High-Dimensional Statistics A Non-Asymptotic Viewpoint ( 2019, Cambridge University Press).pdf

High-Dimensional Statistics A Non-Asymptotic Viewpoint ( 2019, Cambridge University Press).pdf

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“Non-asymptotic,high-dimensionaltheoryiscriticalformodernstatisticsandmachinelearning.Thisbookisuniqueinprovidingacrystalclear,complete,andunifiedtreatmentofthearea.Withtopicsrangingfromconcentrationofmeasuretographicalmodels,theauthorweavestogetherprobabilitytheoryanditsapplicationstostatistics.Idealforgraduatestudentsandresearchers.Thiswillsurelybethestandardreferenceonthetopicformanyyears.”LarryWasserman,CarnegieMellonUniversity“MartinWainwrightbringshislargeboxofanalyticalpowertoolstobearontheproblemsofthedaytheanalysisofmodelsforwidedata.Abroadknowledgeofthisnewareacombineswithhispowerfulanalyticalskillstodeliverthisimpressiveandintimidatingworkboundtobeanessentialreferenceforallthebravesoulsthattrytheirhand.”TrevorHastie,StanfordUniversity“Thisbookprovidesanexcellenttreatmentofperhapsthefastestgrowingareawithinhigh-dimensionaltheoreticalstatisticsnon-asymptotictheorythatseekstoprovideprobabilisticboundsonestimatorsasafunctionofsamplesizeanddimension.Itoffersthemostthorough,clear,andengagingcoverageofthisareatodate,andisthuspoisedtobecomethedefinitivereferenceandtextbookonthistopic.”GeneveraAllen,RiceUniversity“Statisticaltheoryandpracticehaveundergonearenaissanceinthepasttwodecades,withintensivestudyofhigh-dimensionaldataanalysis.Noresearcherhasdeepenedourunderstandingofhigh-dimensionalstatisticsmorethanMartinWainwright.Thisbookbringsthesignatureclarityandincisivenessofhispublishedresearchintobookform.Itwillbeafantasticresourceforbothbeginningstudentsandseasonedresearchers,asthefieldcontinuestomakeexcitingbreakthroughs.”JohnLafferty,YaleUniversity“Thisisanoutstandingbookonhigh-dimensionalstatistics,writtenbyacreativeandcelebratedresearcherinthefield.Itgivescomprehensivetreatmentsofmanyimportanttopicsinstatisticalmachinelearningand,furthermore,isself-contained,fromintroductorymaterialtothemostup-to-dateresultsonvariousresearchfrontiers.Thisbookisamust-readforthosewhowishtolearnandtodevelopmodernstatisticalmachinetheory,methodsandalgorithms.”JianqingFan,PrincetonUniversity“Thisbookprovidesanin-depthmathematicaltreatmentandmethodologicalintuitionforhigh-dimensionalstatistics.Themaintechnicaltoolsfromprobabilitytheoryarecarefullydevelopedandtheconstructionandanalysisofstatisticalmethodsandalgorithmsforhigh-dimensionalproblemsarepresentedinanoutstandinglyclearway.MartinWainwrighthaswrittenatrulyexceptional,inspiring,andbeautifulmasterpiece!

”PeterBuhlmann,ETHZurich“ThisnewbookbyMartinWainwrightcoversmoderntopicsinhigh-dimensionalstatisticalinference,andfocusesprimarilyonexplicitnon-asymptoticresultsrelatedtosparsityandnon-parametricestimation.Thisisamust-readforallgraduatestudentsinmathematicalstatisticsandtheoreticalmachinelearning,bothforthebreadthofrecentadvancesitcoversandthedepthofresultswhicharepresented.Theexpositionisoutstandinglyclear,startingfromthefirstintroductorychaptersonthenecessaryprobabilistictools.Then,thebookcoversstate-of-the-artadvancesinhigh-dimensionalstatistics,withalwaysacleverchoiceofresultswhichhavetheperfectmixofsignificanceandmathematicaldepth.”FrancisBach,INRIAParis“Wainwrightsbookonthosepartsofprobabilitytheoryandmathematicalstatisticscriticaltounderstandingofthenewphenomenaencounteredinhighdimensionsismarkedbytheclarityofitspresentationandthedepthtowhichittravels.Ineverychapterhestartswithintuitiveexamplesandsimulationswhicharesystematicallydevelopedeitherintopowerfulmathematicaltoolsorcompleteanswerstofundamentalquestionsofinference.Itisnoteasy,butelegantandrewardingwhetherreadsystematicallyordippedintoasareference.”PeterBickel,UCBerkeleyHigh-DimensionalStatisticsRecentyearshavewitnessedanexplosioninthevolumeandvarietyofdatacollectedinallscientificdisciplinesandindustrialsettings.Suchmassivedatasetspresentanumberofchallengestoresearchersinstatisticsandmachinelearning.Thisbookprovidesaself-containedintroductiontotheareaofhigh-dimensionalstatistics,aimedatthefirst-yeargraduatelevel.Itincludeschaptersthatarefocusedoncoremethodologyandtheoryincludingtailbounds,concentrationinequalities,uniformlawsandempiricalprocess,andrandommatricesaswellaschaptersdevotedtoin-depthexplorationofparticularmodelclassesincludingsparselinearmodels,matrixmodelswithrankconstraints,graphicalmodels,andvarioustypesofnon-parametricmodels.Withhundredsofworkedexamplesandexercises,thistextisintendedbothforcoursesandforself-studybygraduatestudentsandresearchersinstatistics,machinelearning,andrelatedfieldswhomustunderstand,apply,andadaptmodernstatisticalmethodssuitedtolarge-scaledata.MARTINJ.WAINWRIGHTisaChancellorsProfessorattheUniversityofCalifornia,Berkeley,withajointappointmentbetweentheDepartmentofStatisticsandtheDepartmentofElectricalEngineeringandComputerSciences.Hisresearchliesatthenexusofstatistics,machinelearning,optimization,andinformationtheory,andhehaspublishedwidelyinallofthesedisciplines.Hehaswrittentwootherbooks,oneongraphicalmodelstogetherwithMichaelI.Jordan,andoneonsparselearningtogetherwithTrevorHastieandRobertTibshirani.Amongotherawards,hehasreceivedtheCOPSSPresidentsAward,hasbeenaMedallionLecturerandBlackwellLecturerfortheInstituteofMathematicalStatistics,andhasreceivedBestPaperAwardsfromtheNIPS,ICML,andUAIconferences,aswellasfromtheIEEEInformationTheorySociety.CAMBRIDGESERIESINSTATISTICALANDPROBABILISTICMATHEMATICSEditorialBoardZ.Ghahramani（DepartmentofEngineering,UniversityofCambridge）R.Gill（MathematicalInstitute,LeidenUniversity）F.P.Kelly（DepartmentofPureMathematicsandMathematicalStatistics,UniversityofCambridge）B.D.Ripley（DepartmentofStatistics,UniversityofOxford）S.Ross（DepartmentofIndustrialandSystemsEngineering,UniversityofSouthernCalifornia）M.Stein（DepartmentofStatistics,UniversityofChicago）Thisseriesofhigh-qualityupper-divisiontextbooksandexpositorymonographscoversallaspectsofstochasticapplicablemathematics.Thetopicsrangefrompureandappliedstatisticstoprobabilitytheory,operationsresearch,optimization,andmathematicalprogramming.Thebookscontainclearpresentationsofnewdevelopmentsinthefieldandalsoofthestateoftheartinclassicalmethods.Whileemphasizingrigoroustreatmentoftheoreticalmethods,thebooksalsocontainapplicationsanddiscussionsofnewtechniquesmadepossiblebyadvancesincomputationalpractice.Acompletelistofbooksintheseriescanbefoundatwww.cambridge.org/statistics.Recenttitlesincludethefollowing:

