{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T11:02:52Z","timestamp":1789556572774,"version":"build-2803163510"},"reference-count":62,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T00:00:00Z","timestamp":1770681600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/100005609","name":"Coca-Cola Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100005609","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,9,16]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>We present a computationally efficient online kernel Cumulative Sum method for change-point detection that utilizes the maximum over a set of kernel statistics to account for the unknown change-point location. Our approach exhibits increased sensitivity to small changes compared to existing kernel-based change-point detection methods, including the Scan-B statistic, corresponding to a non-parametric Shewhart chart-type procedure. We provide accurate analytic approximations for two key performance metrics: the average run length (ARL) and expected detection delay, which enable us to establish an optimal window length to be on the order of the logarithm of ARL to ensure minimal power loss relative to an oracle procedure with infinite memory. Moreover, we introduce a recursive calculation procedure for detection statistics to ensure constant computational and memory complexity, which is essential for online implementation. Through extensive experiments on both simulated and real data, we demonstrate the competitive performance of our method and validate our theoretical results.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkag020","type":"journal-article","created":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T12:35:49Z","timestamp":1768048549000},"page":"1251-1277","source":"Crossref","is-referenced-by-count":3,"title":["Online kernel CUSUM for change-point detection"],"prefix":"10.1093","volume":"88","author":[{"given":"Song","family":"Wei","sequence":"first","affiliation":[{"name":"H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology , Atlanta, Georgia 30332 ,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yao","family":"Xie","sequence":"additional","affiliation":[{"name":"H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology , Atlanta, Georgia 30332 ,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,2,10]]},"reference":[{"key":"2026091606123345400_qkag020-B1","author":"Amrouni","year":"2021"},{"key":"2026091606123345400_qkag020-B2","first-page":"1","article-title":"A kernel multiple change-point algorithm via model selection","volume":"20","author":"Arlot","year":"2019","journal-title":"Journal of Machine Learning Research"},{"key":"2026091606123345400_qkag020-B3","article-title":"On the optimality of kernel-embedding based goodness-of-fit tests","volume":"22","author":"Balasubramanian","year":"2021","journal-title":"Journal of Machine Learning Research"},{"key":"2026091606123345400_qkag020-B4","volume-title":"Detection of abrupt changes: Theory and application","author":"Basseville","year":"1993"},{"key":"2026091606123345400_qkag020-B5","author":"Bouchikhi","year":"2019"},{"issue":"1-2","key":"2026091606123345400_qkag020-B6","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1007\/s10479-016-2185-5","article-title":"Multi-sensor slope change detection","volume":"263","author":"Cao","year":"2018","journal-title":"Annals of Operations Research"},{"key":"2026091606123345400_qkag020-B7","author":"Chang","year":"2019"},{"issue":"4","key":"2026091606123345400_qkag020-B8","doi-asserted-by":"publisher","first-page":"2572","DOI":"10.3150\/22-bej1565","article-title":"Kernel MMD two-sample tests for manifold data","volume":"30","author":"Cheng","year":"2023","journal-title":"Bernoulli"},{"key":"2026091606123345400_qkag020-B9","doi-asserted-by":"publisher","first-page":"181","DOI":"10.3150\/21-BEJ1338","article-title":"Finite sample properties of parametric MMD estimation: Robustness to misspecification and