Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems (eBook, PDF)

Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems (eBook, PDF)

École d'Été de Probabilités de Saint-Flour XXXVIII-2008

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The purpose of these lecture notes is to provide an introduction to the general theory of empirical risk minimization with an emphasis on excess risk bounds and oracle inequalities in penalized problems. In recent years, there have been new developments in this area motivated by the study of new classes of methods in machine learning such as large margin classification methods (boosting, kernel machines). The main probabilistic tools involved in the analysis of these problems are concentration and deviation inequalities by Talagrand along with other methods of empirical processes theory (symme...

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