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3. In this question, we examine computing kfold cross-validation on a least squares problem \"Arc b||2, where A is a N x 1: matrix and b is a N-vector. The least squares problem can arise, for example from a data-tting mode] with N data points and p basis functions, and we wish to use lat-fold cross validation to assess our choice of basis functions. We assume for convenience that N can be split into k even-sized folds of size N fit {so is divides N). Let A], . . . ,Ak denote the {N/k) x p blocks of data corresponding to each fold, and b1, . . . , bp denote the corresponding right hand sides for each fold. We also assume N is much larger than p, i.e., N i p, and that columns of A remain linearly independent even when we remove one block Ar. (a) (5 points) Analyse the complexity of the following naive method of performing kfold cross- validation: for each fold 1' = 1,...,k 0 Construct A\(c) (5 points) Based on the observation in part (b), we consider an alternative method to perform k-fold cross validation: . Compute G = ATA, h = ATb. . For each fold i = 1, ..., k, compute 0: = (AT A;)-1ATbi = (G - AT A;)-1(h - AT bi). Analyse the complexity of this method and compare it to the naive method of part (a). When is this method better than the naive one