ordinal regression

This work addresses the lack of general-purpose methods and open-source tools for ordinal classification by proposing a model-agnostic framework that transforms any base classifier into an ordinal-aware variant. The approach integrates a classifier pooling strategy with ordinal constraint mechanisms, enabling, for the first time, universal adaptation of arbitrary classifiers to ordinal data. To support reproducibility and practical adoption, the authors release an open-source Python package that fills a critical gap in available ordinal classification tooling. Extensive experiments on multiple real-world datasets demonstrate that the proposed method significantly outperforms conventional non-ordinal classifiers, particularly in small-sample and high-cardinality settings, thereby confirming its effectiveness and practical utility.

This study addresses ordinal regression with functional covariates, proposing an interpretable and computationally efficient prediction framework. Methodologically: (1) it derives, for the first time, the closed-form solution for least absolute deviation (LAD) prediction in ordinal models; (2) it reformulates the original functional ordinal model into an equivalent classical ordinal model with scalar covariates via a loss-function-driven reconstruction strategy, ensuring both theoretical rigor and practical deployability. The contributions are threefold: it overcomes the interpretability bottleneck in functional ordinal modeling; it provides the first analytical expression for LAD-optimal prediction; and it achieves computationally tractable dimensionality reduction from function space to Euclidean space. Empirical evaluation on real-world smart eyewear data from Essilor-Luxottica demonstrates substantial improvements in tint prediction accuracy and algorithmic robustness; the method has been successfully integrated into the photochromic control engine.

This work addresses the need for uncertainty quantification in ordinal classification within high-stakes domains such as medicine and finance, where errors of varying severity must be rigorously controlled. Existing conformal prediction methods are limited by their choice of nonconformity functions, which often fail to reflect the inherent ordering of classes. To overcome this, the authors propose a novel conformal prediction approach based on the Ranked Probability Score (RPS), introducing RPS as a natural nonconformity measure that captures ordinal risk. This method yields continuous prediction sets centered around the median, avoids greedy search procedures, and maintains model-agnosticism and computational efficiency. It is applicable to both evaluation-based and grouping-based ordinal tasks. Empirical results across multiple image and tabular ordinal datasets demonstrate that the proposed method achieves a superior trade-off between prediction set width and the severity of miscoverage compared to existing approaches.

Deep neural networks for ordinal regression often suffer from overconfident and poorly calibrated predictions due to cross-entropy loss, while their softmax outputs violate the ordinal unimodality constraint. Existing approaches focus on ordinal modeling but neglect calibration. This paper proposes the Ordinal-Calibrated Loss (OCL), the first loss function to integrate ordinal-aware calibration: it jointly employs soft ordinal encoding and ordinal-aware regularization to explicitly enforce unimodality and reliability of predicted probabilities during optimization. OCL requires no post-hoc calibration and ensures end-to-end calibration and ordinal consistency. Evaluated on four standard benchmarks, OCL achieves state-of-the-art calibration—reducing expected calibration error (ECE) by 28–41%—while maintaining top-tier classification accuracy.

Existing ordinal regression methods typically employ standard cross-entropy loss, disregarding the inherent ordinal structure among class labels; moreover, prevailing unimodality modeling strategies lack theoretical foundations and rely on heuristic designs. Method: This paper systematically characterizes the geometric structure of unimodal distributions within the probability simplex for the first time, proposes a theory-driven loss term based on set projection, and designs an end-to-end unimodal neural network architecture. The method strictly constrains predicted distributions to the unimodal set via differentiable projection, enabling efficient optimization. Contribution/Results: On multiple benchmark datasets, the proposed architecture achieves top-2 performance. The new loss significantly outperforms state-of-the-art baselines while maintaining high unimodality—establishing the first theoretically grounded unimodal modeling paradigm for ordinal regression.

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.

This work addresses the performance degradation in ordinal classification caused by existing methods' neglect of the natural order among classes. To this end, we propose ADABORD, a novel framework that, for the first time, integrates both an ordinal splitting criterion and an error function accounting for inter-class distances within AdaBoost. Specifically, ADABORD employs decision stumps based on an ordinal Gini impurity measure as base learners and introduces an absolute ranking probability score to more appropriately update sample and model weights. Experimental results on the TOC-UCO benchmark—the largest evaluation suite for ordinal classification—demonstrate that ADABORD significantly outperforms seven state-of-the-art methods, with particularly pronounced gains on datasets containing five or more ordinal classes.

This work addresses the vulnerability of conditional probability distributions in ordinal regression to noise and poor generalization, particularly under limited sample sizes. To mitigate these issues, the authors propose a scale-invariant unimodality regularization method that enforces strict unimodal constraints on predicted distributions. This approach significantly reduces variance while maintaining low bias, circumventing the unintended biases introduced by scale variations in existing methods. Empirical evaluations demonstrate that the proposed method consistently outperforms current state-of-the-art techniques across both small-sample and large-scale datasets, confirming that precise unimodal constraints effectively enhance the performance and robustness of ordinal regression models.

This work addresses the problem of robust rank estimation under structured ordinal label noise by proposing a stochastic ranking learning framework that explicitly models the uncertainty of ordinal labels as probabilistic ranking relations, thereby moving beyond the conventional assumption of deterministic labels. The method jointly optimizes a discriminative loss and a stochastic ranking loss, integrating discriminative instance-to-centroid interactions with probabilistic ranking constraints in the embedding space to effectively capture the distribution over multiple plausible rankings. Experimental results demonstrate that the proposed framework significantly enhances both the robustness and accuracy of rank estimation across diverse datasets and noise configurations.

This study systematically investigates position bias in large language models (LLMs) for ordinal classification, where predictions are unduly influenced by semantically irrelevant factors such as label order and example placement in prompts, compromising system stability. Through controlled experiments across five datasets, the authors evaluate ten state-of-the-art LLMs, analyzing eight factors spanning prompt design, task formulation, and model architecture, while comparing pointwise, pairwise, and listwise reasoning paradigms alongside multiple debiasing strategies. Findings reveal that all models exhibit sensitivity to three types of position bias; reducing label cardinality concurrently improves both accuracy and stability; listwise methods generally perform best but show inconsistent generalization; and existing debiasing techniques lack universal efficacy. Crucially, predictive performance and stability often diverge, with robustness depending on the entire system configuration rather than the model alone.