An Extension of the Quadratic Error Function for Learning Imprecise Data in Multivariate Nonlinear Regression

Abstract

Multivariate noises in the learning process are most of the time supposed to follow a standard multivariate normal distribution. This hypothesis does not often hold in many real-world situations. In this paper, we consider an approach based on multivariate skew-normal distribution. It allows for a multiple continuous variation from normality to nonnormality. We give an extension of the generalized least squares error function in a context of multivariate nonlinear regression to learn imprecise data. The simulation study and application case on real datasets conducted and based on multilayer perceptron neural networks (MLP) with bivariate continuous response and asymmetric revealed a significant gain in precision using the new quadratic error function for these types of data rather than using a classical generalized least squares error function having any covariance matrix.