question stats/machine learning

Locally weighted linear regression and bias-variance tradeoff. (25 points) Consider a dataset with n data points (xi, yi), xi E RP, following the following linear model yi = B*T "Nitti, i = 1, ...,n, where ci ~ N(0, o? ) are independent (but not identically distributed) Gaussian noise with zero mean and variance o?. (a) (5 points) Show that the ridge regression which introduces a squared 62 norm penalty on the parameter in the maximum likelihood estimate of S can be written as follows B(A) = arg min {(XB - y)"W(XB - y) + >/18113} B for property defined diagonal matrix W, matrix X and vector y