{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T06:49:21Z","timestamp":1775630961119,"version":"3.50.1"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2020,8,1]],"date-time":"2020-08-01T00:00:00Z","timestamp":1596240000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,8,1]],"date-time":"2020-08-01T00:00:00Z","timestamp":1596240000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/N031938\/1"],"award-info":[{"award-number":["EP\/N031938\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2020,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This article focuses on the challenging problem of efficiently detecting changes in mean within multivariate data sequences. Multivariate changepoints can be detected by projecting a multivariate series to a univariate one using a suitable projection direction that preserves a maximal proportion of signal information. However, for some existing approaches the computation of such a projection direction can scale unfavourably with the number of series and might rely on additional assumptions on the data sequences, thus limiting their generality. We introduce BayesProject, a computationally inexpensive Bayesian approach to compute a projection direction in such a setting. The proposed approach allows the incorporation of prior knowledge of the changepoint scenario, when such information is available, which can help to increase the accuracy of the method. A simulation study shows that BayesProject is robust, yields projections close to the oracle projection direction and, moreover, that its accuracy in detecting changepoints is comparable to, or better than, existing algorithms while scaling linearly with the number of series.<\/jats:p>","DOI":"10.1007\/s11222-020-09966-2","type":"journal-article","created":{"date-parts":[[2020,8,1]],"date-time":"2020-08-01T12:02:51Z","timestamp":1596283371000},"page":"1691-1705","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["BayesProject: Fast computation of a projection direction for multivariate changepoint detection"],"prefix":"10.1007","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6008-2720","authenticated-orcid":false,"given":"Georg","family":"Hahn","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paul","family":"Fearnhead","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Idris A.","family":"Eckley","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,8,1]]},"reference":[{"issue":"6B","key":"9966_CR1","doi-asserted-by":"publisher","first-page":"4046","DOI":"10.1214\/09-AOS707","volume":"37","author":"A Aue","year":"2009","unstructured":"Aue, A., H\u00f6rmann, S., Horv\u00e1th, L., Reimherr, M.: Break detection in the covariance structure of multivariate time series models. Ann. Stat. 37(6B), 4046\u20134087 (2009)","journal-title":"Ann. Stat."},{"issue":"1","key":"9966_CR2","doi-asserted-by":"publisher","first-page":"47","DOI":"10.2307\/2998540","volume":"66","author":"J Bai","year":"1998","unstructured":"Bai, J., Perron, P.: Estimating and testing linear models with multiple structural changes. Econometrica 66(1), 47\u201378 (1998)","journal-title":"Econometrica"},{"key":"9966_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1561\/2200000016","volume":"3","author":"S Boyd","year":"2011","unstructured":"Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found Trends Mach. Learn. 3, 1\u2013122 (2011)","journal-title":"Found Trends Mach. Learn."},{"key":"9966_CR4","doi-asserted-by":"publisher","first-page":"2000","DOI":"10.1214\/16-EJS1155","volume":"10","author":"H Cho","year":"2016","unstructured":"Cho, H.: Change-point detection in panel data via double CUSUM statistic. Electron. J. Stat. 10, 2000\u20132038 (2016)","journal-title":"Electron. J. Stat."