Estimation of Multidimensional Regression Model with Multilayer Perceptrons

Abstract

This work concerns estimation of multidimensional nonlinear regression models using multilayer perceptron (MLP). For unidimensional data, the ordinary least squares estimator matches with the Gaussian maximum likelihood estimator. However, in the multidimensional case, the Gaussian maximum likelihood estimator minimize the determinant of the empirical error’s covariance matrix. This paper is devoted to the study of this estimator using a MLP. In particular, we show how to modify the backpropagation algorithm to minimize such cost function and we give heuristic explanations in favor of the use of such function in the multidimensional case.