  Fisher-consistent loss functions play a fundamental role in the construction
of successful binary margin-based classifiers. In this paper we establish the
Fisher-consistency condition for multicategory classification problems. Our
approach uses the margin vector concept which can be regarded as a
multicategory generalization of the binary margin. We characterize a wide class
of smooth convex loss functions that are Fisher-consistent for multicategory
classification. We then consider using the margin-vector-based loss functions
to derive multicategory boosting algorithms. In particular, we derive two new
multicategory boosting algorithms by using the exponential and logistic
regression losses.
