Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems: École d’Été de Probabilités de Saint-Flour XXXVIII-2008: 2033 (Lecture Notes in Mathematics, 2033) - Softcover

Koltchinskii, Vladimir

 
9783642221460: Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems: École d’Été de Probabilités de Saint-Flour XXXVIII-2008: 2033 (Lecture Notes in Mathematics, 2033)
Softcover
ISBN 10: 3642221467 ISBN 13: 9783642221460
Publisher: Springer, 2011

Synopsis

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 (symmetrization inequalities, contraction inequality for Rademacher sums, entropy and generic chaining bounds). Sparse recovery based on l_1-type penalization and low rank matrix recovery based on the nuclear norm penalization are other active areas of research, where the main problems can be stated in the framework of penalized empirical risk minimization, and concentration inequalities and empirical processes tools have proved to be very useful.

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From the Back Cover

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 (symmetrization inequalities, contraction inequality for Rademacher sums, entropy and generic chaining bounds). Sparse recovery based on l_1-type penalization and low rank matrix recovery based on the nuclear norm penalization are other active areas of research, where the main problems can be stated in the framework of penalized empirical risk minimization, and concentration inequalities and empirical processes tools have proved to be very useful.

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Publisher
Springer
Publication date
2011
Language
English
ISBN 10 
3642221467
ISBN 13 
9783642221460
Binding
Paperback
Number of pages
263

Other Popular Editions of the Same Title

9783642221484: Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems: École d'Été de Probabilités de Saint-Flour XXXVIII-2008

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ISBN 10:  3642221483 ISBN 13:  9783642221484
Publisher: Springer, 2011
Softcover