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时间:2019-06-25
《n维单形上带有多项式核最小二乘正则化算法的逼近阶》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、Chap1IntroductionLet(x,d)beacoInPactmetricSPace趴dlety=R.Letpbeaprobabm哆dist曲u一哟n0nZ:=X×y.仉1eastsquare册r(orgen池tione玎0r)(【1儿2】)foraf吼dion,:X_yisdef№daS£(,)=/(,(z)一可)2却(1.1)JZ’mfuI曲onmatmi衄niZesmee啪riscaⅡedme嵫懈s加卢佗c肋咒.ItisgivenbyJcD(z)=/可和(可愀z∈x,(1.2).,ywherep(·Iz)iSthecond
2、itio枷Probabili锣measureatzinducedbyJD.ThetargetoftheregressionProblemist0leammeregressionfunc缸on0rtofhldgood印Proxna矗ons舶mrandomsa】mpleS.Theleast-s(Ⅳareregmarizedalgori№fortheIegressionProblemisadbcreteleast-squareproblemaSsodatedwimaMercerkemel(【3】).I就K:X×X—ybecont.muous,s
3、舯etric,andposi的eSerni-def黼te,i.e.forany觚teset0f拙thlctpoin协{zl⋯.,幻)cx,龇mt呶(K(毛,巧))易;1iSposi曲e双!Im.defirlite.S沁chafunctionijscaUeda^也∞℃盯妇r,zPf.。It伦j呻rod“cf’曙施m讲HfI抛附S妒∞(列}①S)冗KaSS0datedwim日1ek∈ImelK(【3】)isde触dtObe岫clos眦of龀hnearSPanof龀setoffundions.[恐:=K(z,·):z∈x)wimmeimerPr
4、oduct<·,·>HK=<·,·>Ksatis咖g<虬,%>K=K(z,秒).’rhatis,<∑t%恐;,邑岛‰>K=∑晒铫岛K(茁i,协).The婶rodudngpr0Pe啊takes龀fo眦<%,,>K=,(z),比∈x,,∈咒K.DenoteC(X)弱廿1espace0fcontirmousfunc石onsonXwim日1enorm”‰.L.etK=su如∈x、/K(z,z).1henmeabover印roduc咄Prope啊tensllsmatIl,Jl∞≤KJ
5、.厂IIK,W∈咒耳.(1.3)Theleast-squarer
6、e刚aIiZedalg嘶mmformeregressionpr6blemassodatedwim妇1eMercerkEI玎商Kisdef№dt0bememiniInizerof妇舱foUowingkast.square叩小miZa60nproblemmolvmgasetofr姐doms锄叩lesz:={磊)罂1={(戤,挑))銎1∈zmind叩endentlyclrawnaccordingtop:jcE=厶:=耵g舰<去∑(mi)-玑)2酬I州女>.(1.4)】-HereA≥0iSaconstantcaUedthe嘲w砌砌砌栉册朋优舀盯.
7、USuaJlyitischosentod叩endonm:A=A(m),andlimm.∞A(m)=o.ConVergencerates0fre91llarizaHonalgorithl3nsfortheregressionforclassifica血minleamir喀the0巧havebeenstIldiedrecenⅡybymanyInanleIna矗dan.(【1】【2】【4】【5】)Throu曲out眦sp叩eLweaSSumematfors0IneM≥0,p(·lz)isahnosteve哆wheresuPported0n[一M
8、,M,matis,M≤Mahnostsm.ely(wim抡specttop).Itf0Ⅱowsf而m龀definition(1.2)of厶matl厶(z)I≤M.1hee佑den叮0f龀algorimm(1.4)ismeas哦dby岫础erencebe饥een丘and也eregression^mcHon厶.Beca啦旧ofme1eaSt—squarer愠t11re,themeaSl_珊ementistheweighted妒metricin珞de缸edas⋯p=⋯L;x=(厶№)12玩)1/2,where触is廿伧marginaldis劬u
9、矗on0fJD0nX.wecansee【1】mat五一厶ll羔k2占(五)一£(厶).(1.5)Notice她tmeb蛐叫alfom山a舛eldsmeMercerkemelproP嘶:喜眯k矧
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