Reid, Mark D.Williamson, Robert C.2026-01-012026-01-011532-4435https://hdl.handle.net/1885/733798930A composite loss assigns a penalty to a real-valued 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.8en201084862287353