Ordinal Regression

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Overview

Ordinal regression studies prediction when labels have a meaningful order, such as disease stages, proficiency levels, or quality ratings, so confusing neighboring categories is usually less costly than making a distant error. Common approaches include cumulative-link and threshold-based models, ordinal-aware losses and soft-label distributions, and pairwise or contrastive methods that learn rank differences; newer work also incorporates hierarchy, multimodal features, and generative models. Applications span medical grading, age and image-quality estimation, speech assessment, and structured preference prediction, with evaluation often using mean absolute error, ranked probability scores, or quadratic weighted kappa alongside accuracy. A central challenge is that category order is known but the distances between levels and the uncertainty of labels often are not, making calibration, class imbalance, and transfer across datasets persistent concerns.

Latest papers

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38 papers2 papers in the last four weeks, down 67% on the four weeks before. 0.0% of all new papers.

May 27, 2026

A novel ordinal multi-view aggregation scheme for oak defoliation

Forest decline driven by climate and biotic stressors threatens ecosystem functioning, making accurate monitoring of tree health essential. In this work, we address tree defoliation estimation as an ordinal classification problem using ground-level imagery. We propose a novel multi-view ensemble framework that aggregates predictions from Convolutional Neural Networks (CNNs) trained on different perspectives of individual trees (north, south, and crown). This approach leverages complementary visual information while preserving modelling consistency through a homogeneous ensemble design. A comprehensive evaluation is conducted by comparing multiple ordinal classification methods and analysing the contribution of each view and their combinations. Results show that modelling the ordinal structure of defoliation levels improves performance over nominal approaches, while the proposed multi-view ensemble consistently outperforms single-view and pairwise configurations. In particular, the three-view ensemble achieves the most robust and accurate predictions across all evaluation metrics. These findings highlight the potential of combining Deep Learning (DL), Ordinal Classification (OC), and multi-view aggregation for scalable, consistent, and objective forest health assessment in complex ecosystems such as Mediterranean dehesas.

Francisco Bérchez-Moreno, Ricardo Enrique Hernández-Lambraño, David Guijo-Rubio +4

Departamento de Ciencia de la Computación e Inteligencia Artificial, Universidad de Córdoba, Campus Universitario de Rabanales, Edificio Albert Einstein. Ctra. N-IV, Km. 396, Córdoba, 14071, Andalucía, Spain · Department of Forest Engineering, Laboratory of Dendrochronology, Silviculture and Global Change – DendrodatLab, Universidad de Córdoba, Campus Universitario de Rabanales. Ctra. N-IV, Km. 396, Córdoba, 14071, Andalucía, Spain · Departamento de Teoría de la Señal y Comunicaciones, Universidad de Alcala, Escuela Politécnica. Campus Universitario. Ctra. Madrid-Barcelona, Km. 33,600, Madrid, 28805, Madrid, Spain +1

Ensemble LearningMulti-View LearningRemote SensingOrdinal Regression
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Mar 21, 2026

Ordinal Semantic Segmentation Applied to Medical and Odontological Images

Semantic segmentation consists of assigning a semantic label to each pixel according to predefined classes. This process facilitates the understanding of object appearance and spatial relationships, playing an important role in the global interpretation of image content. Although modern deep learning approaches achieve high accuracy, they often ignore ordinal relationships among classes, which may encode important domain knowledge for scene interpretation. In this work, loss functions that incorporate ordinal relationships into deep neural networks are investigated to promote greater semantic consistency in semantic segmentation tasks. These loss functions are categorized as unimodal, quasi-unimodal, and spatial. Unimodal losses constrain the predicted probability distribution according to the class ordering, while quasi-unimodal losses relax this constraint by allowing small variations while preserving ordinal coherence. Spatial losses penalize semantic inconsistencies between neighboring pixels, encouraging smoother transitions in the image space. In particular, this study adapts loss functions originally proposed for ordinal classification to ordinal semantic segmentation. Among them, the Expanded Mean Squared Error (EXP_MSE), the Quasi-Unimodal Loss (QUL), and the spatial Contact Surface Loss using Signal Distance Function (CSSDF) are investigated. These approaches have shown promising results in medical imaging, improving robustness, generalization, and anatomical consistency.

Mariana Dória Prata Lima, Gilson Antonio Giraldi, Jaime S. Cardoso

1, 2National Laboratory for Scientific Computing, Petrópolis, Rio de Janeiro, Brazil. · 3INESC TEC, Faculty of Engineering, University of Porto, Porto, Portugal.

