Question: (Adaboosting) Consider the Adaboosting algorithm for classification in the following example. Suppose we have 3 data points of (Y,, X;) is (Y, X) = (-1,0),

(Adaboosting) Consider the Adaboosting algorithm for classification in the following example. Suppose we have 3 data points of (Y,, X;) is (Y, X) = (-1,0), (1, 1), (-1,2) The three weak learners are hi (x) = sign (x - 0.5) ha (x) = -sign (x - 1.5) h3 () =-1 We consider the original weights w1 = w2 = w3 = = of these three points. Suppose that we choose he (@) = -1 in the first round of Adaboosting, and choose ha (@) = -sign (x - 1.5) in the second round of Adaboosting. This implies that we will choose hi (@) = sign (x - 0.5) in the third round. Now at the end of the third round, the classifier we finally obtain is the form of sign (F()). What is this function F(@) at the end of the third round? O log(5) h_1(x) + log(2) h_2(x) + log(3) h_3(x) O log(3) h_1(x) + log(2) h_2(x) + log(5) h_3(x) O log(3) h_1(x) + log(5) h_2(x) + log(2) h_3(x) O log(5) h_1(x) + log(3) h_2(x) + log(2) h_3(x) O log(2) h_1(x) + log(3) h_2(x) + log(5) h_3(x) O log(2) h_1(x) + log(5) h_2(x) + log(3) h_3(x)
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