Continuously Generalized Ordinal Regression for Linear and Deep Models

TL;DR

This paper introduces a flexible, continuously generalized ordinal logistic regression model that improves over standard models by allowing class-specific effects, and extends it to deep learning with competitive results.

Contribution

It proposes a novel regularization approach for generalized ordinal regression, extending to deep models, and unifies existing models as special cases.

Findings

Outperforms standard ordinal logistic regression on benchmark datasets.

Achieves competitive or lower prediction error in deep learning settings.

Unifies multiple models within a single framework.

Abstract

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.