Semantic SegmentationMedical Image SegmentationOrdinal Regression
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Mar 18, 2026

Classifier Pooling for Modern Ordinal Classification

Ordinal data is widely prevalent in clinical and other domains, yet there is a lack of both modern, machine-learning based methods and publicly available software to address it. In this paper, we present a model-agnostic method of ordinal classification, which can apply any non-ordinal classification method in an ordinal fashion. We also provide an open-source implementation of these algorithms, in the form of a Python package. We apply these models on multiple real-world datasets to show their performance across domains. We show that they often outperform non-ordinal classification methods, especially when the number of datapoints is relatively small or when there are many classes of outcomes. This work, including the developed software, facilitates the use of modern, more powerful machine learning algorithms to handle ordinal data.

Noam H. Rotenberg, Andreia V. Faria, Brian Caffo

Department of Biomedical Engineering, Whiting School of Engineering, Johns Hopkins University, Baltimore, MD, USA. · Department of Radiology, School of Medicine, Johns Hopkins University, Baltimore, MD, USA. · 3*Department of Biostatistics, Bloomberg School of Public Health, Johns Hopkins University, Baltimore, MD, USA.

Ordinal Regression
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Mar 16, 2026

Decision-Level Ordinal Modeling for Multimodal Essay Scoring with Large Language Models

Automated essay scoring (AES) predicts multiple rubric-defined trait scores for each essay, where each trait follows an ordered discrete rating scale. Most LLM-based AES methods cast scoring as autoregressive token generation and obtain the final score via decoding and parsing, making the decision implicit. This formulation is particularly sensitive in multimodal AES, where the usefulness of visual inputs varies across essays and traits. To address these limitations, we propose Decision-Level Ordinal Modeling (DLOM), which makes scoring an explicit ordinal decision by reusing the language model head to extract score-wise logits on predefined score tokens, enabling direct optimization and analysis in the score space. For multimodal AES, DLOM-GF introduces a gated fusion module that adaptively combines textual and multimodal score logits. For text-only AES, DLOM-DA adds a distance-aware regularization term to better reflect ordinal distances. Experiments on the multimodal EssayJudge dataset show that DLOM improves over a generation-based SFT baseline across scoring traits, and DLOM-GF yields further gains when modality relevance is heterogeneous. On the text-only ASAP/ASAP++ benchmarks, DLOM remains effective without visual inputs, and DLOM-DA further improves performance and outperforms strong representative baselines.

Han Zhang, Jiamin Su, Li liu

Automated Essay ScoringOrdinal RegressionMultimodal Large Language Models
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Mar 12, 2026

Diabetic Retinopathy Grading with CLIP-based Ranking-Aware Adaptation:A Comparative Study on Fundus Image

Diabetic retinopathy (DR) is a leading cause of preventable blindness, and automated fundus image grading can play an important role in large-scale screening. In this work, we investigate three CLIP-based approaches for five-class DR severity grading: (1) a zero-shot baseline using prompt engineering, (2) a hybrid FCN-CLIP model augmented with CBAM attention, and (3) a ranking-aware prompting model that encodes the ordinal structure of DR progression. We train and evaluate on a combined dataset of APTOS 2019 and Messidor-2 (n=5,406), addressing class imbalance through resampling and class-specific optimal thresholding. Our experiments show that the ranking-aware model achieves the highest overall accuracy (93.42%, AUROC 0.9845) and strong recall on clinically critical severe cases, while the hybrid FCN-CLIP model (92.49%, AUROC 0.99) excels at detecting proliferative DR. Both substantially outperform the zero-shot baseline (55.17%, AUROC 0.75). We analyze the complementary strengths of each approach and discuss their practical implications for screening contexts.

Sungjun Cho

Hong Kong University of Science and Technology (HKUST), Hong Kong, China

Diabetic Retinopathy GradingRetinal Disease ClassificationVision Foundation Model AdaptationMedical VLMsFundus ImagingOrdinal Regression
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Mar 12, 2026

