基于函数型数据的系数正则化回归的收敛速度-论文.pdf

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1、数学杂志Vo1．35(2015)J．ofMath．(PRC)NO．20NTHEC0NVERGENCERATEoFC0EFFICIENT．BASEDREGULARIZEDREGRESSIoNFoRFUNCTIoNALDATATAOYan-fang．TANGYi。(。D印t．ofBasis，Chan~iangProfessionalCollege，Wuhan430074，Chin。)(2．sc。。：D，M。t．。ndc。mputersc．，n。n(，htersityofNati。礼托tes，乱mi礼g650031，Chi钆a)Abstract：Thispaperinvestigates

2、thegeneralizationperformanceofleastsquareregressionwithfunctionaldataandgl-regularizer．TheestimateoflearningrateisestablishedbyRademacheralveragetechnique．Thetheoreticalresultisanaturalextensionforcoeficientbasedregularizedregressionwheninputspaceisasubsetofinfinite—dimensionalEuclideanspace．K

3、eywords：regression；functionaldata；l—regularizer；Rademacheraverage2010MRSubjectClassification：62J02Documentcode：AArticleID：0255—7797(2O15)02—0281—061IntroductionLet(，d)beametricspaceandYC【一M，M]forsomeM>0．TherelationbetweentheinputX∈andtheoutputY∈isdescribedbyafixed(butunknown)distributionponz：=

4、×．Basedonasetofsamplesz：={Z]m1={(，))1∈z，thegoalofleastsquareregressionistopickaflmctionf：suchthattheexpectedrisk)=()assmallaspossible．ThefunctionthatminimizestheriskiscalledtheregressionfunctionItisgivenby)：(xEX,wherep(．I)istheconditionalprobabilitymeasureatinducedbyP·Inthispaperweconsiderkern

5、el—basedleastsquareregressionwith1一regularizer-RecallthatK：×．一千isaMercerkernelifitisacontinuous，symmetric，andpositivesemi_deftnite．ThecandidatereproducingkernelHilbertspace(RKHS)7-／KassociatedwithaReceiveddate：2012—10—13Accepteddate：2014—01·21Foundationitem：SupportedpartiallybyNationalNaturalS

6、cienceFoundationofChina(61105051)．Biography：TaoYanfang(1981一)，femalebornatWuhan，Hubei，lecturer)majorinstatisticallearningtheory．E-mail：tyf3122@126．com．282JournalofMathematicsV01．35MercerkernelKisdefinedastheclosureofthelinearspanofthesetoffunctions{：：(，‘)：∈)，equippedwiththeinnerproduct(·，·)Kde

7、finedby(Kx，Kv)K=g(x，Y)(see[1】)．Thereproducingpropertyisgivenby(，f)K：f(x)forall∈andf∈7-／K．Thedatadependenthypothesisspace(relatedwithKandz)isdefinedby=(∑：∈=1，⋯，m)Theregressionalgorithmwith1一regularizerisgivenas，z=arg(1．1)倒min{gz(f)+Aa(，)