Composite Multiclass Losses
E Vermet, Bob Williamson and Mark Reid
In: NIPS 2011, December 2011, Grenada Spain.
We consider loss functions for multiclass prediction problems. We show when a multiclass loss can be expressed as a “composite proper 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 also show that the integral representation for binary proper losses can not be extended to multiclass losses. We subsume existing results on “classification calibration” by relating it to properness. We draw conclusions concerning the design of multiclass losses.
|EPrint Type:||Conference or Workshop Item (Paper)|
|Project Keyword:||Project Keyword UNSPECIFIED|
|Subjects:||Theory & Algorithms|
|Deposited By:||Wray Buntine|
|Deposited On:||21 February 2012|