},{"issue":"2","key":"9966_CR5","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1111\/rssb.12079","volume":"77","author":"H Cho","year":"2015","unstructured":"Cho, H., Fryzlewicz, P.: Multiple-change-point detection for high dimensional time series via sparsified binary segmentation. J. R. Stat. Soc. B 77(2), 475\u2013507 (2015)","journal-title":"J. R. Stat. Soc. B"},{"issue":"8","key":"9966_CR6","doi-asserted-by":"publisher","first-page":"2961","DOI":"10.1109\/TSP.2005.851098","volume":"53","author":"F Desobry","year":"2005","unstructured":"Desobry, F., Davy, M., Doncarli, C.: An online kernel change detection algorithm. IEEE Trans. Signal Process. 53(8), 2961\u20132974 (2005)","journal-title":"IEEE Trans. Signal Process."},{"issue":"4","key":"9966_CR7","doi-asserted-by":"publisher","first-page":"2051","DOI":"10.1214\/18-AOS1740","volume":"47","author":"F Enikeeva","year":"2019","unstructured":"Enikeeva, F., Harchaoui, Z.: High-dimensional change-point detection under sparse alternatives. Ann. Stat. 47(4), 2051\u20132079 (2019)","journal-title":"Ann. Stat."},{"issue":"1","key":"9966_CR8","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1109\/TSP.2018.2880669","volume":"67","author":"M Eriksson","year":"2019","unstructured":"Eriksson, M., Olofsson, T.: Computationally efficient off-line joint change point detection in multiple time series. IEEE Trans. Signal Process. 67(1), 149\u2013163 (2019)","journal-title":"IEEE Trans. Signal Process."},{"issue":"3","key":"9966_CR9","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1111\/rssb.12047","volume":"76","author":"K Frick","year":"2014","unstructured":"Frick, K., Munk, A., Sieling, H.: Multiscale change point inference. J. R. Stat. Soc. B Stat. Methodol. 76(3), 495\u2013580 (2014)","journal-title":"J. R. Stat. Soc. B Stat. Methodol."},{"issue":"6","key":"9966_CR10","doi-asserted-by":"publisher","first-page":"2243","DOI":"10.1214\/14-AOS1245","volume":"42","author":"P Fryzlewicz","year":"2014","unstructured":"Fryzlewicz, P.: Wild binary segmentation for multiple change-point detection. Ann. Stat. 42(6), 2243\u20132281 (2014)","journal-title":"Ann. Stat."},{"key":"9966_CR11","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/0898-1221(76)90003-1","volume":"2","author":"D Gabay","year":"1976","unstructured":"Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximations. Comput. Math. Appl. 2, 17\u201340 (1976)","journal-title":"Comput. Math. Appl."},{"key":"9966_CR12","volume-title":"Matrix Computations","author":"G Golub","year":"2012","unstructured":"Golub, G., van Loan, C.: Matrix Computations, 4th edn. Johns Hopkins University Press, New York (2012)","edition":"4"},{"key":"9966_CR13","doi-asserted-by":"crossref","unstructured":"Grundy, T., Killick, R., Mihaylov, G.: Changepoint.geo: geometrically inspired multivariate change point detection. R Package Version 1.0.1. https:\/\/cran.r-project.org\/package=changepoint.geo (2020a)","DOI":"10.32614\/CRAN.package.changepoint.geo"},{"key":"9966_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-020-09940-y","author":"T Grundy","year":"2020","unstructured":"Grundy, T., Killick, R., Mihaylov, G.: High-dimensional changepoint detection via a geometrically inspired mapping. Stat. Comput. (2020b). https:\/\/doi.org\/10.1007\/s11222-020-09940-y","journal-title":"Stat. Comput."},{"issue":"6","key":"9966_CR15","doi-asserted-by":"publisher","first-page":"2641","DOI":"10.1007\/s00180-013-0422-9","volume":"28","author":"Y Gu\u00e9don","year":"2013","unstructured":"Gu\u00e9don, Y.: Exploring the latent segmentation space for the assessment of multiple change-point models. Comput. Stat. 28(6), 2641\u20132678 (2013)","journal-title":"Comput. Stat."},{"issue":"1","key":"9966_CR16","doi-asserted-by":"publisher","first-page":"134","DOI":"10.1080\/10618600.2015.1116445","volume":"26","author":"K Haynes","year":"2017","unstructured":"Haynes, K., Eckley, I., Fearnhead, P.: Computationally efficient changepoint detection for a range of penalties. J. Comput. Graph. Stat. 26(1), 134\u2013143 (2017)","journal-title":"J. Comput. Graph. Stat."