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nnXi=1(Mi mimiXj=1vij)(1)wheretheerrorboundisde...
AaronDefazioAmbiataAustralianNationalUniversit...
JuSunComputerScience&EngineeringUniversityofMinnes...
w1w218w1w2X1nXi3wiXi19w2w1w218w1w2X2nXi3wiXi192120...
x1 NNXi=1xi;(1)2samp x2 x2:(2)Wealsodenoteexactav...
nnXi=1V(f(xi);yi)+kfk2H;(1)where0isaregulariza...
TondthemeanofS2,webeginwiththeidentitynXi=1(Xi)...
case:E[s2]=E[1 NNXi=1(xi x)2]=1 x+NXi=1 x2]Weknow...
y�b1 x(Note: y=1 nPni=1yiand x=1 nPni=1xi.)Proo...
AaronDefazioAmbiataAustralianNationalUniversit...
nnXi=1Xi;Fn;i(Xi);F(1)n;h1;i(Xi);...
NNXi=1f(Ui)(1)convergestoE(f(U))almostsurelywhenNt...
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