{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T12:51:26Z","timestamp":1776689486026,"version":"3.51.2"},"reference-count":18,"publisher":"MIT Press - Journals","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2015,4]]},"abstract":"<jats:p> In this letter, we explore the idea of modeling slack variables in support vector machine (SVM) approaches. The study is motivated by SVM+, which models the slacks through a smooth correcting function that is determined by additional (privileged) information about the training examples not available in the test phase. We take a closer look at the meaning and consequences of smooth modeling of slacks, as opposed to determining them in an unconstrained manner through the SVM optimization program. To better understand this difference we only allow the determination and modeling of slack values on the same information\u2014that is, using the same training input in the original input space. We also explore whether it is possible to improve classification performance by combining (in a convex combination) the original SVM slacks with the modeled ones. We show experimentally that this approach not only leads to improved generalization performance but also yields more compact, lower-complexity models. Finally, we extend this idea to the context of ordinal regression, where a natural order among the classes exists. The experimental results confirm principal findings from the binary case. <\/jats:p>","DOI":"10.1162\/neco_a_00714","type":"journal-article","created":{"date-parts":[[2015,3,3]],"date-time":"2015-03-03T18:02:03Z","timestamp":1425405723000},"page":"954-981","source":"Crossref","is-referenced-by-count":8,"title":["The Benefits of Modeling Slack Variables in SVMs"],"prefix":"10.1162","volume":"27","author":[{"given":"Fengzhen","family":"Tang","sequence":"first","affiliation":[{"name":"School of Computer Science, The University of Birmingham, Edgbaston, Birmingham B15 2TT, U.K."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter","family":"Ti\u0148o","sequence":"additional","affiliation":[{"name":"School of Computer Science, The University of Birmingham, Edgbaston, Birmingham B15 2TT, U.K."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pedro Antonio","family":"Guti\u00e9rrez","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Numerical Analysis, University of C\u00f3rdoba, C\u00f3rdoba 14071, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huanhuan","family":"Chen","sequence":"additional","affiliation":[{"name":"UBRI, School of Computer Science and Technology, University of Science and Technology of China, Hefei, 230027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"281","reference":[{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804441"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1023\/A:1009715923555"},{"key":"B4","first-page":"1393","volume":"8","author":"Cardoso J. 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