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arXiv · 1505.07634

Learning with Symmetric Label Noise: The Importance of Being Unhinged

Brendan van Rooyen·Aditya Krishna Menon·Robert C. Williamson
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Abstract

Convex potential minimisation is the de facto approach to binary classification. However, Long and Servedio [2010] proved that under symmetric label noise (SLN), minimisation of any convex potential over a linear function class can result in classification performance equivalent to random guessing. This ostensibly shows that convex losses are not SLN-robust. In this paper, we propose a convex, classification-calibrated loss and prove that it is SLN-robust. The loss avoids the Long and Servedio [2010] result by virtue of being negatively unbounded. The loss is a modification of the hinge loss, where one does not clamp at zero; hence, we call it the unhinged loss. We show that the optimal unhinged solution is equivalent to that of a strongly regularised SVM, and is the limiting solution for any convex potential; this implies that strong l2 regularisation makes most standard learners SLN-robust. Experiments confirm the SLN-robustness of the unhinged loss.

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Brendan van Rooyen, Aditya Krishna Menon, Robert C. Williamson. 2015-05-28. Learning with Symmetric Label Noise: The Importance of Being Unhinged. https://arxiv.org/abs/1505.07634

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