PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

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.

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EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
ID Code:8981
Deposited By:Bob Williamson
Deposited On:21 February 2012