Online Approximation of Prediction Intervals Using Artificial Neural Networks

Abstract

Prediction intervals offer a means of assessing the uncertainty of artificial neural networks’ point predictions. In this work, we propose a hybrid approach for constructing prediction intervals, combining the Bootstrap method with a direct approximation of lower and upper error bounds. The main objective is to construct high-quality prediction intervals – combining high coverage probability for future observations with small and thus informative interval widths – even when sparse data is available. The approach is extended to adaptive approximation, whereby an online learning scheme is proposed to iteratively update prediction intervals based on recent measurements, requiring a reduced computational cost compared to offline approximation. Our results suggest the potential of the hybrid approach to construct high-coverage prediction intervals, in batch and online approximation, even when data quantity and density are limited. Furthermore, they highlight the need for cautious use and evaluation of the training data to be used for estimating prediction intervals.