Automatic Smoothing Spline Projection Pursuit |
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| Authors: | Charles B Roosen Trevor J Hastie |
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| Institution: | 1. Department of Statistics , Stanford University , Stanford , CA , 94305 , USA;2. Statistics and Data Analysis Research Department , AT&3. T Bell Laboratories , Murray Hill , NJ , 07974 , USA |
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| Abstract: | Abstract A highly flexible nonparametric regression model for predicting a response y given covariates {xk}d k=1 is the projection pursuit regression (PPR) model ? = h(x) = β0 + Σjβjfj(αT jx) where the fj , are general smooth functions with mean 0 and norm 1, and Σd k=1α2 kj=1. The standard PPR algorithm of Friedman and Stuetzle (1981) estimates the smooth functions fj using the supersmoother nonparametric scatterplot smoother. Friedman's algorithm constructs a model with M max linear combinations, then prunes back to a simpler model of size M ≤ M max, where M and M max are specified by the user. This article discusses an alternative algorithm in which the smooth functions are estimated using smoothing splines. The direction coefficients αj, the amount of smoothing in each direction, and the number of terms M and M max are determined to optimize a single generalized cross-validation measure. |
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| Keywords: | GCV Multivariate function approximation Neural networks Nonparametric regression |
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