NONLINEAR PARTIAL LEAST-SQUARES

We propose a new nonparametric regression method for high-dimensional data, nonlinear partial least squares (NLPLS), which is motivated by p rojection-based regression methods, e.g. PLS, projection pursuit regre ssion and feedforward neural networks. The model takes the form of a c omposition of two functions. The first function in the composition pro jects the predictor variables onto a lower-dimensional curve or surfac e yielding scores, and the second predicts the response variable from the scores. We implement NLPLS with feedforward neural networks. NLPLS often will produce a more parsimonious model (fewer score vectors) th an projection-based methods. We extend the model to multiple response variables and discuss situations when multiple response variables shou ld be modeled simultaneously and when they should be modeled with sepa rate regressions. We provide empirical results that evaluate the perfo rmances of NLPLS, projection pursuit, and neural networks On response variable predictions and robustness to starting values. (C) 1997 Elsev ier Science Ltd.