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Suppose we observe a training set {Dox-(1,ail,rar . . , rip)) for i-l, m ,n subjects. We want to fit a linear regression model /(x) otXI ,, to the training data to minimize the residual sum ofsquares RSS(β) Σǐ 1 (Vi r β)2 where β = (A 屆,-. W pm (a)(10%) Please derive the solution ßt. arg ming RSS(β) in terms of Y-|h li) Ar (b)(10%) in ridge regression, we find ßridge rgminß RSS(β) subject to Σ./ Please write out the equivalent Lagrangian form of the optimization problem. st. (c) (10%) Please derive the form of ßridge in terms of Y # (yī and the Lagrange multiplier λ YnF, X x(zh t


ANSWER

d RSS() and so

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