1. Consider a noisy target y = w*Tx+e for generating the data, where is a noise...

 

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1. Consider a noisy target y = w*Tx+e for generating the data, where is a noise term with zero mean and 2 variance, independently generated for every example (x, y). The expected error of the best possible linear fit to this target is thus o. = For the data D{(x1,y1),, (XN, YN)}, denote the noise in yn as n and let = [1, 2,.,EN]; assume that XTX is invertible. By following the steps below, show that the expected in-sample error of linear regression with respect to D is given by ED[Ein (Win)] = 0 = (1-d+1) (a) Show that the in-sample estimate of y is given by = Xw* + He. (H was defined in the exercise two of Homework 6) (b) Show that the in-sample error vector - y can be expressed by a matrix times . What is the matrix? (c) Express Ein (Wlin) in terms of e using (b), and simplify the expression using (c) of exercise two of Homework 6. 1. Consider a noisy target y = w*Tx+e for generating the data, where is a noise term with zero mean and 2 variance, independently generated for every example (x, y). The expected error of the best possible linear fit to this target is thus o. = For the data D{(x1,y1),, (XN, YN)}, denote the noise in yn as n and let = [1, 2,.,EN]; assume that XTX is invertible. By following the steps below, show that the expected in-sample error of linear regression with respect to D is given by ED[Ein (Win)] = 0 = (1-d+1) (a) Show that the in-sample estimate of y is given by = Xw* + He. (H was defined in the exercise two of Homework 6) (b) Show that the in-sample error vector - y can be expressed by a matrix times . What is the matrix? (c) Express Ein (Wlin) in terms of e using (b), and simplify the expression using (c) of exercise two of Homework 6.