Deep Neural Networks with Ordinal Loss for Medical Applications

2026-06-24

AI Summary

This work addresses the challenge that class labels in medical prediction tasks often exhibit clinically meaningful ordinal structures, which standard loss functions fail to account for by treating all misclassifications equally. To this end, the authors propose the Ordinal Cross-Entropy (OCE) framework, which uniquely integrates an asymmetric, distance-sensitive ordinal cost matrix into the cross-entropy loss. This formulation preserves probabilistic interpretability while enhancing optimization stability and ordinal consistency. The method is fully differentiable and amenable to end-to-end training with deep neural networks. Extensive experiments on multiple medical benchmark datasets demonstrate that OCE significantly reduces misclassification costs and improves prediction calibration, outperforming current state-of-the-art ordinal regression approaches.

Abstract

In many prediction problems in medical applications, target labels exhibit an inherent ordinal structure, where class ordering reflects clinically meaningful severity levels. The cost associated with misclassification is often non-uniform and asymmetric, as errors between distant ordinal categories may have substantially more severe consequences than errors between adjacent ones, and overestimating disease severity may have different clinical implications than underestimating it. Traditional loss functions such as multi-class cross-entropy treat all misclassifications equally and fail to incorporate this ordering information. Recent advances in ordinal regression aim to address this limitation by integrating rank-based structures into deep learning models. In this work, we introduce the \textbf{Ordinal Cross-Entropy (OCE)} framework, a general and architecture-independent approach for learning from ordinal data. The proposed method extends the standard cross-entropy formulation to account for misclassification severity through an ordinal cost matrix while preserving the probabilistic interpretation and optimization benefits of the conventional loss. We provide a theoretical analysis of the OCE gradient behavior and show that it yields smoother optimization dynamics and improved ordinal consistency. Experiments on benchmark datasets show that our method achieves lower prediction error costs and better calibration compared to existing state-of-the-art ordinal approaches, establishing OCE as a simple yet effective solution for ordinal regression in deep neural networks.

Problem

• ordinal regression
• medical applications
• misclassification cost
• deep neural networks
• ordinal labels

Innovation

• Ordinal Cross-Entropy
• ordinal regression
• deep neural networks
• cost-sensitive learning
• medical classification