bv_cvxbook_extra_exercises

B consider the case with d 0 1 with c0 0 c1

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Unformatted text preview: sion model. Now suppose we observe samples or data (x(1) , y (1) ), . . . , (x(N ) , y (N ) ) ∈ Rn × R, and wish to fit a generalized additive model to the data. We choose the offset and the regressor functions to minimize 1 N (i) (y − f (x(i) )2 + λC, N i=1 where λ > 0 is a regularization parameter. (The first term is the mean-square error.) (a) Explain how to solve this problem using convex optimization. (b) Carry out the method of part (a) using the data in the file gen_add_reg_data.m. This file contains the data, given as an N × n matrix X (whose rows are (x(i) )T ), a column vector y (which give y (i) ), a vector p that gives the knot points, and the scalar lambda. Give the mean-square error achieved by your generalized additive regression model. Compare the estimated and true regressor functions in a 3 × 3 array of plots (using the plotting code in the data file as a template), over the range −10 ≤ xi ≤ 10. The true regressor functions (to be used only for plotting, of cou...
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