Classification under polynomial entropy and margin assump-tions and randomized estimators
The aim of this paper is two-fold. First we want to develop the PAC-Bayesian point of view [13, 3, 4, 1] 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 pseudodistance (f1, f2) 7→ [f1(X) 6= f2(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].