Accurate and Reliable Uncertainty Estimates for Deterministic Predictions Extensions to Under and Overpredictions

2026-04-09

AI Summary

This work addresses the limitations of existing uncertainty estimation methods, which often incur high computational costs in real-time settings and struggle to model input-dependent, asymmetric, and heavy-tailed error distributions. The authors extend the ACCRUE framework by introducing input-dependent non-Gaussian distributions—such as two-piece Gaussian and asymmetric Laplace—into the calibration of deterministic predictions for the first time. A neural network is employed to learn these complex uncertainty structures, and an end-to-end training procedure is developed using a novel loss function that jointly optimizes predictive accuracy and calibration reliability. Experimental results on both synthetic and real-world datasets demonstrate that the proposed approach effectively captures the skewness and heavy-tailed nature of prediction errors, yielding significantly improved probabilistic forecasting performance.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

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.

Problem

• uncertainty quantification
• non-Gaussian errors
• input-dependent uncertainty
• probabilistic predictions
• deterministic models

Innovation

• input-dependent uncertainty
• non-Gaussian distributions
• asymmetric Laplace
• two-piece Gaussian
• probabilistic forecasting