Deep Ordinal Regression using Optimal Transport Loss and Unimodal Output Probabilities

It is often desired that ordinal regression models yield unimodalpredictions. However, in many recent works this characteristic is eitherabsent, or implemented using soft targets, which do not guarantee unimodaloutputs at inference. In addition, we argue that the standard maximumlikelihood objective is not suitable for ordinal regression problems, and thatoptimal transport is better suited for this task, as it naturally captures theorder of the classes. In this work, we propose a framework for deep ordinalregression, based on unimodal output distribution and optimal transport loss.Inspired by the well-known Proportional Odds model, we propose to modify itsdesign by using an architectural mechanism which guarantees that the modeloutput distribution will be unimodal. We empirically analyze the differentcomponents of our proposed approach and demonstrate their contribution to theperformance of the model. Experimental results on eight real-world datasetsdemonstrate that our proposed approach consistently performs on par with andoften better than several recently proposed deep learning approaches for deepordinal regression with unimodal output probabilities, while having guaranteeon the output unimodality. In addition, we demonstrate that proposed approachis less overconfident than current baselines.