{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,11]],"date-time":"2026-07-11T08:03:41Z","timestamp":1783757021729,"version":"3.55.0"},"reference-count":65,"publisher":"MIT Press","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2013,10]]},"abstract":"<jats:p>We address the problem of estimating the difference between two probability densities. A naive approach is a two-step procedure of first estimating two densities separately and then computing their difference. However, this procedure does not necessarily work well because the first step is performed without regard to the second step, and thus a small estimation error incurred in the first stage can cause a big error in the second stage. In this letter, we propose a single-shot procedure for directly estimating the density difference without separately estimating two densities. We derive a nonparametric finite-sample error bound for the proposed single-shot density-difference estimator and show that it achieves the optimal convergence rate. We then show how the proposed density-difference estimator can be used in L<jats:sup>2<\/jats:sup>-distance approximation. Finally, we experimentally demonstrate the usefulness of the proposed method in robust distribution comparison such as class-prior estimation and change-point detection.<\/jats:p>","DOI":"10.1162\/neco_a_00492","type":"journal-article","created":{"date-parts":[[2013,6,18]],"date-time":"2013-06-18T17:20:49Z","timestamp":1371576049000},"page":"2734-2775","source":"Crossref","is-referenced-by-count":52,"title":["Density-Difference Estimation"],"prefix":"10.1162","volume":"25","author":[{"given":"Masashi","family":"Sugiyama","sequence":"first","affiliation":[{"name":"Tokyo Institute of Technology, Tokyo 152-8552, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Takafumi","family":"Kanamori","sequence":"additional","affiliation":[{"name":"Nagoya University, Nagoya 464-8601, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Taiji","family":"Suzuki","sequence":"additional","affiliation":[{"name":"University of Tokyo, Tokyo 152-8552, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marthinus Christoffel du","family":"Plessis","sequence":"additional","affiliation":[{"name":"Tokyo Institute of Technology, Tokyo 152-8555, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Song","family":"Liu","sequence":"additional","affiliation":[{"name":"Tokyo Institute of Technology, Tokyo 152-8555, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ichiro","family":"Takeuchi","sequence":"additional","affiliation":[{"name":"Nagoya Institute of Technology, Nagoya 464-8552, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"281","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1006\/jmva.1994.1033"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1950-0051437-7"},{"key":"B5","volume-title":"Multiple regression and estimation of the mean of a multivariate normal distribution","author":"Baranchik A. J.","year":"1964"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/85.3.549"},{"key":"B7","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-9473(02)00251-7"},{"key":"B8","doi-asserted-by":"publisher","DOI":"10.1145\/1273496.1273507"},{"key":"B9","doi-asserted-by":"publisher","DOI":"10.1145\/130385.130401"},{"key":"B10","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/9780262033589.001.0001"},{"key":"B11","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1970.1054406"},{"key":"B12","first-page":"442","volume-title":"Advances in neural information processing systems, 23","author":"Cortes C.","year":"2010"},{"key":"B13","doi-asserted-by":"publisher","DOI":"10.1007\/BF00994018"},{"key":"B14","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2005.851098"},{"key":"B16","first-page":"823","volume-title":"Proceedings of 29th International Conference on Machine Learning","author":"du Plessis M. C.","year":"2012"},{"key":"B17","volume-title":"Pattern classification","author":"Duda R. O.","year":"2001","edition":"2"},{"key":"B18","doi-asserted-by":"publisher","DOI":"10.1002\/bimj.200800201"},{"key":"B19","first-page":"1539","volume-title":"Advances in neural information processing systems, 24","author":"Eberts M.","year":"2011"},{"key":"B20","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-4541-9"},{"key":"B21","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177692711"},{"key":"B22","first-page":"76960D","volume-title":"Proceedings of SPIE","author":"Gray D. M.","year":"2010"},{"key":"B23","first-page":"131","volume-title":"Dataset shift in machine learning","author":"Gretton A.","year":"2009"},{"key":"B24","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/75.3.541"},{"key":"B25","first-page":"609","volume-title":"Advances in neural