The perils of being unhinged: On the accuracy of classifiers minimizing a noise-robust convex loss

TL;DR

This paper investigates the limitations of the unhinged loss function in binary classification, showing that minimizing it can lead to classifiers with accuracy no better than chance, even on simple data.

Contribution

It reveals that despite its robustness to noise, the unhinged loss may produce poor classifiers in terms of accuracy on linearly separable data.

Findings

Minimizing unhinged loss can result in classifiers with chance-level accuracy.

The robustness of unhinged loss does not guarantee high accuracy.

Simple data distributions can lead to suboptimal classifiers with this loss.

Abstract

Van Rooyen et al. introduced a notion of convex loss functions being robust to random classification noise, and established that the "unhinged" loss function is robust in this sense. In this note we study the accuracy of binary classifiers obtained by minimizing the unhinged loss, and observe that even for simple linearly separable data distributions, minimizing the unhinged loss may only yield a binary classifier with accuracy no better than random guessing.