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.
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