# Deep and interpretable regression models for ordinal outcomes

arXiv: https://arxiv.org/abs/2010.08376 · HTML: https://mlsanity.com/paper/2010.08376/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Oct 2020.

## Built on by (most cited first, 4 of 4)

- [A New PHO-rmula for Improved Performance of Semi-Structured Networks](https://mlsanity.com/paper/2306.00522/) (2023)
- [Distributional Gradient Boosting Machines](https://mlsanity.com/paper/2204.00778/) (2022)
- [Transformation Models for Flexible Posteriors in Variational Bayes](https://mlsanity.com/paper/2106.00528/) (2021)
- [Single-shot Bayesian approximation for neural networks](https://mlsanity.com/paper/2308.12785/) (2023)

## Abstract (arXiv)

Outcomes with a natural order commonly occur in prediction tasks and often the available input data are a mixture of complex data like images and tabular predictors. Deep Learning (DL) models are state-of-the-art for image classification tasks but frequently treat ordinal outcomes as unordered and lack interpretability. In contrast, classical ordinal regression models consider the outcome's order and yield interpretable predictor effects but are limited to tabular data. We present ordinal neural network transformation models (ONTRAMs), which unite DL with classical ordinal regression approaches. ONTRAMs are a special case of transformation models and trade off flexibility and interpretability by additively decomposing the transformation function into terms for image and tabular data using jointly trained neural networks. The performance of the most flexible ONTRAM is by definition equivalent to a standard multi-class DL model trained with cross-entropy while being faster in training when facing ordinal outcomes. Lastly, we discuss how to interpret model components for both tabular and image data on two publicly available datasets.