11.8 Optimal kernel matrix. Suppose in addition to optimizing the dual variables 2 Rm, as in (11.16), we also wish to optimize over the entries of the PDS kernel matrix K 2 Rmm.

min K0 max

????> ???? >K + 2>y ; s:t: kKk2  1

(a) What is the closed-form solution for the optimal K for the joint optimization?

(b) Optimizing over the choice of kernel matrix will provide a better value of the objective function. Explain, however, why the resulting kernel matrix is not useful in practice.