Normality Testing for Vectors on Perceptron Layers

Abstract

Designing optimal topology of network graph is one of the most prevalent issues in neural network applications. Number of hidden layers, number of nodes in layers, activation functions, and other parameters of neural networks must suit the given data set and the prevailing problem. Massive learning datasets prompt a researcher to exploit probability methods in an attempt to find optimal structure of a neural network. Classic Bayesian estimation of network hyperparameters assumes distribution of specific random parameters to be Gaussian. Multivariate Normality Analysis methods are widespread in contemporary applied mathematics. In this article, the normality of probability distribution of vectors on perceptron layers was examined by the Multivariate Normality Test. Ten datasets from University of California, Irvine were selected for the computing experiment. The result of our hypothesis on Gaussian distribution is negative, ensuring that none of the set of vectors passed the criteria of normality.