Aleatoric and Epistemic Uncertainty Measures for Ordinal Classification Through Binary Reduction

Haas, Stefan und Hüllermeier, Eyke (6. March 2026): Aleatoric and Epistemic Uncertainty Measures for Ordinal Classification Through Binary Reduction. In: Machine Learning, Vol. 115, No. 3

Abstract

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 minimal 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.

• Item Type: Journal article
• Form of publication: Publisher's Version
• Faculties: Mathematics, Computer Science and Statistics > Computer Science > Artificial Intelligence and Machine Learning
• Subjects: 000 Computer science, information and general works > 004 Data processing computer science
• ISSN: 0885-6125
• Language: English