The Convexity and Design of Composite Multiclass Losses
  We consider composite loss functions for multiclass prediction comprising a proper (i.e., Fisher-consistent) loss over probability distributions and an inverse link function. We establish conditions for their (strong) convexity and explore the implications. We also show how the separation of concerns afforded by using this composite representation allows for the design of families of losses with the same Bayes risk. 
Mark Reid (The Australian National University and NICTA), Robert   Williamson (The Australian National University and NICTA)...
cs.LG stat.ML