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Machine Learning
book

Machine Learning

by Sergios Theodoridis
April 2015
Intermediate to advanced content levelIntermediate to advanced
1062 pages
40h 35m
English
Academic Press
Content preview from Machine Learning

11.9 Kernel Ridge Regression Revisited

The kernel ridge regression was introduced in Section 11.7. Here, it will be restated via its dual representation form. The ridge regression in its primal representation can be cast as

minimize with respect toθ,ξJ(θ,ξ)=n=1Nξn2+Cθ2,subject toynθTxn=ξn,n=1,2,,N,

si176_e  (11.51)

which leads to the following Lagrangian:

L(θ,ξ,λ)=n=1Nξn2+Cθ2+n=1Nλn(ynθTxnξn),n=1,2,,N.

si177_e  (11.52)

Differentiating with respect to θ and ξn, n = 1,2,…,N, and equating to zero, we obtain

θ=12Cn=1Nλnxn

  (11.53)

and

ξn

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Publisher Resources

ISBN: 9780128015223