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

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

Classification under polynomial entropy and margin assumptions and randomized estimators


Code(s) de Classification MSC:

Résumé: The aim of this paper is two-fold. First we want to develop the PAC-Bayesian point of view \cite{McA99,Cat02,Cat03b,Aud03b} and show how the efficiency of a Gibbs estimator relies on the weights given by the prior distribution to the balls centered at the best function in the model and associated with the pseudo-distance $(f_1,f_2) \mapsto \dsP[f_1(X) \neq f_2(X)]$. Secondly, we show how to recover and improve results under empirical and non empirical polynomial entropy assumptions and Tsybakov's margin assumption. We also study the links between empirical and non empirical nets and give an observable version of the integral entropy [6, 9, 14].

Mots Clés: Gibbs classifiers ; entropy assumptions ; margin assumptions ; PAC-Bayesian bounds ; chaining ; oracle inequalities ; VC theory

Date: 2004-04-29

Prépublication numéro: PMA-908