000 02856nam a22004575i 4500
001 978-3-642-22147-7
003 DE-He213
005 20190213151639.0
007 cr nn 008mamaa
008 110727s2011 gw | s |||| 0|eng d
020 _a9783642221477
_9978-3-642-22147-7
024 7 _a10.1007/978-3-642-22147-7
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
_2bisacsh
072 7 _aPBT
_2thema
072 7 _aPBWL
_2thema
082 0 4 _a519.2
_223
100 1 _aKoltchinskii, Vladimir.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aOracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems
_h[electronic resource] :
_bÉcole d’Été de Probabilités de Saint-Flour XXXVIII-2008 /
_cby Vladimir Koltchinskii.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2011.
300 _aIX, 254 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aÉcole d'Été de Probabilités de Saint-Flour,
_x0721-5363 ;
_v2033
520 _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.
650 0 _aDistribution (Probability theory.
650 1 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642221460
776 0 8 _iPrinted edition:
_z9783642221484
830 0 _aÉcole d'Été de Probabilités de Saint-Flour,
_x0721-5363 ;
_v2033
856 4 0 _uhttps://doi.org/10.1007/978-3-642-22147-7
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c11399
_d11399