# Unimodality-Promoting Regularized Learning for Ordinal Regression

arXiv: https://arxiv.org/abs/2608.08359 · HTML: https://mlsanity.com/paper/2608.08359/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 38 references that are in the map.
- First posted on arXiv 8 Aug 2026.

## Builds on (most cited first, 11 of 11)

- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [Rank consistent ordinal regression for neural networks with application to age estimation](https://mlsanity.com/paper/1901.07884/) (2019)
- [Unimodal probability distributions for deep ordinal classification](https://mlsanity.com/paper/1705.05278/) (2017)
- [Unimodal Distributions for Ordinal Regression](https://mlsanity.com/paper/2303.04547/) (2023)
- [Parallel Algorithm for Optimal Threshold Labeling of Ordinal Regression Methods](https://mlsanity.com/paper/2405.12756/) (2024)
- [Ordinal-Aware Calibration for Ordinal Classification](https://mlsanity.com/paper/2410.15658/) (2024)
- [Label Smoothing is Robustification against Model Misspecification](https://mlsanity.com/paper/2305.08501/) (2023)
- [Remarks on Loss Function of Threshold Method for Ordinal Regression Problem](https://mlsanity.com/paper/2405.13288/) (2024)
- [Approximately Unimodal Likelihood Models for Ordinal Regression](https://mlsanity.com/paper/2510.00122/) (2025)

## Abstract (arXiv)

Ordinal regression, also called ordinal classification, is classification of ordinal data, in which the underlying target variable is categorical and considered to have a natural ordinal relation. Previous works have indicated that, in many real-world ordinal data, the conditional probability distribution (CPD) of the target variable given a value of the explanatory variable would be unimodal in a large domain of the explanatory variable and close to be unimodal even in a remaining domain. Therefore, unimodality-promoting regularized learning (UPRL), which promotes a predicted CPD closer to be unimodal with the aim of decreasing a prediction variance without inducing much bias for ordinal data of the unimodality, is promising to improve the prediction performance especially with small-size training data. In this study, we show that previous UPRL methods promote a predicted CPD to not only become closer to be unimodal but also have a larger scale (in other words, be smoother or less-confident). Therefore, we develop a novel method that more strictly reflects the idea of UPRL and evades a scale-related bias, and verify through experimental comparison that the unimodality-promotion indeed contributes to improve the prediction performance. Additionally, while our proposed UPRL method could perform better for smaller-scale data or with larger-size training data compared to a previous UPRL method, our analysis explains this experimental observation in terms of the presence or absence of an unexpected scale-related bias.