Stat841f09 - Wiki Course Notes

# Thus we can obtain the further simplification that

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Unformatted text preview: t the least squared solution of , where .Then we have . Based on the Radial Basis Function Network, by ,where is the hat matrix for this model. depends on the input vector but not on By taking the derivative of with respect to Now, substituing this into . , we can easily obtain: ,we get wikicour senote.com/w/index.php?title= Stat841&pr intable= yes 55/74 10/09/2013 Stat841 - Wiki Cour se Notes Here, we can tell that , the sum of the diagonal elements of . Thus, we can obtain the further simplification that , where a basis set spanned by is the dimension of . Since , the number of basis functions. If considering intercept, then Then, is a projection of input matrix onto . . SURE Algorithm We use this method to find the optimum number of basis function by choosing the model with smallest MSE over the set of models considered. Given a set of models indexed by the number of basis functions, . Then, where is the number of training samples and the noise,σ2, can be estimated from the training data as . By applying SURE algorithm to SPECT Heart data, we get the optimal number of basis functions is . Pls take a look at figure 27.1 on the right, which shows that is smallest when Figure 27.1 . Calculating the SURE value is easy if you have access to . sr_r =err-nmdt_on *sga. 2+2*sga.2*(u_ai_ucin +1; ueEr ro u_aapit im ^ im ^ nmbssfntos ) If is not known, it can be estimated using the error. err=(upt-epce_upt . 2 ro otu xetdotu) ^ ; sga=(o(r,oe(,nmdt_on) /(u_aapit)/(u_aapit-1; im dter ns1 u_aapit) nmdt_on) nmdt_on ) sr_r =err-nmdt_on *sga. 2+2*sga.2*(u_ai_ucin +1; ueEr ro u_aapit im ^ im ^ nmbssfntos ) SURE for RBF network & Support Vector Machine - November 13th, 2009 SURE for RBF network M inimizing M SE By Stein's unbiased risk estimate (SURE) for Radial Basis Function (RBF) Network we get: (28.1) (mean square error)= (training error)= ( number of hidden units)= Goal: To minimize MSE 1. If is known, then it is no impact (i.e. a constant), and we can ignore it. Only need to minimize 2. In reality, we do not kno...
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## This document was uploaded on 03/07/2014.

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