# Aleatoric and Epistemic Uncertainty Measures for Ordinal Classification through Binary Reduction

arXiv: https://arxiv.org/abs/2507.00733 · HTML: https://mlsanity.com/paper/2507.00733/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2025.

## Built on by (most cited first, 3 of 3)

- [Evaluating Evidence Grounding Under User Pressure in Instruction-Tuned Language Models](https://mlsanity.com/paper/2603.20162/) (2026)
- [Reliable Conformal Prediction for Ordinal Classification Using the Ranked Probability Score](https://mlsanity.com/paper/2606.24959/) (2026)
- [Latent Uncertainty Representations for Video-based Driver Action and Intention Recognition](https://mlsanity.com/paper/2510.05006/) (2025)

## Abstract (arXiv)

Ordinal classification problems, where labels exhibit a natural order, are prevalent in high-stakes fields such as medicine and finance. Accurate uncertainty quantification, including the decomposition into aleatoric (inherent variability) and epistemic (lack of knowledge) components, is crucial for reliable decision-making. However, existing research has primarily focused on nominal classification and regression. In this paper, we introduce a novel class of measures of aleatoric and epistemic uncertainty in ordinal classification, which is based on a suitable reduction to (entropy- and variance-based) measures for the binary case. These measures effectively capture the trade-off in ordinal classification between exact hit-rate and minimial error distances. We demonstrate the effectiveness of our approach on various tabular ordinal benchmark datasets using ensembles of gradient-boosted trees and multi-layer perceptrons for approximate Bayesian inference. Our method significantly outperforms standard and label-wise entropy and variance-based measures in error detection, as indicated by misclassification rates and mean absolute error. Additionally, the ordinal measures show competitive performance in out-of-distribution (OOD) detection. Our findings highlight the importance of considering the ordinal nature of classification problems when assessing uncertainty.