Composite Multiclass Losses
Elodie Vernet, Ens de Cachan, Robert C. Williamson, Mark D. Reid Anu · ANU Open Research (Australian National University) · 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. 1