Deep Gaussian processes and infinite neural networks for the analysis of EEG signals in Alzheimer’s diseases

Abstract

Deep neural network models (DGPs) can be represented hierarchically by a sequential composition of layers. When the prior distribution over the weights and biases are independently identically distributed, there is an equivalence with Gaussian processes (GP) in the limit of an infinite net[1]work width. DGPs are non-parametric statistical models used to character[1]ize patterns of complex non-linear systems due to their flexibility, greater generalization capacity, and a natural way of making inferences about the parameters and states of the system. This article proposes a hierarchi[1]cal Bayesian structure to model the weights and biases of a deep neural network. We deduce a general formula to calculate the integrals of Gaussian processes with non-linear transfer densities and obtain a kernel to estimate the covariance functions. In the methodology, we conduct an empirical study analyzing an electroencephalogram (EEG) database for diagnosing Alzheimer’s disease. Additionally, the DGPs models are esti[1]mated and compared with the NN models for 5, 10, 50, 100, 500, and 1000 neurons in the hidden layer, considering two transfer functions: Recti[1]fied Linear Unit (ReLU) and hyperbolic Tangent (Tanh). The results show good performance in the classification of the signals. Finally, we use the mean square error as a goodness of fit measure to validate the proposed models, obtaining low estimation errors.