| Université Paris 6 Pierre et Marie Curie | Université Paris 7 Denis Diderot | |
| CNRS U.M.R. 7599 | ||
| ``Probabilités et Modèles Aléatoires'' | ||
Auteur(s):
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