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

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 62G07 Density estimation
- 62G08 Nonparametric regression
- 62H30 Classification and discrimination; cluster analysis [See also 68T10]
- 68T10 Pattern recognition, speech recognition {For cluster analysis, see 62H30}

**Résumé:** We consider the problem of adaptation to the margin in binary classification.
We suggest a penalized empirical risk minimization classifier that adaptively attains, up to
a logarithmic factor, fast optimal
rates of convergence for the excess risk, i.e.\ rates that can be faster than $n^{-1/2}$,
where $n$ is the sample size.
%for the excess risk of classification.
We show that
our method also gives adaptive estimators for the problem of edge estimation.

**Mots Clés:** *Binary classification ; edge estimation ; adaptation ; margin ; penalized classification
rule ; square root penalty ; sparsity ; block thresholding*

**Date:** 2003-05-19

**Prépublication numéro:** *PMA-820*