PAC-Bayesian bounds for randomized empirical risk minimizers

The aim of this paper is to generalize the PAC-Bayesian theorems proved by Catoni [6, 8] 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 estimator...

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Bibliographic Details
Published in:Mathematical methods of statistics 2008-12, Vol.17 (4), p.279-304
Main Author: Alquier, P.
Format: Article
Language:English
Subjects:
Econometrics
Machine Learning
Mathematics
Mathematics and Statistics
Statistical Theory and Methods
Statistics
Statistics Theory
Studies
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Summary:The aim of this paper is to generalize the PAC-Bayesian theorems proved by Catoni [6, 8] 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 of the risk of the latter. These results allow us to bound the risk of very general estimation procedures, as well as to perform model selection.
ISSN:1066-5307
1934-8045
DOI:10.3103/S1066530708040017