CLEAR: Calibrated Learning for Epistemic and Aleatoric Risk

TL;DR

CLEAR is a calibration method that effectively combines aleatoric and epistemic uncertainties to produce more reliable predictive intervals across diverse datasets, improving coverage and interval width.

Contribution

We introduce CLEAR, a novel calibration approach with two parameters that balances and combines aleatoric and epistemic uncertainties for better predictive interval coverage.

Findings

Achieves 28.3% and 17.5% improvements in interval width over baselines.

Maintains nominal coverage across 17 datasets.

Effective in high uncertainty scenarios.

Abstract

Accurate uncertainty quantification is critical for reliable predictive modeling. Existing methods typically address either aleatoric uncertainty due to measurement noise or epistemic uncertainty resulting from limited data, but not both in a balanced manner. We propose CLEAR, a calibration method with two distinct parameters, $\gamma_1$ and $\gamma_2$, to combine the two uncertainty components and improve the conditional coverage of predictive intervals for regression tasks. CLEAR is compatible with any pair of aleatoric and epistemic estimators; we show how it can be used with (i) quantile regression for aleatoric uncertainty and (ii) ensembles drawn from the Predictability-Computability-Stability (PCS) framework for epistemic uncertainty. Across 17 diverse real-world datasets, CLEAR achieves an average improvement of 28.3\% and 17.5\% in the interval width compared to the two individually calibrated baselines while maintaining nominal coverage. Similar improvements are observed when applying CLEAR to Deep Ensembles (epistemic) and Simultaneous Quantile Regression (aleatoric). The benefits are especially evident in scenarios dominated by high aleatoric or epistemic uncertainty. Project page: https://unco3892.github.io/clear/