrancescaCrucinio/SMC-WFR","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[{"method_slug":"focus","method_name":"Focus"},{"method_slug":"speed","method_name":"SPEED"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}