ordinal diagnosis prediction

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 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 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.

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.

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 existing regression methods struggle to handle arbitrary ordinal data—whether continuous or discrete—without imposing restrictive assumptions such as predefined transformation forms or distributional specifications, which limits their ability to model mean-variance relationships flexibly. To overcome this, the authors propose a monotonic transformation linear regression framework based on an extended rank likelihood, treating the mean-variance relationship as a nuisance parameter and thereby avoiding explicit specification of data type or transformation. Parameter estimation is carried out via Bayesian inference with Gibbs sampling, and conformal calibration is integrated to construct predictive intervals. Theoretical analysis and experiments demonstrate that the approach incurs no asymptotic information loss in both continuous and binary extremes and maintains valid marginal frequentist coverage even under model misspecification, achieving both estimation accuracy and prediction reliability.

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.

Existing predictability measures struggle to provide consistent numerical interpretations across diverse dynamical systems. To address this limitation, this work proposes the Gauge-Fixed Ordinal Network (GON), which formulates short-trajectory predictability as a five-level ordinal estimation problem. By introducing anchor points and a variance-based objective to fix the scoring gauge, and by integrating 2-jet geometric trajectory features with temporal convolutional networks, GON resolves for the first time the “gauge freedom” inherent in ordinal scoring. This enables a transferable and comparable scalar measure of predictability across systems. Experiments demonstrate that a pre-trained GON significantly outperforms models trained from scratch on five unseen dynamical systems, while zero-shot predictions retain the correct ordinal structure, confirming both the method’s efficacy and its strong generalization capability.

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 study addresses the challenges of limited interpretability, missing ordinal structure, and difficulty in handling zero values when modeling ordinal compositional data. To this end, it proposes a transformation-free linear regression framework. The method employs column-stochastic matrices to preserve simplex geometry and utilizes a weighted 1-Wasserstein distance as the loss function to incorporate ordinal information. Variable interactions are effectively characterized through a deterministic constraint model and a novel ordinal tensor product, while a Wasserstein coefficient of determination and an order-preserving index are introduced as diagnostic tools. Global optimality is efficiently achieved via linear programming. Both simulation studies and empirical applications demonstrate that the proposed framework delivers robust predictive performance alongside high interpretability.