LEADER 02986nam 2200589 a 450 001 9910483134303321 005 20200520144314.0 010 $a9783642221477 010 $a3642221475 024 7 $a10.1007/978-3-642-22147-7 035 $a(CKB)2670000000100004 035 $a(SSID)ssj0000506049 035 $a(PQKBManifestationID)11324558 035 $a(PQKBTitleCode)TC0000506049 035 $a(PQKBWorkID)10513728 035 $a(PQKB)11243775 035 $a(DE-He213)978-3-642-22147-7 035 $a(MiAaPQ)EBC3067041 035 $z(PPN)258846763 035 $a(PPN)156309912 035 $a(EXLCZ)992670000000100004 100 $a20110714d2011 uy 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 $eEcole d'Ete de Probabilites de Saint-Flour XXXVIII-2008 /$fVladimir Koltchinskii 205 $a1st ed. 2011. 210 $aBerlin $cSpringer$d2011 215 $a1 online resource (IX, 254 p.) 225 1 $aLecture notes in mathematics,$x0075-8434 ;$v2033 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a9783642221460 311 08$a3642221467 320 $aIncludes bibliographical references and index. 330 $aThe purpose of these lecture notes is to provide an introduction to the general theory of empirical risk minimization with an emphasis on excess risk bounds and oracle inequalities in penalized problems. In recent years, there have been new developments in this area motivated by the study of new classes of methods in machine learning such as large margin classification methods (boosting, kernel machines). The main probabilistic tools involved in the analysis of these problems are concentration and deviation inequalities by Talagrand along with other methods of empirical processes theory (symmetrization inequalities, contraction inequality for Rademacher sums, entropy and generic chaining bounds). Sparse recovery based on l_1-type penalization and low rank matrix recovery based on the nuclear norm penalization are other active areas of research, where the main problems can be stated in the framework of penalized empirical risk minimization, and concentration inequalities and empirical processes tools have proved to be very useful. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v2033. 606 $aMachine learning$vCongresses 606 $aRisk management$vCongresses 615 0$aMachine learning 615 0$aRisk management 676 $a519.5/36 700 $aKoltchinskii$b Vladimir$0478961 712 12$aEcole d'ete de probabilites de Saint-Flour$d(38th :$f2008) 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483134303321 996 $aOracle inequalities in empirical risk minimization and sparse recovery problems$9261795 997 $aUNINA