Oracle inequalities in empirical risk minimization and sparse recovery problems
École d'été de probabilités de Saint-Flour XXXVIII-2008
École d'été de probabilités de Saint-Flour XXXVIII-2008
Koltchinskii, Vladimir.
creator
Ecole d'été de probabilités de Saint-Flour 2008)
text
bibliography
Electronic books.
Conference papers and proceedings.
gw
Berlin
Heidelberg
New York
Springer Verlag
2011
monographic
eng
1 online resource (ix, 254 pages)
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.
Empirical and Rademacher processes -- Bounding expected sup-norms of empirical and Rademacher processes -- Excess risk bounds -- Examples of excess risk bounds in prediction problems -- Penalized empirical risk minimization and model selection problems -- Linear programming in sparse recovery -- Convex penalization in sparse recovery -- Low rank matrix recovery : nuclear norm penalization.
Vladimir Koltchinskii.
Includes bibliographical references and index.
Regression analysis
Congresses
Estimation theory
Congresses
Nonparametric statistics
Congresses
Probabilities
Inequalities (Mathematics)
Sparse matrices
Estimation theory
Inequalities (Mathematics)
Nonparametric statistics
Probabilities
Regression analysis
Sparse matrices
QA278.2 .K65 2011eb
519.5/36
Oracle inequalities in empirical risk minimization and sparse recovery problems
Koltchinskii, Vladimir.
Berlin ; Heidelberg ; New York : Springer Verlag 2011
(DLC) 2011934366
(OCoLC)733246860
Lecture notes in mathematics (Springer-Verlag) ; 2033
9783642221477
3642221475
https://link-springer-com.libraryproxy.ist.ac.at/10.1007/978-3-642-22147-7
https://link-springer-com.libraryproxy.ist.ac.at/10.1007/978-3-642-22147-7
GW5XE
111215
20200626135416.0
ocn768427720
eng