Problem 1.5 [16pts] (Optimum decision rules for empirical data) Let y := {1.0, 2.0, 3.0, 4.0, 5.0, 6.0) be a label-space of real-valued positive integers. A dataset has n = 12 examples all of which have the same feature vector x, but different labels from y given by D(x) := (y1 = 2.0, y2 = 1.0, y; = 5.0, y4 = 3.0, ys = 2.0, y6 = 4.0, y7 = 1.0, yg = 4.0, yo = 6.0, y10 = 4.0, y1 1 = 2.0, )12 = 6.0}. (a) [4pts] (Empirical average zero-one loss given x) Let Lerror(yx) := " Ejl(y # y;). Compute h(x) := argmin Lerror(y/x). This label-choice has the yEy minimum average disagreement with the labels of the twelve examples having feature vector x. (b) [5pts] (Empirical average squared-error loss given x) Let LMSE(yx) := Ejl(y - y;) . Compute h(x) := argmin LMSE(yx). This label-choice has the YER minimum average squared-error with the labels of the twelve examples having feature vector x. (c) [7pts] (Empirical average absolute-error loss given x) Let LMAE()|X) := En_ly - y;l. Compute h(x) := argmin LMAE(y(x). This label-choice has the yER minimum average absolute-error with the labels of the twelve examples having feature vector x