The problem of estimating an unknown function from a finite number of noisy data points (examples) is an ill-posed problem of fundamental importance for many applications, such as machine vision, pattern recognition, and process control. Recently, several new computational techniques for non-parametric regression have been proposed by statisticians, and by researchers in artificial neural networks. However, there is little interaction between the two research communities. The goal of this paper is twofold. First, we present a critical survey of statistical and neural network techniques for non-parametric regression. Second, we present comparisons between a representative neural network technique called Constrained Topological Mapping, and several statistical methods, for low-dimensional regression problems.