{"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/optimally-weighted-herding-is-bayesian-1","title":"Optimally-Weighted Herding is Bayesian Quadrature","arxiv_id":"1204.1664","date":"2012-04-07","proceeding":null,"authors":["Ferenc Huszár","David Duvenaud"],"abstract":"Herding and kernel herding are deterministic methods of choosing samples\nwhich summarise a probability distribution. A related task is choosing samples\nfor estimating integrals using Bayesian quadrature. We show that the criterion\nminimised when selecting samples in kernel herding is equivalent to the\nposterior variance in Bayesian quadrature. We then show that sequential\nBayesian quadrature can be viewed as a weighted version of kernel herding which\nachieves performance superior to any other weighted herding method. We\ndemonstrate empirically a rate of convergence faster than O(1/N). Our results\nalso imply an upper bound on the empirical error of the Bayesian quadrature\nestimate.","url_abs":"http://arxiv.org/abs/1204.1664v3","url_pdf":"http://arxiv.org/pdf/1204.1664v3.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":"optimally-weighted-herding-is-bayesian-1","repo_url":"https://github.com/duvenaud/herding-paper","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1204.1664","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}