  Gamma-Phi losses constitute a family of multiclass classification loss
functions that generalize the logistic and other common losses, and have found
application in the boosting literature. We establish the first general
sufficient condition for the classification-calibration (CC) of such losses. To
our knowledge, this sufficient condition gives the first family of nonconvex
multiclass surrogate losses for which CC has been fully justified. In addition,
we show that a previously proposed sufficient condition is in fact not
sufficient. This contribution highlights a technical issue that is important in
the study of multiclass CC but has been neglected in prior work.
