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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 meansquare 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 meansquare 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
 F.Borrelli
 The Aeneid

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