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

Koltchinskii, Vladimir

 
9783642221460: Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems: École d’Été de Probabilités de Saint-Flour XXXVIII-2008
Softcover
ISBN 10: 3642221467 ISBN 13: 9783642221460
Verlag: Springer, 2011

Inhaltsangabe

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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Von der hinteren Coverseite

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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Verlag
Springer
Erscheinungsdatum
2011
Sprache
Englisch
ISBN 10 
3642221467
ISBN 13 
9783642221460
Einband
Taschenbuch
Anzahl der Seiten
268
Kontakt zum Hersteller
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ProductSafety@springernature.com

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Darmstadt
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Deutschland

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Vorgestellte Ausgabe

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