04335nam 22008535 450 991014461790332120230810202148.03-540-44507-210.1007/b99352(CKB)1000000000231434(SSID)ssj0000326895(PQKBManifestationID)11258164(PQKBTitleCode)TC0000326895(PQKBWorkID)10298187(PQKB)11487771(DE-He213)978-3-540-44507-4(MiAaPQ)EBC6302410(MiAaPQ)EBC5591844(Au-PeEL)EBL5591844(OCoLC)1066195452(PPN)155176072(EXLCZ)99100000000023143420121227d2004 u| 0engurnn|008mamaatxtccrStatistical Learning Theory and Stochastic Optimization Ecole d'Eté de Probabilités de Saint-Flour XXXI - 2001 /by Olivier Catoni ; edited by Jean Picard1st ed. 2004.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2004.1 online resource (VIII, 284 p.) École d'Été de Probabilités de Saint-Flour ;1851Bibliographic Level Mode of Issuance: Monograph3-540-22572-2 Includes bibliographical references and index.Universal Lossless Data Compression -- Links Between Data Compression and Statistical Estimation -- Non Cumulated Mean Risk -- Gibbs Estimators -- Randomized Estimators and Empirical Complexity -- Deviation Inequalities -- Markov Chains with Exponential Transitions -- References -- Index.Statistical learning theory is aimed at analyzing complex data with necessarily approximate models. This book is intended for an audience with a graduate background in probability theory and statistics. It will be useful to any reader wondering why it may be a good idea, to use as is often done in practice a notoriously "wrong'' (i.e. over-simplified) model to predict, estimate or classify. This point of view takes its roots in three fields: information theory, statistical mechanics, and PAC-Bayesian theorems. Results on the large deviations of trajectories of Markov chains with rare transitions are also included. They are meant to provide a better understanding of stochastic optimization algorithms of common use in computing estimators. The author focuses on non-asymptotic bounds of the statistical risk, allowing one to choose adaptively between rich and structured families of models and corresponding estimators. Two mathematical objects pervade the book: entropy and Gibbs measures. The goal is to show how to turn them into versatile and efficient technical tools, that will stimulate further studies and results.École d'Été de Probabilités de Saint-Flour ;1851ProbabilitiesStatisticsMathematical optimizationArtificial intelligenceComputer scienceMathematicsNumerical analysisProbability TheoryStatistical Theory and MethodsOptimizationArtificial IntelligenceMathematical Applications in Computer ScienceNumerical AnalysisProbabilities.Statistics.Mathematical optimization.Artificial intelligence.Computer scienceMathematics.Numerical analysis.Probability Theory.Statistical Theory and Methods.Optimization.Artificial Intelligence.Mathematical Applications in Computer Science.Numerical Analysis.519.5Catoni Olivierauthttp://id.loc.gov/vocabulary/relators/aut478894Picard Jeanedthttp://id.loc.gov/vocabulary/relators/edtEcole d'été de probabilités de Saint-Flour(31st :2001)MiAaPQMiAaPQMiAaPQBOOK9910144617903321Statistical learning theory and stochastic optimization262229UNINA