# Unimodal probability distributions for deep ordinal classification

arXiv: https://arxiv.org/abs/1705.05278 · HTML: https://mlsanity.com/paper/1705.05278/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 May 2017.

## Built on by (most cited first, 28 of 28)

- [ZoeDepth: Zero-shot Transfer by Combining Relative and Metric Depth](https://mlsanity.com/paper/2302.12288/) (2023)
- [Ord2Seq: Regarding Ordinal Regression as Label Sequence Prediction](https://mlsanity.com/paper/2307.09004/) (2023)
- [Class Distance Weighted Cross-Entropy Loss for Ulcerative Colitis Severity Estimation](https://mlsanity.com/paper/2202.05167/) (2022)
- [CLIP-Lung: Textual Knowledge-Guided Lung Nodule Malignancy Prediction](https://mlsanity.com/paper/2304.08013/) (2023)
- [Recursively Conditional Gaussian for Ordinal Unsupervised Domain Adaptation](https://mlsanity.com/paper/2107.13467/) (2021)
- [Unimodal Distributions for Ordinal Regression](https://mlsanity.com/paper/2303.04547/) (2023)
- [Robust Image Ordinal Regression with Controllable Image Generation](https://mlsanity.com/paper/2305.04213/) (2023)
- [Meta Ordinal Regression Forest for Medical Image Classification with Ordinal Labels](https://mlsanity.com/paper/2203.07725/) (2022)
- [Meta ordinal weighting net for improving lung nodule classification](https://mlsanity.com/paper/2102.00456/) (2021)
- [Poisson Ordinal Network for Gleason Group Estimation Using Bi-Parametric MRI](https://mlsanity.com/paper/2407.05796/) (2024)
- [Discretizing Continuous Action Space with Unimodal Probability Distributions for On-Policy Reinforcement Learning](https://mlsanity.com/paper/2408.00309/) (2024)
- [Fusing Echocardiography Images and Medical Records for Continuous Patient Stratification](https://mlsanity.com/paper/2401.07796/) (2024)
- [OrderChain: Towards General Instruct-Tuning for Stimulating the Ordinal Understanding Ability of MLLM](https://mlsanity.com/paper/2504.04801/) (2025)
- [Controlling Class Layout for Deep Ordinal Classification via Constrained Proxies Learning](https://mlsanity.com/paper/2303.00396/) (2023)
- [Exploring Ordinality in Text Classification: A Comparative Study of Explicit and Implicit Techniques](https://mlsanity.com/paper/2405.11775/) (2024)
- [Remarks on Loss Function of Threshold Method for Ordinal Regression Problem](https://mlsanity.com/paper/2405.13288/) (2024)
- [Learning Ordinality in Semantic Segmentation](https://mlsanity.com/paper/2407.20959/) (2024)
- [Approximately Unimodal Likelihood Models for Ordinal Regression](https://mlsanity.com/paper/2510.00122/) (2025)
- [Reliable Conformal Prediction for Ordinal Classification Using the Ranked Probability Score](https://mlsanity.com/paper/2606.24959/) (2026)
- [Approximate Bayesian Computation for an Explicit-Duration Hidden Markov Model of COVID-19 Hospital Trajectories](https://mlsanity.com/paper/2105.00773/) (2021)
- [CORE: Learning Consistent Ordinal REpresentations for Image Ordinal Estimation](https://mlsanity.com/paper/2301.06122/) (2023)
- [Classifying Phonotrauma Severity from Vocal Fold Images with Soft Ordinal Regression](https://mlsanity.com/paper/2511.09702/) (2025)
- [Conveyance: A Versatile Framework for Learning in Structured Class Spaces](https://mlsanity.com/paper/2605.28420/) (2026)
- [Demographic Metadata as Construct-Irrelevant Noise in DistilBERT-Based Automated Essay Scoring](https://mlsanity.com/paper/2606.21066/) (2026)
- [Deep Neural Networks with Ordinal Loss for Medical Applications](https://mlsanity.com/paper/2606.25769/) (2026)
- [D3O: Dynamic Distribution Distillation for Ordinal Regression](https://mlsanity.com/paper/2607.23575/) (2026)
- [Unimodality-Promoting Regularized Learning for Ordinal Regression](https://mlsanity.com/paper/2608.08359/) (2026)
- [Differentiable Fuzzy Inference Layer: A Monotone, Compositional Ordinal Reasoning Head for Large Language Models](https://mlsanity.com/paper/2609.26113/) (2026)

## Abstract (arXiv)

Probability distributions produced by the cross-entropy loss for ordinal classification problems can possess undesired properties. We propose a straightforward technique to constrain discrete ordinal probability distributions to be unimodal via the use of the Poisson and binomial probability distributions. We evaluate this approach in the context of deep learning on two large ordinal image datasets, obtaining promising results.