Accurate and Reliable Uncertainty Estimates for Deterministic Predictions Extensions to Under and Overpredictions
2026-04-09 • Computational Engineering, Finance, and Science
Computational Engineering, Finance, and ScienceMachine Learning
AI summaryⓘ
The authors address the challenge of predicting uncertain outcomes in complex models, especially when quick decisions are needed. They improve on current methods by creating a system that learns uncertainty patterns depending on the input, without assuming these uncertainties follow simple symmetrical shapes like Gaussian curves. Their approach uses a neural network and special mathematical forms to better capture real-world uncertainty, including uneven and heavy-tailed behaviors. Tests on both fake and real data show their method makes more reliable and accurate uncertainty predictions compared to other techniques.
probabilistic predictionuncertainty quantificationnon-Gaussian distributiontwo-piece Gaussianasymmetric Laplaceneural networkspredictive accuracyloss functiondistribution-free methodsinput-dependent uncertainty
Authors
Rileigh Bandy, Enrico Camporeale, Andong Hu, Thomas Berger, Rebecca Morrison
Abstract
Computational models support high-stakes decisions across engineering and science, and practitioners increasingly seek probabilistic predictions to quantify uncertainty in such models. Existing approaches generate predictions either by sampling input parameter distributions or by augmenting deterministic outputs with uncertainty representations, including distribution-free and distributional methods. However, sampling-based methods are often computationally prohibitive for real-time applications, and many existing uncertainty representations either ignore input dependence or rely on restrictive Gaussian assumptions that fail to capture asymmetry and heavy-tailed behavior. Therefore, we extend the ACCurate and Reliable Uncertainty Estimate (ACCRUE) framework to learn input-dependent, non-Gaussian uncertainty distributions, specifically two-piece Gaussian and asymmetric Laplace forms, using a neural network trained with a loss function that balances predictive accuracy and reliability. Through synthetic and real-world experiments, we show that the proposed approach captures an input-dependent uncertainty structure and improves probabilistic forecasts relative to existing methods, while maintaining flexibility to model skewed and non-Gaussian errors.