Kernel ridge regression in closed form

ProofIntermediate⏱ 30 minClassical MLkernel ridgeclosed formrepresenter

Theory: Kernels, RKHS and the Representer Theorem →

Problem

Derive $\alpha = (\mathbf K+n\lambda I)^{-1}y$ for kernel ridge regression from the representer theorem, and show the resulting predictor is $\hat f(x) = k(x)^\top(\mathbf K+n\lambda I)^{-1}y$ with $k(x)_i = K(x_i,x)$ .

Write a complete argument. Every inequality you use should be one you could state precisely.

Solution

Opening this before you have a real attempt on paper is the fastest way to feel like you understand something you cannot reproduce.

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