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

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

Square root penalty: adaptation to the margin in classification and in edge estimation

Auteur(s):

Code(s) de Classification MSC:

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