Deep and interpretable regression models for ordinal outcomes. (February 2022)

• Record Type: Journal Article
• Authors: Kook, Lucas; Herzog, Lisa; Hothorn, Torsten; Dürr, Oliver; Sick, Beate
• Is Part Of: Pattern recognition. Volume 122(2022)
• Publication Date: 2022-02
• Subjects: Deep learning -- Interpretability -- Distributional regression -- Ordinal regression -- Transformation models; Pattern perception -- Periodicals; Perception des structures -- Périodiques; Patroonherkenning; 006.4
• DOI: 10.1016/j.patcog.2021.108263
• Languages: English
• ISSNs: 0031-3203

Abstract

Highlights: We present interpretable ordinal DL models incorporating image and tabular data. ONTRAMs are interpretable and achieve on-par performance with common DL models. Model components possess a direct statistical interpretation on the odds scale. ONTRAMs show a higher training efficiency for ordinal outcomes than softmax DL models. Abstract: Outcomes with a natural order commonly occur in prediction problems 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 (ontram s), which unite DL with classical ordinal regression approaches. ontram s 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.