PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Statistical Performance of Support Vector Machines
Gilles Blanchard, Olivier Bousquet and Pascal Massart
Annals of Statistics Volume 36, Number 2, pp. 489-531, 2008. ISSN 00905364

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 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.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:2533
Deposited By:Gilles Blanchard
Deposited On:22 November 2006