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Originally Posted by tsweetser
Is it also possible to use the regularized normal equation? I'm looking at Lecture 12, Slide 11.

Yes, you can use any result given in the lectures.
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It seems funny to me to choose the parameters to minimize one error measure (mean square), yet evaluate {E_in} and {E_out} using another (binary classification).

Ideally, we would work exclusively with binary classification error in this case, but because of the intractability of optimization of that error, the meansquared error is used for the optimization part.