Cross-Correlation Estimation in Artificial Neural Network for Uncertainty Assessment

One of the main challenges in Artificial Neural Networks (ANNs) is the development of reliable, valid, and reproducible systems. Prediction networks have had a disruptive impact, bringing numerous advantages in various fields, but for their common usage, it's necessary to quantify their quality. In particular, evaluating the uncertainty of the measurements obtained with these approaches allows their correct utilization. This work aims to analyze the covariances of the inputs of different neurons, particularly in those of the hidden layers of ANNs. Evaluating the covariance of the inputs of a single neuron finds primary use in the law of propagation of uncertainty, particularly for evaluating the correlation term in mathematical development, as defined by ISO GUM. Based on numerical evaluation, the proposed procedure aims to evaluate the PDFs of inputs to individual nodes and, therefore, the correlations among all inputs propagating within the network architecture.

I. Introduction

An ANN is a machine learning process that uses nodes or neurons interconnected in a layered structure resembling the human brain to teach computers to process data in a way inspired by the human reasoning. ANNs performing regression predict a continuous output variable based on the input variables [1]. They can be considered compelling tools in modeling complex, nonlinear input-output relationships and can be applied to various areas of scientific research and industry. Although an ANN may seem complex at first glance, it is essentially a straight line of logic that connects the inputs to the output following a structure composed of layers of interconnected nodes to process large amounts of data. Each node takes the input data, processes it in a specific way, and passes it on to the next node [2].