PAC-Bayesian Bounds for Randomized Empirical Risk Minimizers

Details PAC-Bayesian Bounds for Randomized Empirical Risk Minimizers PAC-Bayesian Bounds for Randomized Empirical Risk Minimizers

2007-12-11

arxiv.org/abs/0712.1698v3

Mathematical Methods of Statistics 17, 4 (2008) 279-304

Statistics

Machine Learning

Scientific paper

10.3103/S1066530708040017

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.

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