Generalized projection pursuit regression

Projection pursuit regression (PPR) can be used to estimate a smooth function of several variables from noisy and scattered data. The estimate is a sum of smoothed one-dimensional projections of the variables. This paper discusses an extension of PPR to exponential family distributions, called generalized projection pursuit regression (GPPR). The proposed model allows multiple responses and nonlinear projections of the variables. Estimators are defined as minimizers of penalized cost functionals, and estimation is related to the local scoring procedure for generalized additive models (GAMs). Smooths are updated using a blockwise Gauss–Seidel (BGS) method, and convergence is shown for this procedure. The use of generalized cross validation (GCV) to estimate smoothing parameters is discussed. Experimental results are shown for two types of data.