{"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/convergence-analysis-of-deterministic-kernel","title":"Convergence Analysis of Deterministic Kernel-Based Quadrature Rules in Misspecified Settings","arxiv_id":"1709.00147","date":"2017-09-01","proceeding":null,"authors":["Motonobu Kanagawa","Bharath K. Sriperumbudur","Kenji Fukumizu"],"abstract":"This paper presents a convergence analysis of kernel-based quadrature rules\nin misspecified settings, focusing on deterministic quadrature in Sobolev\nspaces. In particular, we deal with misspecified settings where a test\nintegrand is less smooth than a Sobolev RKHS based on which a quadrature rule\nis constructed. We provide convergence guarantees based on two different\nassumptions on a quadrature rule: one on quadrature weights, and the other on\ndesign points. More precisely, we show that convergence rates can be derived\n(i) if the sum of absolute weights remains constant (or does not increase\nquickly), or (ii) if the minimum distance between design points does not\ndecrease very quickly. As a consequence of the latter result, we derive a rate\nof convergence for Bayesian quadrature in misspecified settings. We reveal a\ncondition on design points to make Bayesian quadrature robust to\nmisspecification, and show that, under this condition, it may adaptively\nachieve the optimal rate of convergence in the Sobolev space of a lesser order\n(i.e., of the unknown smoothness of a test integrand), under a slightly\nstronger regularity condition on the integrand.","url_abs":"http://arxiv.org/abs/1709.00147v2","url_pdf":"http://arxiv.org/pdf/1709.00147v2.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":"convergence-analysis-of-deterministic-kernel","repo_url":"https://github.com/motonobuk/kernel-quadrature","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1709.00147","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}