Learning with Symmetric Label Noise: The Importance of Being Unhinged

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

Restoring stability in a neglected acetabular fracture with dual mobility total hip arthroplasty: a case report

Neglected acetabular fractures present with varied degrees of soft tissue and bone loss and distorted anatomy resulting in high hip centres. The basic principles of achieving stability and restoring motion are to augment the acetabular bone loss, prevent protrusio in the long term and use a prosthesis that prevents dislocation. We report a case of a 22 year old neglected acetabular fracture managed successfully with a femoral head autograft, anti protrusio cage and dual mobility total hip arthroplasty