TornadoNet: Real-Time Building Damage Detection with Ordinal Supervision

We present TornadoNet, a comprehensive benchmark for automated street-level building damage assessment evaluating how modern real-time object detection architectures and ordinal-aware supervision strategies perform under realistic post-disaster conditions. TornadoNet provides the first controlled benchmark demonstrating how architectural design and loss formulation jointly influence multi-level damage detection from street-view imagery, delivering methodological insights and deployable tools for disaster response. Using 3,333 high-resolution geotagged images and 8,890 annotated building instances from the 2021 Midwest tornado outbreak, we systematically compare CNN-based detectors from the YOLO family against transformer-based models (RT-DETR) for multi-level damage detection. Models are trained under standardized protocols using a five-level damage classification framework based on IN-CORE damage states, validated through expert cross-annotation. Baseline experiments reveal complementary architectural strengths. CNN-based YOLO models achieve highest detection accuracy and throughput, with larger variants reaching 46.05% [email protected] at 66-276 FPS on A100 GPUs. Transformer-based RT-DETR models exhibit stronger ordinal consistency, achieving 88.13% Ordinal Top-1 Accuracy and MAOE of 0.65, indicating more reliable severity grading despite lower baseline mAP. To align supervision with the ordered nature of damage severity, we introduce soft ordinal classification targets and evaluate explicit ordinal-distance penalties. RT-DETR trained with calibrated ordinal supervision achieves 44.70% [email protected], a 4.8 percentage-point improvement, with gains in ordinal metrics (91.15% Ordinal Top-1 Accuracy, MAOE = 0.56). These findings establish that ordinal-aware supervision improves damage severity estimation when aligned with detector architecture. Model & Data: https://github.com/crumeike/TornadoNet

Robinson Umeike, Cuong Pham, Ryan Hausen +8

The University of Alabama · University of South Alabama · Johns Hopkins University +2

Disaster Damage AssessmentBuilding Damage AssessmentReal-Time Object DetectionOrdinal RegressionDetection Transformer
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Feb 25, 2026

Directed Ordinal Diffusion Regularization for Progression-Aware Diabetic Retinopathy Grading

Diabetic Retinopathy (DR) progresses as a continuous and irreversible deterioration of the retina, following a well-defined clinical trajectory from mild to severe stages. However, most existing ordinal regression approaches model DR severity as a set of static, symmetric ranks, capturing relative order while ignoring the inherent unidirectional nature of disease progression. As a result, the learned feature representations may violate biological plausibility, allowing implausible proximity between non-consecutive stages or even reverse transitions. To bridge this gap, we propose Directed Ordinal Diffusion Regularization (D-ODR), which explicitly models the feature space as a directed flow by constructing a progression-constrained directed graph that strictly enforces forward disease evolution. By performing multi-scale diffusion on this directed structure, D-ODR imposes penalties on score inversions along valid progression paths, thereby effectively preventing the model from learning biologically inconsistent reverse transitions. This mechanism aligns the feature representation with the natural trajectory of DR worsening. Extensive experiments demonstrate that D-ODR yields superior grading performance compared to state-of-the-art ordinal regression and DR-specific grading methods, offering a more clinically reliable assessment of disease severity. Our code is available on https://github.com/HovChen/D-ODR.

Huangwei Chen, Junhao Jia, Ruocheng Li +7

Zhejiang Key Laboratory of Accessible Perception and Intelligent Systems, College of Computer Science and Technology, Zhejiang University · Hangzhou Pujian Medical Technology Co., Ltd · Hangzhou Dianzi University +1

Diabetic Retinopathy GradingOrdinal Regression
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Aug 27, 2025

An Effective Strategy for Modeling Score Ordinality and Non-uniform Intervals in Automated Speaking Assessment

A recent line of research on automated speaking assessment (ASA) has benefited from self-supervised learning (SSL) representations, which capture rich acoustic and linguistic patterns in non-native speech without underlying assumptions of feature curation. However, speech-based SSL models capture acoustic-related traits but overlook linguistic content, while text-based SSL models rely on ASR output and fail to encode prosodic nuances. Moreover, most prior arts treat proficiency levels as nominal classes, ignoring their ordinal structure and non-uniform intervals between proficiency labels. To address these limitations, we propose an effective ASA approach combining SSL with handcrafted indicator features via a novel modeling paradigm. We further introduce a multi-margin ordinal loss that jointly models both the score ordinality and non-uniform intervals of proficiency labels. Extensive experiments on the TEEMI corpus show that our method consistently outperforms strong baselines and generalizes well to unseen prompts.

Tien-Hong Lo, Szu-Yu Chen, Yao-Ting Sung +1

Department of Computer Science and Information Engineering, National Taiwan Normal University · Department of Educational Psychology and Counseling, National Taiwan Normal University

Speech ProcessingOrdinal RegressionAutomated Spoken Language Assessment
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