  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.
