MACHINE LEARNING

1. [15 points) Suppose you are given the following feature vectors: x1 = (1,1),x2 = (2, 1), x3 = (1, -1),x4 = (-1,-1),X5 = (-2,1) Their corresponding labels are y = 1, y2 = 1, y3 = -1, y = -1,ys = -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 hj 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: hi(x) = sign((Wi, x) +bi), for i = 1,2. The parameters are wi = [1,0), b1 = -1.5, w2 = [0,1], b2 =0. Using hy and h2, we will now create an ensamble classifier H using boosting. Answer the following questions. The calculations below have been rounded to 2 decimal places. If there is no exact match, choose the closest value. Only one of the answers is fully correct; mark the answer that is fully correct in the answer sheet. Note that you will not get any credit if you mark multiple answers (even if one of the answers marked is fully correct.) 1.5 A A 0.5 h2 hi 0 -0.5 -1 o o -1.5 -2 -3 -2 -1 0 1 2 3 (a) (5 points] Suppose we choose hi as our weak learner in the first round of boosting. What is value of ai? 1. 0.69 2. 0.20 3. -0.69 4. 0.30 5. -0.20 (b) (5 points) Suppose we choose h2 as our weak learner in the second round of boosting. What is the value of az? 1. 0.67 2.-0.42 3. 0.42 4. 0.97 5. 0.13 (c) [5 points] Given a new data point Xu = [.5,1), what is the weighted sum _=1 Qihi(xu)? 1. 0.14 2. 0.15 3. 0.16 4. 0.17 5. None of the above