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:**

- 62G05 Estimation
- 62G20 Asymptotic properties

**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