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1、StatisticalLearningTheoryMachineLearningSummerSchool,Kyoto,JapanAlexander(Sasha)RakhlinUniversityofPennsylvania,TheWhartonSchoolPennResearchinMachineLearning(PRiML)August27-28,20121/130ReferencesPartsoftheselecturesarebasedonLO.Bousquet,S.Boucheron,G.Lugosi:Introd
2、uctiontoStatisticalLearningTheory",2004.LMLSSnotesbyO.BousquetLS.Mendelson:AFewNotesonStatisticalLearningTheory"LLecturenotesbyS.Shalev-ShwartzLLecturenotes(S.R.andK.Sridharan)http://stat.wharton.upenn.edu/~rakhlin/courses/stat928/stat928_notes.pdfPrerequisites:ab
3、asicfamiliaritywithProbabilityisassumed.2/130OutlineIntroductionStatisticalLearningTheoryTheSettingofSLTConsistency,NoFreeLunchTheorems,Bias-VarianceTradeo ToolsfromProbability,EmpiricalProcessesFromFinitetoIn niteClassesUniformConvergence,Symmetrization,andRademac
4、herComplexityLargeMarginTheoryforClassi cationPropertiesofRademacherComplexityCoveringNumbersandScale-SensitiveDimensionsFasterRatesModelSelectionSequentialPrediction/OnlineLearningMotivationSupervisedLearningOnlineConvexandLinearOptimizationOnline-to-BatchConversi
5、on,SVMoptimization3/130Example#1:HandwrittenDigitRecognitionImagineyouareaskedtowriteacomputerprogramthatrecognizespostalcodesonenvelopes.Youobservethehugeamountofvariationandambiguityinthedata:Onecantrytohard-codeallthepossibilities,butlikelytofail.Itwouldbeniceif
6、aprogramlookedatalargecorpusofdataandlearnedthedistinctions!ThispictureofMNISTdatasetwasyankedfromhttp://www.heikoho mann.de/htmlthesis/node144.html4/130Example#1:HandwrittenDigitRecognitionNeedtorepresentdatainthecomputer.Pixelintensitiesisonepossibility,butnotnec
7、essarilythebestone.Featurerepresentation:1.15.36.22.92.3..featuremap.Wealsoneedtospecifythelabel"ofthisexample:3".Thelabeledexampleisthen1.15.3(6.22.92.3..(.,3Afterlookingatmanyoftheseexamples,wewanttheprogramtopredictthelabelofthenexthand-writtendigit.5/130Examp
8、le#2:PredictTopicofaNewsArticleYouwouldliketoautomaticallycollectnewsstoriesfromthewebanddisplaythemtothereaderinthebestpossibleway.Youwouldliket
