{"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/kernel-embedding-of-maps-for-sequential","title":"Kernel embedding of maps for sequential Bayesian inference: The variational mapping particle filter","arxiv_id":"1805.11380","date":"2018-05-29","proceeding":null,"authors":["Manuel Pulido","Peter Jan vanLeeuwen"],"abstract":"In this work, a novel sequential Monte Carlo filter is introduced which aims\nat efficient sampling of high-dimensional state spaces with a limited number of\nparticles. Particles are pushed forward from the prior to the posterior density\nusing a sequence of mappings that minimizes the Kullback-Leibler divergence\nbetween the posterior and the sequence of intermediate densities. The sequence\nof mappings represents a gradient flow. A key ingredient of the mappings is\nthat they are embedded in a reproducing kernel Hilbert space, which allows for\na practical and efficient algorithm. The embedding provides a direct means to\ncalculate the gradient of the Kullback-Leibler divergence leading to quick\nconvergence using well-known gradient-based stochastic optimization algorithms.\nEvaluation of the method is conducted in the chaotic Lorenz-63 system, the\nLorenz-96 system, which is a coarse prototype of atmospheric dynamics, and an\nepidemic model that describes cholera dynamics. No resampling is required in\nthe mapping particle filter even for long recursive sequences. The number of\neffective particles remains close to the total number of particles in all the\nexperiments.","url_abs":"http://arxiv.org/abs/1805.11380v1","url_pdf":"http://arxiv.org/pdf/1805.11380v1.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":"kernel-embedding-of-maps-for-sequential","repo_url":"https://github.com/ZoneTsuyoshi/pyassim","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"},{"task_slug":"sequential-bayesian-inference","task_name":"Sequential Bayesian Inference"},{"task_slug":"stochastic-optimization","task_name":"Stochastic Optimization"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}