23.AppliedAsymptotics,byA.R.Brazzale,A.C.DavisonandN.Reid24.RandomNetworksforCommunication,byMassimoFranceschettiandRonaldMeester25.DesignofComparativeExperiments,byR.A.Bailey26.SymmetryStudies,byMarlosA.G.Viana27.ModelSelectionandModelAveraging,byGerdaClaeskensandNilsLidHjort28.BayesianNonparametrics,editedbyNilsLidHjortetal.29.FromFiniteSampletoAsymptoticMethodsinStatistics,byPranabK.Sen,JulioM.SingerandAntonioC.PedrosadeLima30.BrownianMotion,byPeterMortersandYuvalPeres31.Probability:

TheoryandExamples（FourthEdition）,byRickDurrett33.StochasticProcesses,byRichardF.Bass34.RegressionforCategoricalData,byGerhardTutz35.ExercisesinProbability（SecondEdition）,byLocChaumontandMarcYor36.StatisticalPrinciplesfortheDesignofExperiments,byR.Mead,S.G.GilmourandA.Mead37.QuantumStochastics,byMou-HsiungChang38.NonparametricEstimationunderShapeConstraints,byPietGroeneboomandGeurtJongbloed39.LargeSampleCovarianceMatricesandHigh-DimensionalDataAnalysis,byJianfengYao,ShurongZhengandZhidongBai40.MathematicalFoundationsofInfinite-DimensionalStatisticalModels,byEvaristGineandRichardNickl41.Confidence,Likelihood,Probability,byToreSchwederandNilsLidHjort42.ProbabilityonTreesandNetworks,byRussellLyonsandYuvalPeres43.RandomGraphsandComplexNetworks（Volume1）,byRemcovanderHofstad44.FundamentalsofNonparametricBayesianInference,bySubhashisGhosalandAadvanderVaart45.Long-RangeDependenceandSelf-Similarity,byVladasPipirasandMuradS.Taqqu46.PredictiveStatistics,byBertrandS.ClarkeandJenniferL.Clarke47.High-DimensionalProbability,byRomanVershynin48.High-DimensionalStatistics,byMartinJ.Wainwright49.Probability:

TheoryandExamples（FifthEdition）,byRickDurrettHigh-DimensionalStatisticsANon-AsymptoticViewpointMartinJ.WainwrightUniversityofCalifornia,BerkeleyUniversityPrintingHouse,CambridgeCB28BS,UnitedKingdomOneLibertyPlaza,20thFloor,NewYork,NY10006,USA477WilliamstownRoad,PortMelbourne,VIC3207,Australia314321,3rdFloor,Plot3,SplendorForum,JasolaDistrictCentre,NewDelhi110025,India79AnsonRoad,#0604/06,Singapore079906CambridgeUniversityPressispartoftheUniversityofCambridge.ItfurtherstheUniversitysmissionbydisseminatingknowledgeinthepursuitofeducation,learning,andresearchatthehighestinternationallevelsofexcellence.www.cambridge.orgInformationonthistitle:

www.cambridge.org/9781108498029DOI:

10.1017/9781108627771MartinJ.Wainwright2019Thispublicationisincopyright.Subjecttostatutoryexceptionandtotheprovisionsofrelevantcollectivelicensingagreements,noreproductionofanypartmaytakeplacewithoutthewrittenpermissionofCambridgeUniversityPress.Firstpublished2019PrintedintheUnitedKingdombyTJInternationalLtd.PadstowCornwallAcataloguerecordforthispublica