Bounds on the Risk for M-SVMs
Identifieur interne : 003992 ( Crin/Corpus ); précédent : 003991; suivant : 003993Bounds on the Risk for M-SVMs
Auteurs : Yann Guermeur ; André Elisseeff ; Dominique ZelusSource :
- Applied Stochastic Models in Business and Industry ; 2003.
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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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