# An interpretable neural network-based non-proportional odds model for ordinal regression

arXiv: https://arxiv.org/abs/2303.17823 · HTML: https://mlsanity.com/paper/2303.17823/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 48 references that are in the map.
- First posted on arXiv 31 Mar 2023.

## Builds on (most cited first, 7 of 7)

- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [Deep Lattice Networks and Partial Monotonic Functions](https://mlsanity.com/paper/1709.06680/) (2017)
- [Certified Monotonic Neural Networks](https://mlsanity.com/paper/2011.10219/) (2020)
- [Deep Conditional Transformation Models](https://mlsanity.com/paper/2010.07860/) (2020)
- [Most Likely Transformations](https://mlsanity.com/paper/1508.06749/) (2015)
- [Deep transformation models: Tackling complex regression problems with neural network based transformation models](https://mlsanity.com/paper/2004.00464/) (2020)
- [Continuously Generalized Ordinal Regression for Linear and Deep Models](https://mlsanity.com/paper/2202.07005/) (2022)

## Built on by (most cited first, 1 of 1)

- [ADABORD: a novel AdaBoost approach for ordinal classification](https://mlsanity.com/paper/2607.21003/) (2026)

## Abstract (arXiv)

This study proposes an interpretable neural network-based non-proportional odds model (N3POM) for ordinal regression. N3POM is different from conventional approaches to ordinal regression with non-proportional models in several ways: (1) N3POM is defined for both continuous and discrete responses, whereas standard methods typically treat the ordered continuous variables as if they are discrete, (2) instead of estimating response-dependent finite-dimensional coefficients of linear models from discrete responses as is done in conventional approaches, we train a non-linear neural network to serve as a coefficient function. Thanks to the neural network, N3POM offers flexibility while preserving the interpretability of conventional ordinal regression. We establish a sufficient condition under which the predicted conditional cumulative probability locally satisfies the monotonicity constraint over a user-specified region in the covariate space. Additionally, we provide a monotonicity-preserving stochastic (MPS) algorithm for effectively training the neural network. We apply N3POM to several real-world datasets.