information processing systems, 21","author":"Harchaoui Z.","year":"2009"},{"key":"B26","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-17146-8"},{"key":"B27","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-21606-5"},{"key":"B28","doi-asserted-by":"publisher","DOI":"10.4135\/9781412986113"},{"key":"B29","doi-asserted-by":"crossref","first-page":"601","DOI":"10.7551\/mitpress\/7503.003.0080","volume-title":"Advances in neural information processing systems, 19","author":"Huang J.","year":"2007"},{"key":"B30","first-page":"1391","volume":"10","author":"Kanamori T.","year":"2009","journal-title":"Journal of Machine Learning Research"},{"key":"B31","doi-asserted-by":"publisher","DOI":"10.1007\/s10994-011-5266-3"},{"key":"B32","doi-asserted-by":"publisher","DOI":"10.1002\/sam.10124"},{"key":"B33","doi-asserted-by":"publisher","DOI":"10.1109\/ICDM.2007.78"},{"key":"B34","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177729694"},{"key":"B35","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2010.01.002"},{"key":"B36","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2013.01.012"},{"key":"B37","doi-asserted-by":"publisher","DOI":"10.1081\/SAC-120017494"},{"key":"B38","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2010.2068870"},{"key":"B39","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177704472"},{"key":"B40","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2008.4595271"},{"key":"B41","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/85.3.619"},{"key":"B42","volume-title":"Linear statistical inference and its applications","author":"Rao C. R.","year":"1965"},{"key":"B43","first-page":"131","volume-title":"Advances in learning theory: Methods, models and applications","author":"Rifkin R.","year":"2003"},{"key":"B44","doi-asserted-by":"publisher","DOI":"10.1515\/9781400873173"},{"key":"B45","doi-asserted-by":"publisher","DOI":"10.1162\/089976602753284446"},{"key":"B46","doi-asserted-by":"publisher","DOI":"10.1198\/004017001316975880"},{"key":"B47","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2010.04.011"},{"key":"B48","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-3324-9"},{"key":"B49","volume-title":"Support vector machines","author":"Steinwart I.","year":"2008"},{"key":"B50","doi-asserted-by":"publisher","DOI":"10.1214\/009053606000001226"},{"key":"B51","doi-asserted-by":"publisher","DOI":"10.1587\/transinf.E93.D.2690"},{"key":"B52","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/9780262017091.001.0001"},{"key":"B53","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2009.07.007"},{"key":"B54","first-page":"985","volume":"8","author":"Sugiyama M.","year":"2007","journal-title":"Journal of Machine Learning Research"},{"key":"B55","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139035613"},{"key":"B56","doi-asserted-by":"publisher","DOI":"10.1007\/s10463-011-0343-8"},{"key":"B57","volume-title":"Advances in neural information processing systems","volume":"25","author":"Sugiyama M.","year":"2012"},{"key":"B58","doi-asserted-by":"publisher","DOI":"10.1007\/s10463-008-0197-x"},{"key":"B59","doi-asserted-by":"publisher","DOI":"10.1587\/transinf.E93.D.583"},{"key":"B60","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2010.10.005"},{"key":"B61","doi-asserted-by":"publisher","DOI":"10.1162\/NECO_a_00407"},{"key":"B62","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2006.1599387"},{"key":"B63","doi-asserted-by":"publisher","DOI":"10.1162\/153244303322753742"},{"key":"B64","volume-title":"Statistical learning theory","author":"Vapnik V. N.","year":"1998"},{"key":"B65","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.103.214101"},{"key":"B66","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2005.853314"},{"key":"B67","first-page":"549","volume-title":"Proceedings of the Twenty-Fifth AAAI Conference on Artificial Intelligence","author":"Yamada M.","year":"2011"},{"key":"B68","doi-asserted-by":"publisher","DOI":"10.1162\/NECO_a_00442"}],"container-title":["Neural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mitpressjournals.org\/doi\/pdf\/10.1162\/NECO_a_00492","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,2]],"date-time":"2023-07-02T12:41:15Z","timestamp":1688301675000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/neco\/article\/25\/10\/2734-2775\/7921"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,10]]},"references-count":65,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2013,10]]}},"alternative-id":["10.1162\/NECO_a_00492"],"URL":"https:\/\/doi.org\/10.1162\/neco_a_00492","relation":{},"ISSN":["0899-7667","1530-888X"],"issn-type":[{"value":"0899-7667","type":"print"},{"value":"1530-888X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,10]]}}}