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April 2008 Statistical performance of support vector machines
Gilles Blanchard, Olivier Bousquet, Pascal Massart
Ann. Statist. 36(2): 489-531 (April 2008). DOI: 10.1214/009053607000000839

Abstract

The support vector machine (SVM) algorithm is well known to the computer learning community for its very good practical results. The goal of the present paper is to study this algorithm from a statistical perspective, using tools of concentration theory and empirical processes.

Our main result builds on the observation made by other authors that the SVM can be viewed as a statistical regularization procedure. From this point of view, it can also be interpreted as a model selection principle using a penalized criterion. It is then possible to adapt general methods related to model selection in this framework to study two important points: (1) what is the minimum penalty and how does it compare to the penalty actually used in the SVM algorithm; (2) is it possible to obtain “oracle inequalities” in that setting, for the specific loss function used in the SVM algorithm? We show that the answer to the latter question is positive and provides relevant insight to the former. Our result shows that it is possible to obtain fast rates of convergence for SVMs.

Citation

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Gilles Blanchard. Olivier Bousquet. Pascal Massart. "Statistical performance of support vector machines." Ann. Statist. 36 (2) 489 - 531, April 2008. https://doi.org/10.1214/009053607000000839

Information

Published: April 2008
First available in Project Euclid: 13 March 2008

zbMATH: 1133.62044
MathSciNet: MR2396805
Digital Object Identifier: 10.1214/009053607000000839

Subjects:
Primary: 62G05 , 62G20

Keywords: ‎classification‎ , Model selection , Oracle inequality , Support Vector Machine

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 2 • April 2008
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