{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,20]],"date-time":"2026-07-20T09:52:27Z","timestamp":1784541147928,"version":"3.55.0"},"reference-count":17,"publisher":"MIT Press","issue":"7","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2001,7,1]]},"abstract":"<jats:p> Suppose you are given some data set drawn from an underlying probability distribution P and you want to estimate a \u201csimple\u201d subset S of input space such that the probability that a test point drawn from P lies outside of S equals some a priori specified value between 0 and 1. <\/jats:p><jats:p> We propose a method to approach this problem by trying to estimate a function f that is positive on S and negative on the complement. The functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data; it is regularized by controlling the length of the weight vector in an associated feature space. The expansion coefficients are found by solving a quadratic programming problem, which we do by carrying out sequential optimization over pairs of input patterns. We also provide a theoretical analysis of the statistical performance of our algorithm. <\/jats:p><jats:p> The algorithm is a natural extension of the support vector algorithm to the case of unlabeled data. <\/jats:p>","DOI":"10.1162\/089976601750264965","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T11:55:01Z","timestamp":1027770901000},"page":"1443-1471","source":"Crossref","is-referenced-by-count":4523,"title":["Estimating the Support of a High-Dimensional Distribution"],"prefix":"10.1162","volume":"13","author":[{"given":"Bernhard","family":"Sch\u00f6lkopf","sequence":"first","affiliation":[{"name":"Microsoft Research Ltd, Cambridge CB2 3NH, U.K."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"John C.","family":"Platt","sequence":"additional","affiliation":[{"name":"Microsoft Research, Redmond, WA 98052, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"John","family":"Shawe-Taylor","sequence":"additional","affiliation":[{"name":"Royal Holloway, University of London, Egham, Surrey TW20 OEX, U.K."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alex J.","family":"Smola","sequence":"additional","affiliation":[{"name":"Department of Engineering, Australian National University, Canberra 0200, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robert C.","family":"Williamson","sequence":"additional","affiliation":[{"name":"Department of Engineering, Australian National University, Canberra 0200, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"281","reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.1997.1507"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1030741073"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1137\/0138038"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176348670"},{"issue":"1","key":"p_9","first-page":"26","volume":"6","author":"Gayraud G.","year":"1997","journal-title":"Mathematical Methods of Statistics"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1162\/089976698300017269"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.2307\/2289162"},{"key":"p_18","doi-asserted-by":"publisher","DOI":"10.1016\/0047-259X(91)90106-C"},{"key":"p_21","doi-asserted-by":"publisher","DOI":"10.1006\/jmva.1995.1067"},{"key":"p_22","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176324626"},{"key":"p_24","doi-asserted-by":"publisher","DOI":"10.2307\/2286331"},{"key":"p_30","doi-asserted-by":"publisher","DOI":"10.1162\/089976600300015565"},{"key":"p_33","author":"Shawe-Taylor J.","year":"2000","journal-title":"IEEE Transactions on Information Theory. 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