On Robust Training of Regression Neural Networks

Abstract

Estimation, prediction or smoothing of curves represents a fundamental task of functional data analysis. Nonlinear regression methods allow to search for the best-fit curves explaining the dependence of a response variable on available independent variables. Neural networks, commonly used for the task of nonlinear regression, are however highly vulnerable to the presence of outlying measurements in the data. New robust versions of common types of neural networks, namely multilayer perceptrons and radial basis function networks, are proposed here based on nonlinear regression quantiles or highly robust loss functions. Three datasets are analyzed to illustrate the performance of the novel robust approaches, which turn out to outperform standard neural networks or other competing regression tools over contaminated data.