},{"key":"9966_CR17","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/s11749-014-0368-4","volume":"23","author":"L Horv\u00e1th","year":"2014","unstructured":"Horv\u00e1th, L., Rice, G.: Extensions of some classical methods in change point analysis. Test 23, 219\u2013255 (2014)","journal-title":"Test"},{"key":"9966_CR18","unstructured":"James, B., James, K.L., Siegmund, D.: Tests for a change-point. Technical Report No. 35, The Office for Naval Research, pp. 1\u201330 (1985)"},{"issue":"2","key":"9966_CR19","doi-asserted-by":"publisher","first-page":"637","DOI":"10.1214\/08-AOAS232","volume":"3","author":"C L\u00e9vy-Leduc","year":"2009","unstructured":"L\u00e9vy-Leduc, C., Roueff, F.: Detection and localization of change-points in high-dimensional network traffic data. Ann. Appl. Stat. 3(2), 637\u2013662 (2009)","journal-title":"Ann. Appl. Stat."},{"key":"9966_CR20","doi-asserted-by":"publisher","first-page":"918","DOI":"10.1214\/16-EJS1131","volume":"10","author":"H Li","year":"2016","unstructured":"Li, H., Munk, A.: FDR-control in multiscale change-point segmentation. Electron. J. Stat. 10, 918\u2013959 (2016)","journal-title":"Electron. J. Stat."},{"issue":"6","key":"9966_CR21","doi-asserted-by":"publisher","first-page":"1201","DOI":"10.1007\/s11222-017-9788-9","volume":"28","author":"M Ludkin","year":"2018","unstructured":"Ludkin, M., Eckley, I., Neal, P.: Dynamic stochastic block models: parameter estimation and detection of changes in community structure. Stat. Comput. 28(6), 1201\u20131213 (2018)","journal-title":"Stat. Comput."},{"issue":"2","key":"9966_CR22","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1007\/s11222-011-9240-5","volume":"22","author":"A Lung-Yut-Fong","year":"2012","unstructured":"Lung-Yut-Fong, A., L\u00e9vy-Leduc, C., Capp\u00e9, O.: Distributed detection\/localization of change-points in high-dimensional network traffic data. Stat. Comput. 22(2), 485\u2013496 (2012)","journal-title":"Stat. Comput."},{"issue":"2","key":"9966_CR23","doi-asserted-by":"publisher","first-page":"519","DOI":"10.1007\/s11222-016-9636-3","volume":"27","author":"R Maidstone","year":"2017","unstructured":"Maidstone, R., Hocking, T., Rigaill, G., Fearnhead, P.: On optimal multiple changepoint algorithms for large data. Stat. Comput. 27(2), 519\u2013533 (2017)","journal-title":"Stat. Comput."},{"issue":"505","key":"9966_CR24","doi-asserted-by":"publisher","first-page":"334","DOI":"10.1080\/01621459.2013.849605","volume":"109","author":"D Matteson","year":"2012","unstructured":"Matteson, D., James, N.: A nonparametric approach for multiple change point analysis of multivariate data. J. Am. Stat. Assoc. 109(505), 334\u2013345 (2012)","journal-title":"J. Am. Stat. Assoc."},{"issue":"2","key":"9966_CR25","doi-asserted-by":"publisher","first-page":"194","DOI":"10.1080\/00401706.2014.902776","volume":"57","author":"C Nam","year":"2015","unstructured":"Nam, C., Aston, J., Eckley, I., Killick, R.: The uncertainty of storm season changes: quantifying the uncertainty of autocovariance changepoints. Technometrics 57(2), 194\u2013206 (2015)","journal-title":"Technometrics"},{"issue":"1\/2","key":"9966_CR26","doi-asserted-by":"publisher","first-page":"110","DOI":"10.2307\/2333009","volume":"41","author":"E Page","year":"1954","unstructured":"Page, E.: Continuous inspection scheme. Biometrika 41(1\/2), 110\u2013115 (1954)","journal-title":"Biometrika"},{"issue":"510","key":"9966_CR27","doi-asserted-by":"publisher","first-page":"654","DOI":"10.1080\/01621459.2014.920613","volume":"110","author":"P Preu\u00df","year":"2015","unstructured":"Preu\u00df, P., Puchstein, R., Dette, H.: Detection of multiple structural breaks in multivariate time series. J. Am. Stat. Assoc. 110(510), 654\u2013668 (2015)","journal-title":"J. Am. Stat. Assoc."},{"key":"9966_CR28","unstructured":"Rosenberg, A., Hirschberg, J.: V-measure: a conditional entropy-based external cluster evaluation measure. In: Proceedings of the 2007 Joint Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Learning, pp. 410\u2013420 (2007)"},{"issue":"424","key":"9966_CR29","doi-asserted-by":"publisher","first-page":"1273","DOI":"10.1080\/01621459.1993.10476408","volume":"88","author":"P Rousseeuw","year":"1993","unstructured":"Rousseeuw, P., Croux, C.: Alternatives to the median absolute deviation. J. Am. Stat. Assoc. 