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024 7 $a10.1007/978-3-642-22147-7
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100   $a20110727d2011      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aOracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems$b[electronic resource] $eÉcole d?Été de Probabilités de Saint-Flour XXXVIII-2008 /$fby Vladimir Koltchinskii
205   $a1st ed. 2011.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2011.
215   $a1 online resource (IX, 254 p.) 
225 1 $aÉcole d'Été de Probabilités de Saint-Flour,$x0721-5363 ;$v2033
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-642-22146-7 
320   $aIncludes bibliographical references and index.
330   $aThe purpose of these lecture notes is to provide an introduction to the general theory of empirical risk minimization with an emphasis on excess risk bounds and oracle inequalities in penalized problems. In recent years, there have been new developments in this area motivated by the study of new classes of methods in machine learning such as large margin classification methods (boosting, kernel machines). The main probabilistic tools involved in the analysis of these problems are concentration and deviation inequalities by Talagrand along with other methods of empirical processes theory (symmetrization inequalities, contraction inequality for Rademacher sums, entropy and generic chaining bounds). Sparse recovery based on l_1-type penalization and low rank matrix recovery based on the nuclear norm penalization are other active areas of research, where the main problems can be stated in the framework of penalized empirical risk minimization, and concentration inequalities and empirical processes tools have proved to be very useful.
410  0$aÉcole d'Été de Probabilités de Saint-Flour,$x0721-5363 ;$v2033
606   $aProbabilities
606   $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004
615  0$aProbabilities.
615 14$aProbability Theory and Stochastic Processes.
676   $a519.5/36
700   $aKoltchinskii$b Vladimir$4aut$4http://id.loc.gov/vocabulary/relators/aut$0478961
712 12$aEcole d'e?te? de probabilite?s de Saint-Flour$d(38th :$f2008)
906   $aBOOK
912   $a996466620403316
996   $aOracle inequalities in empirical risk minimization and sparse recovery problems$9261795
997   $aUNISA