# Unimodal Distributions for Ordinal Regression

arXiv: https://arxiv.org/abs/2303.04547 · HTML: https://mlsanity.com/paper/2303.04547/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 36 references that are in the map.
- First posted on arXiv 8 Mar 2023.

## Builds on (most cited first, 8 of 8)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BACH: Grand Challenge on Breast Cancer Histology Images](https://mlsanity.com/paper/1808.04277/) (2018)
- [Unimodal probability distributions for deep ordinal classification](https://mlsanity.com/paper/1705.05278/) (2017)
- [DRvertGRADUATE: uncertainty-aware deep learning-based diabetic retinopathy grading in eye fundus images](https://mlsanity.com/paper/1910.11777/) (2019)
- [Class Distance Weighted Cross-Entropy Loss for Ulcerative Colitis Severity Estimation](https://mlsanity.com/paper/2202.05167/) (2022)
- [Robust Subjective Visual Property Prediction from Crowdsourced Pairwise Labels](https://mlsanity.com/paper/1501.06202/) (2015)
- [Encoding Visual Sensitivity by MaxPol Convolution Filters for Image Sharpness Assessment](https://mlsanity.com/paper/1808.00617/) (2018)
- [Non-parametric Uni-modality Constraints for Deep Ordinal Classification](https://mlsanity.com/paper/1911.10720/) (2019)

## Built on by (most cited first, 9 of 9)

- [dlordinal: a Python package for deep ordinal classification](https://mlsanity.com/paper/2407.17163/) (2024)
- [Ordinal-Aware Calibration for Ordinal Classification](https://mlsanity.com/paper/2410.15658/) (2024)
- [Learning Ordinality in Semantic Segmentation](https://mlsanity.com/paper/2407.20959/) (2024)
- [Reliable Conformal Prediction for Ordinal Classification Using the Ranked Probability Score](https://mlsanity.com/paper/2606.24959/) (2026)
- [Classifying Phonotrauma Severity from Vocal Fold Images with Soft Ordinal Regression](https://mlsanity.com/paper/2511.09702/) (2025)
- [Ordinal Semantic Segmentation Applied to Medical and Odontological Images](https://mlsanity.com/paper/2603.26736/) (2026)
- [From Kellgren-Lawrence to Calcium Pyrophosphate Crystal Deposition: A Soft-Labelling Framework for Knee Osteoarthritis Assessmen](https://mlsanity.com/paper/2605.28176/) (2026)
- [ADABORD: a novel AdaBoost approach for ordinal classification](https://mlsanity.com/paper/2607.21003/) (2026)
- [Unimodality-Promoting Regularized Learning for Ordinal Regression](https://mlsanity.com/paper/2608.08359/) (2026)

## Abstract (arXiv)

In many real-world prediction tasks, class labels contain information about the relative order between labels that are not captured by commonly used loss functions such as multicategory cross-entropy. Recently, the preference for unimodal distributions in the output space has been incorporated into models and loss functions to account for such ordering information. However, current approaches rely on heuristics that lack a theoretical foundation. Here, we propose two new approaches to incorporate the preference for unimodal distributions into the predictive model. We analyse the set of unimodal distributions in the probability simplex and establish fundamental properties. We then propose a new architecture that imposes unimodal distributions and a new loss term that relies on the notion of projection in a set to promote unimodality. Experiments show the new architecture achieves top-2 performance, while the proposed new loss term is very competitive while maintaining high unimodality.