Pareto optimal prediction intervals with hypernetworks Articles uri icon

publication date

  • January 2023

start page

  • 1

end page

  • 14


  • 109930


  • 133

International Standard Serial Number (ISSN)

  • 1568-4946

Electronic International Standard Serial Number (EISSN)

  • 1872-9681


  • 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 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.


  • Computer Science
  • Statistics


  • direct prediction intervals estimation; hypernetworks; multi-objective optimization; probabilistic forecasting; deep neural networks