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Possible error in pb11 exam2018

Here is the formula of the kernelized ridge regression, shouldn't there be the lambda term acting as penalizer?

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I think that the formula is correct. If you expand the left term you find 1/2 lambda a.T @ a which is the regularization term

I am sorry I didn't understand your answer, is there another explanation because I checked and the formula always mentions an extra lambda.

The regularization term \( \lambda \Vert \alpha\Vert^2\) is hidden in (and is exactly) the term \(\alpha^\top \lambda I_N \alpha\). However the matrix \(X\) needs to be full rank for this problem to be equivalent to ridge regression.

Could I ask how to get this formula? I am sorry that I cannot deduce this.

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