MULTILAYER PERCEPTRON ARTIFICIAL NEURAL NETWORKS: AN APPROACH FOR LEARNING THROUGH THE BAYESIAN FRAMEWORK

Abstract

The machine learning area has recently gained prominence and artificial neural networks are among the most popular techniques in this field. Such techniques have the learning capacity that occurs during an iterative process of model fitting. Multilayer perceptron (MLP) is one of the first networks that emerged and, for this architecture, backpropagation and its modifications are widely used learning algorithms. In this article, the learning of the MLP neural network was approached from the Bayesian perspective by using Monte Carlo via Markov Chains (MCMC) simulations. The MLP architecture consists of the input, hidden and output layers. In the structure, there are several weights that connect each neuron in each layer. The input layer is composed of the covariates of the model. In the hidden layer there are activation functions. In the output layer, there are the result which is compared with the observed value and the loss function is calculated. We analyzed the network learning through simulated data of known weights in order to understand the estimation by the Bayesian method. Subsequently, we predicted the price of WTI oil and obtained a credibility interval for the forecasts. We provide an R implementation and the datasets as supplementary materials.