dependence","volume":"28","author":"Ch\u00e9rief-Abdellatif","year":"2022","journal-title":"Bernoulli"},{"key":"2026091606123345400_qkag020-B10","author":"Cobb","year":"2022"},{"issue":"3","key":"2026091606123345400_qkag020-B11","doi-asserted-by":"publisher","first-page":"109022","DOI":"10.1016\/j.patcog.2022.109022","article-title":"Online change-point detection with kernels","volume":"133","author":"Ferrari","year":"2023","journal-title":"Pattern Recognition"},{"key":"2026091606123345400_qkag020-B12","author":"Flynn","year":"2019"},{"issue":"2","key":"2026091606123345400_qkag020-B13","doi-asserted-by":"publisher","first-page":"4440","DOI":"10.1214\/18-EJS1513","article-title":"Consistent change-point detection with kernels","volume":"12","author":"Garreau","year":"2018","journal-title":"Electronic Journal of Statistics"},{"key":"2026091606123345400_qkag020-B14","first-page":"513","article-title":"A kernel method for the two-sample-problem","volume":"19","author":"Gretton","year":"2006","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026091606123345400_qkag020-B15","first-page":"723","article-title":"A kernel two-sample test","volume":"13","author":"Gretton","year":"2012","journal-title":"Journal of Machine Learning Research"},{"key":"2026091606123345400_qkag020-B16","article-title":"Optimal kernel choice for large-scale two-sample tests","volume":"25","author":"Gretton","year":"2012","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026091606123345400_qkag020-B17","author":"Harchaoui","year":"2007"},{"key":"2026091606123345400_qkag020-B18","article-title":"Kernel change-point analysis","volume":"21","author":"Harchaoui","year":"2008","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026091606123345400_qkag020-B19","first-page":"601","article-title":"Correcting sample selection bias by unlabeled data","volume":"19","author":"Huang","year":"2006","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"10","key":"2026091606123345400_qkag020-B20","doi-asserted-by":"publisher","first-page":"999","DOI":"10.1080\/0740817X.2013.855848","article-title":"High-dimensional process monitoring and change point detection using embedding distributions in reproducing kernel Hilbert space","volume":"46","author":"Huang","year":"2014","journal-title":"IIE Transactions: Industrial Engineering Research & Development"},{"key":"2026091606123345400_qkag020-B21","doi-asserted-by":"publisher","author":"Hushchyn","year":"2020","DOI":"10.48550\/arXiv.2010.01388"},{"issue":"9","key":"2026091606123345400_qkag020-B22","doi-asserted-by":"publisher","first-page":"1687","DOI":"10.1111\/mee3.v12.9","article-title":"A kernel-based change detection method to map shifts in phytoplankton communities measured by flow cytometry","volume":"12","author":"Jones","year":"2021","journal-title":"Methods in Ecology and Evolution"},{"issue":"4","key":"2026091606123345400_qkag020-B23","doi-asserted-by":"publisher","first-page":"613","DOI":"10.1111\/j.2517-6161.1995.tb02052.x","article-title":"Sequential changepoint detection in quality control and dynamical systems","volume":"57","author":"Lai","year":"1995","journal-title":"Journal of the Royal Statistical Society: Series B (Methodological)"},{"issue":"2","key":"2026091606123345400_qkag020-B24","first-page":"303","article-title":"Sequential analysis: Some classical problems and new challenges","volume":"11","author":"Lai","year":"2001","journal-title":"Statistica Sinica"},{"key":"2026091606123345400_qkag020-B25","doi-asserted-by":"publisher","author":"Lee","year":"2022","DOI":"10.48550\/arXiv.2210.17312"},{"key":"2026091606123345400_qkag020-B26","author":"Lee","year":"2023"},{"issue":"4","key":"2026091606123345400_qkag020-B27","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1080\/07474946.2019.1686886","article-title":"Scan B-statistic for kernel change-point detection","volume":"38","author":"Li","year":"2019","journal-title":"Sequential Analysis"},{"issue":"334","key":"2026091606123345400_qkag020-B28","first-page":"1","article-title":"On the optimality of Gaussian kernel based nonparametric tests against smooth alternatives","volume":"25","author":"Li","year":"2024","journal-title":"Journal of Machine Learning Research"},{"key":"2026091606123345400_qkag020-B29","article-title":"Statistical model criticism