2007/12/31 by Pierre Alquier · 1 citation
Computer Science · Mathematics · #Applied mathematics #Artificial intelligence #Bayesian Methods and Mixture Models #Bayesian inference #Bayesian probability #Computer science #Econometrics #Estimator #Inference #Machine Learning and Algorithms #Mathematics #Model selection #Selection (genetic algorithm) #Statistical Methods and Inference #Statistical inference #Statistics #math.ST #stat.ML #stat.TH
paper · pdf · doi:10.3103/s1066530708040017
published as Mathematical Methods of Statistics 17, 4 (2008) 279-304
openalex publication_date 2008/12/01 · arxiv created 2009/01/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.