{"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/scan-b-statistic-for-kernel-change-point","title":"Scan $B$-Statistic for Kernel Change-Point Detection","arxiv_id":"1507.01279","date":"2015-07-05","proceeding":null,"authors":["Shuang Li","Yao Xie","Hanjun Dai","Le Song"],"abstract":"Detecting the emergence of an abrupt change-point is a classic problem in\nstatistics and machine learning. Kernel-based nonparametric statistics have\nbeen used for this task which enjoy fewer assumptions on the distributions than\nthe parametric approach and can handle high-dimensional data. In this paper we\nfocus on the scenario when the amount of background data is large, and propose\ntwo related computationally efficient kernel-based statistics for change-point\ndetection, which are inspired by the recently developed $B$-statistics. A novel\ntheoretical result of the paper is the characterization of the tail probability\nof these statistics using the change-of-measure technique, which focuses on\ncharacterizing the tail of the detection statistics rather than obtaining its\nasymptotic distribution under the null distribution. Such approximations are\ncrucial to control the false alarm rate, which corresponds to the significance\nlevel in offline change-point detection and the average-run-length in online\nchange-point detection. Our approximations are shown to be highly accurate.\nThus, they provide a convenient way to find detection thresholds for both\noffline and online cases without the need to resort to the more expensive\nsimulations or bootstrapping. We show that our methods perform well on both\nsynthetic data and real data.","url_abs":"http://arxiv.org/abs/1507.01279v5","url_pdf":"http://arxiv.org/pdf/1507.01279v5.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":"scan-b-statistic-for-kernel-change-point","repo_url":"https://github.com/Wang-ZH-Stat/SBSK","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"change-point-detection","task_name":"Change Point Detection"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1507.01279","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}