Bounding the Capacity Measure of Multi-Class Discriminant Models

Yann Guermeur (1) , André Elisseeff , Dominique Zelus

1 MODBIO - Computational models in molecular biology

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). Multi-class discriminant analysis has only been studied independently in recent years. 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 discriminant models. This technical report deals with the computation of the capacity measures involved in these bounds on the expected risk. It considers more specifically the case of multi-class SVMs.

Mots clés: complexité en échantillon; sample complexity; multi-class discriminant analysis; discrimination multi-classe; fat-shattering dimension

Domaines: Autre [cs.OH]

Yann Guermeur, André Elisseeff, Dominique Zelus. Bounding the Capacity Measure of Multi-Class Discriminant Models. [Intern report] A02-R-028 || guermeur02b, 2002, 20 p. ⟨inria-00100733⟩