Bounds on the Risk for M-SVMs

Yann Guermeur 1 André Elisseeff 2 Dominique Zelus
1 MODBIO - Computational models in molecular biology
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : Vapnik's statistical learning theory has mainly been developed for two types of problems: pattern recognition (computation of dichotomies) and regression (estimation of real-valued functions). Only in recent years has multi-class discriminant analysis been studied independently. Extending several standard results, among which a famous theorem by Bartlett, we have derived distribution-free uniform strong laws of large numbers devoted to multi-class large margin discriminant models. The capacity measure appearing in the confidence interval, a covering number, has been bounded from above in terms of a new generalized VC dimension. In this paper, the aforementioned theorems are applied to the architecture shared by all the multi-class SVMs proposed so far, which provides us with a simple theoretical framework to study them, compare their performance and design new machines.
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Article dans une revue
Applied Stochastic Models in Business and Industry, Wiley, 2003
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Soumis le : mardi 26 septembre 2006 - 09:39:00
Dernière modification le : jeudi 11 janvier 2018 - 06:19:51

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  • HAL Id : inria-00099587, version 1

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Yann Guermeur, André Elisseeff, Dominique Zelus. Bounds on the Risk for M-SVMs. Applied Stochastic Models in Business and Industry, Wiley, 2003. 〈inria-00099587〉

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