# Interval-Based AUC (iAUC): Extending ROC Analysis to Uncertainty-Aware Classification

arXiv: https://arxiv.org/abs/2602.04775 · HTML: https://mlsanity.com/paper/2602.04775/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 20 references that are in the map.
- First posted on arXiv 4 Feb 2026.

## Builds on (most cited first, 4 of 4)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [SelectiveNet: A Deep Neural Network with an Integrated Reject Option](https://mlsanity.com/paper/1901.09192/) (2019)

## Abstract (arXiv)

In high-stakes risk prediction, quantifying uncertainty through interval-valued predictions is essential for reliable decision-making. However, standard evaluation tools like the receiver operating characteristic (ROC) curve and the area under the curve (AUC) are designed for point scores and fail to capture the impact of predictive uncertainty on ranking performance. We propose an uncertainty-aware ROC framework specifically for interval-valued predictions, introducing two new measures: AUCL and AUCU. This framework enables an informative three-region decomposition of the ROC plane, partitioning pairwise rankings into correct, incorrect, and uncertain orderings. This approach naturally supports selective prediction by allowing models to abstain from ranking cases with overlapping intervals, thereby optimizing the trade-off between abstention rate and discriminative reliability. We prove that under valid class-conditional coverage, AUCL and AUCU provide formal lower and upper bounds on the theoretical optimal AUC (AUC^*), characterizing the physical limit of achievable discrimination. The proposed framework applies broadly to interval-valued prediction models, regardless of the interval construction method. Experiments on real-world benchmark datasets, using bootstrap-based intervals as one instantiation, validate the framework's correctness and demonstrate its practical utility for uncertainty-aware evaluation and decision-making.