using kernel two sample tests","volume":"28","author":"Lloyd","year":"2015","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"6","key":"2026091606123345400_qkag020-B30","doi-asserted-by":"publisher","first-page":"1897","DOI":"10.1214\/aoms\/1177693055","article-title":"Procedures for reacting to a change in distribution","volume":"42","author":"Lorden","year":"1971","journal-title":"The Annals of Mathematical Statistics"},{"issue":"1","key":"2026091606123345400_qkag020-B31","doi-asserted-by":"publisher","first-page":"46","DOI":"10.2307\/1269551","article-title":"A multivariate exponentially weighted moving average control chart","volume":"34","author":"Lowry","year":"1992","journal-title":"Technometrics: A Journal of Statistics for the Physical, Chemical, and Engineering Sciences"},{"issue":"4","key":"2026091606123345400_qkag020-B32","doi-asserted-by":"publisher","first-page":"1379","DOI":"10.1214\/aos\/1176350164","article-title":"Optimal stopping times for detecting changes in distributions","volume":"14","author":"Moustakides","year":"1986","journal-title":"Annals of Statistics"},{"issue":"1-2","key":"2026091606123345400_qkag020-B33","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1561\/2200000060","article-title":"Kernel mean embedding of distributions: A review and beyond","volume":"10","author":"Muandet","year":"2017","journal-title":"Foundations and Trends\u00ae in Machine Learning"},{"issue":"11","key":"2026091606123345400_qkag020-B34","doi-asserted-by":"publisher","first-page":"5847","DOI":"10.1109\/TIT.2010.2068870","article-title":"Estimating divergence functionals and the likelihood ratio by convex risk minimization","volume":"56","author":"Nguyen","year":"2010","journal-title":"IEEE Transactions on Information Theory"},{"issue":"1-2","key":"2026091606123345400_qkag020-B35","doi-asserted-by":"publisher","first-page":"100","DOI":"10.1093\/biomet\/41.1-2.100","article-title":"Continuous inspection schemes","volume":"41","author":"Page","year":"1954","journal-title":"Biometrika"},{"key":"2026091606123345400_qkag020-B36","author":"Ramdas","year":"2015"},{"key":"2026091606123345400_qkag020-B37","author":"Reddi","year":"2015"},{"key":"2026091606123345400_qkag020-B38","volume-title":"Learning with kernels: Support vector machines, regularization, optimization, and beyond","author":"Sch\u00f6lkopf","year":"2002"},{"key":"2026091606123345400_qkag020-B39","volume-title":"Approximation theorems of mathematical statistics","author":"Serfling","year":"2009"},{"key":"2026091606123345400_qkag020-B40","doi-asserted-by":"publisher","author":"Shashua","year":"2009","DOI":"10.48550\/arXiv.0904.3664"},{"issue":"152","key":"2026091606123345400_qkag020-B41","doi-asserted-by":"publisher","first-page":"546","DOI":"10.1080\/01621459.1925.10502930","article-title":"The application of statistics as an aid in maintaining quality of a manufactured product","volume":"20","author":"Shewhart","year":"1925","journal-title":"Journal of the American Statistical Association"},{"issue":"1","key":"2026091606123345400_qkag020-B42","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1137\/1108002","article-title":"On optimum methods in quickest detection problems","volume":"8","author":"Shiryaev","year":"1963","journal-title":"Theory of Probability & Its Applications"},{"key":"2026091606123345400_qkag020-B43","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-1862-1","volume-title":"Sequential analysis: Tests and confidence intervals","author":"Siegmund","year":"1985"},{"key":"2026091606123345400_qkag020-B44","volume-title":"Sequential analysis: Tests and confidence intervals","author":"Siegmund","year":"2013"},{"issue":"1","key":"2026091606123345400_qkag020-B45","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1214\/aos\/1176324466","article-title":"Using the generalized likelihood ratio statistic for sequential detection of a change-point","volume":"23","author":"Siegmund","year":"1995","journal-title":"Annals of Statistics"},{"key":"2026091606123345400_qkag020-B46","volume-title":"The statistics of gene