Pareto Optimal Prediction Intervals with Hypernetworks

As the relevance of probabilistic forecasting grows, the need of estimating multiple high-quality prediction intervals (PI) also increases. In the current state of the art, most deep neural network gradient descent-based methods take into account interval width and coverage into a single loss func-tion, focusing on a unique nominal coverage target, and adding additional parameters to control the coverage-width trade-off. The Pareto Optimal Prediction Interval Hypernetwork (POPI-HN) approach developed in this work has been derived to treat this coverage-width trade-off as a multi-objective problem, obtaining a complete set of Pareto Optimal solutions (Pareto front). POPI-HN are able to be trained through gradient descent with no need to add extra parameters to control the width-coverage trade-off of PIs. Once the Pareto set has been obtained, users can extract the PI with the required coverage. Comparative results with recently introduced Quality-Driven loss show similar behavior in coverage while improving interval width for the majority of the studied domains, making POPI-HN a competing alternative for estimating uncertainty in regression tasks where PIs with multiple coverages are needed. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Automated summary

As the relevance of probabilistic forecasting grows, the need for estimating multiple high-quality prediction intervals (PI) also increases. The Pareto Optimal Prediction Interval Hypernetwork (POPI-HN) approach treats the coverage-width trade-off as a multi-objective problem and obtains a complete set of Pareto Optimal solutions. POPI-HN can be trained through gradient descent without needing extra parameters and allows users to extract the PI with the required coverage.