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Model Selection A k-piece-constant function is define by k-l thresholds-100 < tǐく2 < . . The function is defined as follows If z < h then f (x) = al . İft1S z < t2 then/ (z) = a2 < tk-1く100 and k values ai, a2, . . . , ak lft,-1 < x < ti then f (z) ai . If tk-1 < x then f (x) = ak Let f be a k. piece-constant function. Suppose you are given n data points ((2 , n ) , . . . , (zn, )) each of which is generated in the following way I, first, x is drawn according to the uniform distribution over the range [-100, 100]. 2. second y is chosen to be f (x) + a, where w is drawn according to the normal distribution N (0, o) You partition the data into a training set and a test set of equal sizes. For each j = 1,2. . . . you find the j-piece-constant function gj that minimizes the root-mean-square-error on the training set. Denote by train (j) the RMSE on the training set and by test (j) the RMSE on the test set.

Which of the following statements is correct? O train (j) is a monotonically non-increasing function O test (j) is a monotonically non-increasing function. O test (j) has a minimum close toj- k O train (j) has a minimum close toj k O if j > n/2, train (j) 0

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