On Classification-Calibration of Gamma-Phi Losses

Understand

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.