Inria / Raweb 2004
Project-Team: MODBIO

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Project-Team : modbio

Section: New Results

Keywords: Statistical learning theory, support vector machine, model selection.

Structural risk minimization inductive principle for multi-class discriminant analysis

Participants: Yannick Darcy, Yann Guermeur, Frédéric Sur.

We have continued our study of the generalization error of large margin multi-class discriminant models. Two types of contributions have been made, for the general case, and the specific case of M-SVMs. The general case has been tackled through the pathway initially proposed by Vapnik: first connect the capacity measure appearing in the confidence interval of the guaranteed risk to a generalized Vapnik-Chervonenkis (VC) dimension, then bound this VC dimension. This is the subject of [21], where we have extended our previous works on scale-sensitive $ \Psi$-dimensions. These extensions mainly deal with generalized Sauer's lemmas and the computation of bounds on the margin Natarajan dimension. Two independent studies are currently underway to characterize the generalization performance of M-SVMs. The aim of the first one is to extend to the multi-class case the estimates based on the leave-one-out procedure. Those estimates were initially derived by Chapelle and Vapnik. In the second one, we make use of theorems relating covering problems and the degree of compactness of operators. This work can be seen as a continuation of [8]. First results can be found in [25].