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.
Ordinal regression is widely used in scenarios where labels are discrete yet inherently ordered. In practice, however, ordinal labels are often obtained by discretizing underlying continuous semantics through subjective human judgment, resulting in ambiguous boundaries and annotation noise. Such uncertainty challenges existing methods that rely on fixed supervision targets, which may reinforce biased ordering under subjective annotations. To address this limitation, we propose D3O, a dynamic distribution distillation framework that replaces static supervision with training-driven evolution of ordinal label distributions via self-distillation. Specifically, we introduce a contrastive ordinal-aware label enhancement module that leverages vision-language alignment to recover refined label distributions capturing both inter-class ambiguity and instance-level uncertainty. Furthermore, we design a CDF-based cross-layer interaction distillation mechanism to propagate cumulative ordinal structure across network hierarchy, ensuring consistent ordinal geometry in intermediate representations. Extensive experiments on four general ordinal regression tasks demonstrate that our proposed D3O consistently outperforms existing approaches, particularly under severe class imbalance and noisy supervision. These results highlight the effectiveness of dynamic supervision in learning robust ordinal representations beyond fixed targets. The code will be publicly available.
Standard cross-entropy loss causes neural networks trained on ordinal classification tasks to hedge predictions toward center classes, a failure mode we term \emph{center-class hedging}. This occurs because predicting the middle class minimizes expected symmetric loss, making it the path of least resistance regardless of the true label. Existing ordinal losses address related problems such as large-error penalization and rank consistency, but none directly suppresses center-class hedging as a function of where the true label lies relative to the ordinal center. We propose the Adaptive Margin Ordinal Loss (AMOL), a multiplicative weight applied to per-class loss terms of the form m(k,y)=1+α⋅(1−∣k−c∣/c)⋅(∣y−c∣/c), where c is the center class, k is the candidate class, and y is the true label. The weight encodes a joint condition: it is large only when the candidate class is near center and the true label is far from center, collapsing to standard behavior otherwise. We further introduce the Center-Hedging Rate (CHR) as a diagnostic metric that directly quantifies this failure mode. Across four ordinal classification benchmarks and five random seeds, AMOL achieves the best or tied-best Quadratic Weighted Kappa (QWK) on all four datasets compared to cross-entropy, OLL, and SORD baselines. An asymmetric variant (AMOL-asym) eliminates center-class hedging entirely on the Abalone dataset (CHR=0.000±0.000 across all five seeds, n≈266 extreme-class test samples per run), compared to 0.074±0.005 for standard cross-entropy.
Ordinal Classification (OC) deals with classification tasks where the classes follow a natural order. Despite the progress in OC, many existing approaches fail to fully leverage the ordinal information, treating the problem as nominal classification and thereby losing performance potential. In this work, ADABORD, an AdaBoost framework specifically designed for ordinal classification problems, is introduced. The ordinal nature of the classes is incorporated into two key components of the well-known AdaBoost algorithm: 1) the base estimator, where decision trees with the ordinal Gini splitting criterion are proposed; 2) the error function used to update sample weights at each stage and the weights of the classifier in the final ensemble model, given by the absolute ranked probability score, a measure that accounts for both the ordering and the distance between classes. ADABORD is extensively compared against seven state-of-the-art methods on the TOC-UCO repository, the largest benchmark collection for OC to date. The experimental results, supported by statistical analysis, show that ADABORD significantly outperforms competing methods, particularly on datasets with five or more classes, where the ordinal structure becomes more pronounced. Source code, along with all experimental protocols, is publicly available to ensure reproducibility and facilitate future research in OC.
Rafael Ayllón-Gavilán, Francisco José Martínez-Estudillo, David Guijo-Rubio +2