Testing the number of parameters with multidimensional MLP

TL;DR

This paper introduces a method for testing the number of parameters in a single hidden layer MLP by analyzing the asymptotic distribution of the log determinant of the error covariance matrix, assuming identifiable models.

Contribution

It provides a new asymptotic distribution result for parameter testing in single hidden layer MLPs under model identifiability assumptions.

Findings

Derives a simple asymptotic distribution for the test statistic.

Applicable when the number of hidden units is known.

Uses the log determinant of the error covariance matrix as a cost function.

Abstract

This work concerns testing the number of parameters in one hidden layer multilayer perceptron (MLP). For this purpose we assume that we have identifiable models, up to a finite group of transformations on the weights, this is for example the case when the number of hidden units is know. In this framework, we show that we get a simple asymptotic distribution, if we use the logarithm of the determinant of the empirical error covariance matrix as cost function.