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machine learning

(3) Suppose you are given the following feature vectors: 21 = (1, 1), 22 = (2,1), 13 = (1, -1), 04 = (-1,-1), 25 = (-2,1) Their corresponding labels are y1 = 1, y2 = 1, y3 = -1, y4 = -1, y = -1 This data is plotted below where class 1 is represented by triangles and -1 by circles. Also shown in the figure are two weak learners hy and h2, represented by an offset and an arrow. The arrow points in the direction in which the weak learner predicts 1. More formally, the weak-learners are: h;() = sign((Wi, 2)+b;), for i = 1, 2. The parameters are wi = [1,0], b1 = -1.5, w2 = [0, 1], b2 = 0. 2 1.5 @ A A 0.5 he ht 0 -0.5 -1.5 Using h1 and h2, we will now create an ensamble classifier H using boosting. Answer the following questions. (a) (4 points) Suppose we pick hy as the weak learner in the first round of boosting. What is value of ai? (b) (4 points) Suppose we pick hy as the weak learner in the second round. What is the value of az? (c) (2 points) Given a new data point Iu = [.5, 1], what is the weighted sum _{= @ihi(Tu)? (3) Suppose you are given the following feature vectors: 21 = (1, 1), 22 = (2,1), 13 = (1, -1), 04 = (-1,-1), 25 = (-2,1) Their corresponding labels are y1 = 1, y2 = 1, y3 = -1, y4 = -1, y = -1 This data is plotted below where class 1 is represented by triangles and -1 by circles. Also shown in the figure are two weak learners hy and h2, represented by an offset and an arrow. The arrow points in the direction in which the weak learner predicts 1. More formally, the weak-learners are: h;() = sign((Wi, 2)+b;), for i = 1, 2. The parameters are wi = [1,0], b1 = -1.5, w2 = [0, 1], b2 = 0. 2 1.5 @ A A 0.5 he ht 0 -0.5 -1.5 Using h1 and h2, we will now create an ensamble classifier H using boosting. Answer the following questions. (a) (4 points) Suppose we pick hy as the weak learner in the first round of boosting. What is value of ai? (b) (4 points) Suppose we pick hy as the weak learner in the second round. What is the value of az? (c) (2 points) Given a new data point Iu = [.5, 1], what is the weighted sum _{= @ihi(Tu)