Deep and interpretable regression models for ordinal outcomes

TL;DR

This paper introduces ONTRAMs, a novel deep learning framework that combines the interpretability of classical ordinal regression with the flexibility of deep neural networks for mixed data types, improving training efficiency and interpretability.

Contribution

The paper proposes ONTRAMs, a new class of models that unify deep learning with ordinal regression, enabling effective handling of mixed data types with interpretable components.

Findings

ONTRAMs match the performance of standard multi-class DL models on ordinal tasks.

ONTRAMs are faster to train for ordinal outcomes.

Model components can be interpreted for both tabular and image data.

Abstract

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.