In this problem, we generalize the Ridge Regression to incorporate the importance of individual training samples. Specifically, besides training set S = {(x1, y1),(x2, y2),...,(xn, yn)} where xi 2 Rd and yi 2 R, we are also given positive weights a1, a2,...,an where ai is the importance (weight) of ith training data. Show that the solution to the weighted least squares problem with `2 regularization w = arg min w2Rd 1 2 Xn i=1 ai w>xi yi 2 2 kwk2 is given by the formula w = X>AX I 1 X>Ay where X 2 Rnd is the data matrix (defined in class), y 2 Rn is the labels vector, I is d d identity matrix, and A 2 Rnn is a diagonal matrix where Aii = ai, i.e