Coverage-driven deep prediction intervals method

Abstract

Prediction Intervals (PIs) provide a method to quantify the uncertainty of deep neural networks' point forecasts. High-quality PIs should be as narrow as possible while covering a designated percentage of data points, which is an axiomatic theory. Lower Upper Bound Estimation (LUBE) method is the first to incorporate this axiom into the neural networks loss function, however it pays much attention to the interval width, and thus the coverage probability does not achieve the desired result. Consequently, the PIs are unreliable and their practical application risks are elevated. In this paper, prioritizing coverage probability, we propose a coverage-driven approach that is generalized to any neural networks model, combining bootstrap method with improved LUBE method. We show that PIs constructed by our method are more reliable, and model uncertainty is quantified using bootstrap. Moreover, compared with two novel PI methods, benchmark experiments show our method is able to reduce the mean PI width by more than 7.5% while obtaining the better results in coverage probability.