88(424), 1273\u20131283 (1993)","journal-title":"J. Am. Stat. Assoc."},{"issue":"1","key":"9966_CR30","doi-asserted-by":"publisher","first-page":"40","DOI":"10.3150\/08-BEJ141","volume":"15","author":"K Rufibach","year":"2009","unstructured":"Rufibach, K., D\u00fcmbgen, L.: Maximum likelihood estimation of a log-concave density and its distribution function: basic properties and uniform consistency. Bernoulli 15(1), 40\u201368 (2009)","journal-title":"Bernoulli"},{"key":"9966_CR31","unstructured":"Rufibach, K., D\u00fcmbgen, L.: logcondens: Estimate a log-concave probability density from IID observations. R Package Version 2.1.5. https:\/\/cran.r-project.org\/package=logcondens (2016)"},{"issue":"2A","key":"9966_CR32","doi-asserted-by":"publisher","first-page":"645","DOI":"10.1214\/10-AOAS400","volume":"5","author":"D Siegmund","year":"2011","unstructured":"Siegmund, D., Yakir, B., Zhang, N.: Detecting simultaneous variant intervals in aligned sequences. Ann. Appl. Stat. 5(2A), 645\u2013668 (2011)","journal-title":"Ann. Appl. Stat."},{"issue":"393","key":"9966_CR33","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1080\/01621459.1986.10478260","volume":"81","author":"M Srivastava","year":"1986","unstructured":"Srivastava, M., Worsley, K.: Likelihood ratio tests for a change in the multivariate normal mean. J. Am. Stat. Assoc. 81(393), 199\u2013204 (1986)","journal-title":"J. Am. Stat. Assoc."},{"key":"9966_CR34","unstructured":"Truong, C., Oudre, L., Vayatis, N.: Selective review of offline change point detection methods. arXiv:1801.00718, pp 1\u201346 (2018)"},{"key":"9966_CR35","doi-asserted-by":"crossref","unstructured":"Wang, T., Samworth, R.: InspectChangepoint: high-dimensional change point estimation via sparse projection. R Package Version 1.0.1. https:\/\/cran.r-project.org\/package=InspectChangepoint (2016)","DOI":"10.1111\/rssb.12243"},{"issue":"1","key":"9966_CR36","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1111\/rssb.12243","volume":"80","author":"T Wang","year":"2017","unstructured":"Wang, T., Samworth, R.: High dimensional change point estimation via sparse projection. J. R. Stat. Soc. B Stat. Methodol. 80(1), 57\u201383 (2017)","journal-title":"J. R. Stat. Soc. B Stat. Methodol."},{"key":"9966_CR37","unstructured":"Yu, M., Chen, X.: Finite sample change point inference and identification for high-dimensional mean vectors. arXiv:1711.08747, pp. 1\u201371 (2020)"},{"issue":"3","key":"9966_CR38","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1093\/biomet\/asq025","volume":"97","author":"N Zhang","year":"2010","unstructured":"Zhang, N., Siegmund, D., Ji, H., Li, J.: Detecting simultaneous changepoints in multiple sequences. Biometrika 97(3), 631\u2013645 (2010)","journal-title":"Biometrika"}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-020-09966-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11222-020-09966-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-020-09966-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,11]],"date-time":"2024-08-11T05:29:19Z","timestamp":1723354159000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11222-020-09966-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,1]]},"references-count":38,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2020,11]]}},"alternative-id":["9966"],"URL":"https:\/\/doi.org\/10.1007\/s11222-020-09966-2","relation":{},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"value":"0960-3174","type":"print"},{"value":"1573-1375","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,8,1]]},"assertion":[{"value":"16 July 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 July 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 August 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}