Convexity of Proper Composite Binary Losses

A composite loss assigns a penalty to a realvalued prediction by associating the prediction with a probability via a link function then applying a class probability estimation (CPE) loss. If the risk for a composite loss is always minimised by predicting the value associated with the true class probability the composite loss is proper. We provide a novel, explicit and complete characterisation of the convexity of any proper composite loss in terms of its link and its "weight function" associated with its proper CPE loss.

• Type: Journal
• Year: 2010
• Where: JMLR
• Authors: Mark D. Reid, Robert C. Williamson
• Keywords: Class Probability, Composite Loss, JMLR 2010, Proper Composite Loss