{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T16:17:02Z","timestamp":1768407422434,"version":"3.49.0"},"reference-count":12,"publisher":"MIT Press - Journals","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2000,6,1]]},"abstract":"<jats:p> The mixtures-of-experts (ME) methodology provides a tool of classification when experts of logistic regression models or Bernoulli models are mixed according to a set of local weights. We show that the Vapnik-Chervonenkis dimension of the ME architecture is bounded below by the number of experts m and above by O (m<jats:sup>4<\/jats:sup>s<jats:sup>2<\/jats:sup>), where s is the dimension of the input. For mixtures of Bernoulli experts with a scalar input, we show that the lower bound m is attained, in which case we obtain the exact result that the VC dimension is equal to the number of experts. <\/jats:p>","DOI":"10.1162\/089976600300015367","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T11:57:56Z","timestamp":1027771076000},"page":"1293-1301","source":"Crossref","is-referenced-by-count":7,"title":["The VC Dimension for Mixtures of Binary Classifiers"],"prefix":"10.1162","volume":"12","author":[{"given":"Wenxin","family":"Jiang","sequence":"first","affiliation":[{"name":"Department of Statistics, Northwestern University, Evanston, IL 60208, U.S.A."}]}],"member":"281","reference":[{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1989.1.1.151"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176995384"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1016\/0890-5401(92)90010-D"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1996.8.6.1277"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1991.3.1.79"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1162\/089976699300016403"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1994.6.2.181"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.1997.1477"},{"key":"p_15","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.1997.1479"},{"key":"p_17","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.45.6056"},{"key":"p_18","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(98)00019-5"},{"key":"p_21","doi-asserted-by":"publisher","DOI":"10.1145\/1968.1972"}],"container-title":["Neural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mitpressjournals.org\/doi\/pdf\/10.1162\/089976600300015367","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,12]],"date-time":"2021-03-12T21:48:01Z","timestamp":1615585681000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/neco\/article\/12\/6\/1293-1301\/6383"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,6,1]]},"references-count":12,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2000,6,1]]}},"alternative-id":["10.1162\/089976600300015367"],"URL":"https:\/\/doi.org\/10.1162\/089976600300015367","relation":{},"ISSN":["0899-7667","1530-888X"],"issn-type":[{"value":"0899-7667","type":"print"},{"value":"1530-888X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,6,1]]}}}