Paper Info
Title
On the Representer Theorem and Equivalent Degrees of Freedom of SVR
Abstract
Support Vector Regression (SVR) for discrete data is considered. An alternative formulation of the representer theorem is derived. This result is based on the newly introduced notion of pseudoresidual and the use of subdifferential calculus. The representer theorem is exploited to analyze the sensitivity properties of ε-insensitive SVR and introduce the notion of approximate degrees of freedom. The degrees of freedom are shown to play a key role in the evaluation of the optimism, that is the difference between the expected in-sample error and the expected empirical risk. In this way, it is possible to define a Cp-like statistic that can be used for tuning the parameters of SVR. The proposed tuning procedure is tested on a simulated benchmark problem and on a real world problem (Boston Housing data set).
Year
DOI
Venue
2007
10.5555/1314498.1314578
Journal of Machine Learning Research
Keywords
Field
DocType
expected in-sample error,cp-like statistic,proposed tuning procedure,insensitive svr,regularization theory,representer theorem,boston housing data,rep- resenter theorem,support vector machines,reproducing kernel hilbert spaces,equivalent degrees,discrete data,real world problem,expected empirical risk,statistical learning,simulated benchmark problem,reproducing kernel hilbert space,support vector machine,regularization,degree of freedom,support vector regression,sampling error
Statistic,Support vector machine,Subderivative,Representer theorem,Artificial intelligence,Mathematics,Machine learning
Journal
Volume
ISSN
Citations 
8,
1532-4435
11
PageRank 
References 
Authors
0.58
16
6
Name
Order
Citations
PageRank
Francesco Dinuzzo126116.03
Marta Neve2121.28
Giuseppe De Nicolao373876.26
Ugo Pietro Gianazza4110.58
NicolaoGiuseppe De5110.58
GianazzaUgo Pietro6110.58