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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
1 N (i)
(y − f (x(i) )2 + λC,
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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- Fall '13
- The Aeneid