2. More about AdaBoost. Consider the binary-class classification task. Suppose we are given a dataset with m samples, (21, V1), (12, 12), . . ., (Im, ym), where for each i, y; E {-1, +1}. The loss we are using here is the 0 - 1 loss: L = ,. EM, 1(H(x,) # yi). Recall that in class we have gone through the Boosting algorithm for this binary-class classi- fication task, which follows the following procedure: Algorithm 1: AdaBoost algorithms while L is minimized do initialize Di (i) = > for i = 1, . .., m; for t=1, . . ., T do Using Dt, get weak learner he, where he can only take value -1 or +1; Choose ot ER, update using the rule: ZI = _ Di(x.) exp (-caythe(24)), Drti(i) = Di(i) exp (-awihi(zi)) i=1 end Final classifier f(x) = Commi(x), H(x) = sign (f(2)) , and loss end In this question, we are going to figure out the value of of for t = 1, . .., T. (a) (5 points) Find the minimizer o E R that minimizes Z = (1 - c)e- + ce". (b) (5 points) Show that for all values of a and either y = -1 or y = +1, 1(H(x) # y) S exp (-uf(x)) = exp (-y Each(2) (c) (10 points) Show by induction that Then together with part (a), conclude that choosing or = } In 1," can minimize the upper bound of loss L, where 4 = D.(i) 1 (he(z.) # yi)