Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Optimal Aggregation of Classifiers in Statistical Learning


Code(s) de Classification MSC:

Résumé: The problem of statistical learning can be considered as a problem of nonparametric estimation of sets, where the risk is defined by means of a specific distance function between sets associated to the misclassification error. The rates of convergence of classifiers depend on two parameters: the complexity of the class of candidate sets and the "margin" parameter. The dependence is explicitly given, in particular the optimal rates up to $O(n^{-1})$ can be attained, where $n$ is the sample size, and the proposed classifiers have the property of robustness to the margin. The main result of the paper concerns optimal aggregation of classifiers: we suggest a classifier that automatically adapts both to the complexity and to the margin, and attains the optimal fast rates, up to a logarithmic factor.

Mots Clés: Statistical learning ; aggregation of classifiers ; optimal rates ; empirical processes ; margin ; complexity of classes of sets

Date: 2001-09-06

Prépublication numéro: PMA-682

Postscript file : PMA-692.ps