PAC-Bayesian Bounds for Randomized Empirical Risk Minimizers

Pierre Alquier (1, 2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 CREST - Centre de Recherche en Économie et Statistique

The aim of this paper is to generalize the PAC-Bayesian theorems proved by Catoni in the classification setting to more general problems of statistical inference. We show how to control the deviations of the risk of randomized estimators. A particular attention is paid to randomized estimators drawn in a small neighborhood of classical estimators, whose study leads to control the risk of the latter. These results allow to bound the risk of very general estimation procedures, as well as to perform model selection.

Mots clés: Regression estimation; classification; adaptative inference; statistical learning; randomized estimator; empirical risk minimization; empirical bound

Domaines: Machine Learning [stat.ML]; Statistiques [math.ST]

Pierre Alquier. PAC-Bayesian Bounds for Randomized Empirical Risk Minimizers. 2007. ⟨hal-00195698v1⟩