# Continuously Generalized Ordinal Regression for Linear and Deep Models

arXiv: https://arxiv.org/abs/2202.07005 · HTML: https://mlsanity.com/paper/2202.07005/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 43 references that are in the map.
- First posted on arXiv 14 Feb 2022.

## Builds on (most cited first, 6 of 6)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [Over the Air Deep Learning Based Radio Signal Classification](https://mlsanity.com/paper/1712.04578/) (2017)
- [Should we really use post-hoc tests based on mean-ranks?](https://mlsanity.com/paper/1505.02288/) (2015)
- [On the Consistency of Ordinal Regression Methods](https://mlsanity.com/paper/1408.2327/) (2014)

## Built on by (most cited first, 3 of 3)

- [An interpretable neural network-based non-proportional odds model for ordinal regression](https://mlsanity.com/paper/2303.17823/) (2023)
- [More Options for Prelabor Rupture of Membranes, A Bayesian Analysis](https://mlsanity.com/paper/2408.10876/) (2024)
- [Bayesian Meta-Analyses Could Be More: A Case Study in Trial of Labor After a Cesarean-section Outcomes and Complications](https://mlsanity.com/paper/2601.10089/) (2026)

## Abstract (arXiv)

Ordinal regression is a classification task where classes have an order and prediction error increases the further the predicted class is from the true class. The standard approach for modeling ordinal data involves fitting parallel separating hyperplanes that optimize a certain loss function. This assumption offers sample efficient learning via inductive bias, but is often too restrictive in real-world datasets where features may have varying effects across different categories. Allowing class-specific hyperplane slopes creates generalized logistic ordinal regression, increasing the flexibility of the model at a cost to sample efficiency. We explore an extension of the generalized model to the all-thresholds logistic loss and propose a regularization approach that interpolates between these two extremes. Our method, which we term continuously generalized ordinal logistic, significantly outperforms the standard ordinal logistic model over a thorough set of ordinal regression benchmark datasets. We further extend this method to deep learning and show that it achieves competitive or lower prediction error compared to previous models over a range of datasets and modalities. Furthermore, two primary alternative models for deep learning ordinal regression are shown to be special cases of our framework.