Composite Multiclass Losses
Elodie Vernet, Bob Williamson and Mark Reid
In: NIPS2011, Granada(2011).
We consider loss functions for multiclass prediction problems. We show when
a multiclass loss can be expressed as a “proper composite loss”, which is the
composition of a proper loss and a link function. We extend existing results for
binary losses to multiclass losses. We determine the stationarity condition, Bregman
representation, order-sensitivity, existence and uniqueness of the composite
representation for multiclass losses. We subsume existing results on “classification
calibration” by relating it to properness and show that the simple integral
representation for binary proper losses can not be extended to multiclass losses.