Statistical and neural network techniques for nonparametric regression

The problem of estimating an unknown function from a finite number of noisy data points has fundamental importance for many applications. Recently, several computational techniques for non-parametric regression have been proposed by statisticians and by researchers in artificial neural networks, but there is little interaction between the two communities. This paper presents a common taxonomy of statistical and neural network methods for nonparametric regression. Performance of many methods critically depends on the strategy for positioning knots along the regression surface. A novel method for adaptive positioning of knots called Constrained Topological Mapping(CTM) is discussed in some detail. This method achieves adaptive placement of knots of the regression surface by using a neural network model of self-organization.