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.