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Risk and linear regression Consider training data [(xi, 321-)]1-=1_m where x1- 6 Rd and yl- 6 IR. Suppose x ~ N(0, Id): where Id is
Risk and linear regression Consider training data [(xi, 321-)]1-=1_"m where x1- 6 Rd and yl- 6 IR. Suppose x ~ N(0, Id): where Id is the d x d identity matrix. Suppose 321- = x9*+i, where 6" 6 Rd and 61- is a zeromean random variable with variance oz, independent of xi. (a) Consider a predictor given by f9 : le > IR, with fax) : x'B. Show that the risk of f9 with respect to the square loss is Ros) = \"6\" 6II2 + or\". (b) Show that the solution to least squares linear regression, 9 is unbiased in the sense that 18(9) 2 6*
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