{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T23:59:08Z","timestamp":1772150348312,"version":"3.50.1"},"reference-count":9,"publisher":"MIT Press - Journals","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2004,5,1]]},"abstract":"<jats:p> In this letter, we investigate the impact of choosing different loss functions from the viewpoint of statistical learning theory. We introduce a convexity assumption, which is met by all loss functions commonly used in the literature, and study how the bound on the estimation error changes with the loss. We also derive a general result on the minimizer of the expected risk for a convex loss function in the case of classification. The main outcome of our analysis is that for classification, the hinge loss appears to be the loss of choice. Other things being equal, the hinge loss leads to a convergence rate practically indistinguishable from the logistic loss rate and much better than the square loss rate. Furthermore, if the hypothesis space is sufficiently rich, the bounds obtained for the hinge loss are not loosened by the thresholding stage. <\/jats:p>","DOI":"10.1162\/089976604773135104","type":"journal-article","created":{"date-parts":[[2004,4,7]],"date-time":"2004-04-07T23:15:12Z","timestamp":1081379712000},"page":"1063-1076","source":"Crossref","is-referenced-by-count":342,"title":["Are Loss Functions All the Same?"],"prefix":"10.1162","volume":"16","author":[{"given":"Lorenzo","family":"Rosasco","sequence":"first","affiliation":[{"name":"INFM\u2014DISI, Universit\u00e1 di Genova, 16146 Genova, Italy,"}]},{"given":"Ernesto De","family":"Vito","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e1 di Modena, 41100 Modena, Italy, and INFN, Sezione di Genova, 16146 Genova, Italy,"}]},{"given":"Andrea","family":"Caponnetto","sequence":"additional","affiliation":[{"name":"DISI, Universit\u00e1 di Genova, 16146 Genova, Italy,"}]},{"given":"Michele","family":"Piana","sequence":"additional","affiliation":[{"name":"INFM\u2014DIMA, Universit\u00e1 di Genova, 16146 Genova, Italy,"}]},{"given":"Alessandro","family":"Verri","sequence":"additional","affiliation":[{"name":"INFM\u2014DISI, Universit\u00e1 di Genova, 16146 Genova, Italy,"}]}],"member":"281","reference":[{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.2307\/1990404"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1007\/s102080010030"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-01-00923-5"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1023\/A:1018946025316"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1995.7.2.219"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1023\/A:1013951620650"},{"key":"p_10","author":"Lugosi G.","journal-title":"Annals of Statistics."},{"key":"p_17","author":"Zhang T.","journal-title":"Annals of Statistics."},{"key":"p_18","doi-asserted-by":"publisher","DOI":"10.1006\/jcom.2002.0635"}],"container-title":["Neural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mitpressjournals.org\/doi\/pdf\/10.1162\/089976604773135104","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,12]],"date-time":"2021-03-12T21:51:06Z","timestamp":1615585866000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/neco\/article\/16\/5\/1063-1076\/6828"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,5,1]]},"references-count":9,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2004,5,1]]}},"alternative-id":["10.1162\/089976604773135104"],"URL":"https:\/\/doi.org\/10.1162\/089976604773135104","relation":{},"ISSN":["0899-7667","1530-888X"],"issn-type":[{"value":"0899-7667","type":"print"},{"value":"1530-888X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,5,1]]}}}