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:**

- 62H30 Classification and discrimination; cluster analysis [See also 68T10]
- 68Q32 Computational learning theory [See also 68T05]

**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*