The problem is to compute the maximum likelihood

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Unformatted text preview: he offset, and fj : R → R, with fj (0) = 0. The functions fj are called the regressor functions. When each fj is linear, i.e., has the form wj xj , the generalized additive model is the same as the standard (linear) regression model. Roughly speaking, a generalized additive model takes into account nonlinearities in each regressor xj , but not nonlinear interactions among the regressors. To visualize a generalized additive model, it is common to plot each regressor function (when n is not too large). We will restrict the functions fj to be piecewise-affine, with given knot points p1 < · · · < pK . This means that fj is affine on the intervals (−∞, p1 ], [p1 , p2 ], . . . , [pK −1 , pK ], [pK , ∞), and continuous at p1 , . . . , pK . Let C denote the total (absolute value of) change in slope across all regressor functions and all knot points. The value C is a measure of nonlinearity of the regressor functions; when C = 0, the generalized additive model reduces to a linear regres...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.

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