dc.contributor.author Pontil, Massimiliano en_US dc.contributor.author Mukherjee, Sayan en_US dc.contributor.author Girosi, Federico en_US dc.date.accessioned 2004-10-20T21:04:28Z dc.date.available 2004-10-20T21:04:28Z dc.date.issued 1998-10-01 en_US dc.identifier.other AIM-1651 en_US dc.identifier.other CBCL-168 en_US dc.identifier.uri http://hdl.handle.net/1721.1/7259 dc.description.abstract Support Vector Machines Regression (SVMR) is a regression technique which has been recently introduced by V. Vapnik and his collaborators (Vapnik, 1995; Vapnik, Golowich and Smola, 1996). In SVMR the goodness of fit is measured not by the usual quadratic loss function (the mean square error), but by a different loss function called Vapnik"s \$epsilon\$- insensitive loss function, which is similar to the "robust" loss functions introduced by Huber (Huber, 1981). The quadratic loss function is well justified under the assumption of Gaussian additive noise. However, the noise model underlying the choice of Vapnik's loss function is less clear. In this paper the use of Vapnik's loss function is shown to be equivalent to a model of additive and Gaussian noise, where the variance and mean of the Gaussian are random variables. The probability distributions for the variance and mean will be stated explicitly. While this work is presented in the framework of SVMR, it can be extended to justify non-quadratic loss functions in any Maximum Likelihood or Maximum A Posteriori approach. It applies not only to Vapnik's loss function, but to a much broader class of loss functions. en_US dc.format.extent 2520205 bytes dc.format.extent 186978 bytes dc.format.mimetype application/postscript dc.format.mimetype application/pdf dc.language.iso en_US dc.relation.ispartofseries AIM-1651 en_US dc.relation.ispartofseries CBCL-168 en_US dc.title On the Noise Model of Support Vector Machine Regression en_US
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