Efficient Estimation of Multidimensional Regression Model with Multilayer Perceptron

TL;DR

This paper proposes a novel method for estimating multidimensional nonlinear regression models with multilayer perceptrons, using a cost function based on the log-determinant of the error covariance matrix to achieve asymptotic optimality.

Contribution

It introduces a new cost function for MLP-based regression that does not require prior knowledge of the noise covariance matrix.

Findings

The proposed estimator is asymptotically optimal.

Using the log-determinant of the error covariance improves estimation.

The method simplifies the estimation process for multidimensional models.

Abstract

This work concerns estimation of multidimensional nonlinear regression models using multilayer perceptron (MLP). The main problem with such model is that we have to know the covariance matrix of the noise to get optimal estimator. however we show that, if we choose as cost function the logarithm of the determinant of the empirical error covariance matrix, we get an asymptotically optimal estimator.