mapping","author":"Siegmund","year":"2007"},{"issue":"3","key":"2026091606123345400_qkag020-B47","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1080\/07474946.2010.487428","article-title":"Tail approximations for maxima of random fields by likelihood ratio transformations","volume":"29","author":"Siegmund","year":"2010","journal-title":"Sequential Analysis"},{"key":"2026091606123345400_qkag020-B48","author":"Smola","year":"2007"},{"key":"2026091606123345400_qkag020-B49","author":"Song","year":"2024"},{"key":"2026091606123345400_qkag020-B50","first-page":"2389","article-title":"Universality, characteristic kernels and RKHS embedding of measures","volume":"12","author":"Sriperumbudur","year":"2011","journal-title":"Journal of Machine Learning Research"},{"key":"2026091606123345400_qkag020-B51","author":"Sun","year":"2021"},{"key":"2026091606123345400_qkag020-B52","doi-asserted-by":"crossref","DOI":"10.1201\/b17279","volume-title":"Sequential analysis: Hypothesis testing and changepoint detection","author":"Tartakovsky","year":"2014"},{"issue":"24","key":"2026091606123345400_qkag020-B53","doi-asserted-by":"publisher","first-page":"6204","DOI":"10.1109\/TSP.78","article-title":"Greedy kernel change-point detection","volume":"67","author":"Truong","year":"2019","journal-title":"IEEE Transactions on Signal Processing"},{"key":"2026091606123345400_qkag020-B54","author":"Vyetrenko","year":"2020"},{"key":"2026091606123345400_qkag020-B55","article-title":"Using the Nystr\u00f6m method to speed up kernel machines","volume":"13","author":"Williams","year":"2000","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"9","key":"2026091606123345400_qkag020-B56","doi-asserted-by":"crossref","first-page":"5990","DOI":"10.1109\/TIT.2023.3274646","article-title":"Window-limited CUSUM for sequential change detection","volume":"69","author":"Xie","year":"2023","journal-title":"IEEE Transactions on Information Theory"},{"issue":"2","key":"2026091606123345400_qkag020-B57","doi-asserted-by":"publisher","first-page":"747","DOI":"10.1109\/JSAIT.2021.3072960","article-title":"Sequential change detection by optimal weighted \u21132 divergence","volume":"2","author":"Xie","year":"2021","journal-title":"IEEE Journal on Selected Areas in Information Theory"},{"issue":"2","key":"2026091606123345400_qkag020-B58","doi-asserted-by":"publisher","first-page":"494","DOI":"10.1109\/JSAIT.2021.3072962","article-title":"Sequential (quickest) change detection: Classical results and new directions","volume":"2","author":"Xie","year":"2021","journal-title":"IEEE Journal on Selected Areas in Information Theory"},{"issue":"2","key":"2026091606123345400_qkag020-B59","doi-asserted-by":"publisher","first-page":"670","DOI":"10.1214\/13-AOS1094","article-title":"Sequential multi-sensor change-point detection","volume":"41","author":"Xie","year":"2013","journal-title":"Annals of Statistics"},{"key":"2026091606123345400_qkag020-B60","doi-asserted-by":"crossref","DOI":"10.1002\/9781118720608","volume-title":"Extremes in random fields: A theory and its applications","author":"Yakir","year":"2013"},{"key":"2026091606123345400_qkag020-B61","article-title":"B-test: A non-parametric, low variance kernel two-sample test","volume":"26","author":"Zaremba","year":"2013","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026091606123345400_qkag020-B62","first-page":"5785","article-title":"Nonparametric detection of anomalous data streams","volume-title":"IEEE Transactions on Signal Processing","author":"Zou","year":"2017"}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/88\/4\/1251\/66837377\/qkag020.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/88\/4\/1251\/66837377\/qkag020.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T10:12:45Z","timestamp":1789553565000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/88\/4\/1251\/8470848"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,10]]},"references-count":62,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2026,2,10]]},"published-print":{"date-parts":[[2026,9,16]]}},"URL":"https:\/\/doi.org\/10.1093\/jrsssb\/qkag020","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,9]]},"published":{"date-parts":[[2026,2,10]]}}}