Alcántara Mata, AntonioGalván, Inés M.Aler, Ricardo2023-09-272023-09-272023-01Alcántara, A., Galván, I. M., & Aler-Mur, R. (2023). Pareto optimal prediction intervals with hypernetworks. Applied Soft Computing, 133, 109930.1568-4946https://hdl.handle.net/10016/38454As 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 function, 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.14eng© 2022 The Author(s).Atribución-NoComercial-SinDerivadas 3.0 EspañaDirect prediction intervals estimationHypernetworksMulti-objective optimizationProbabilistic forecastingDeep neural networksresearch articleEstadísticaInformáticahttps://doi.org/10.1016/j.asoc.2022.109930open access110993014Applied Soft Computing133AR/0000031614