Statistical analysis of some multi-category large margin classification methods

The purpose of this paper is to investigate statistical properties of risk minimization based multicategory classification methods. These methods can be considered as natural extensions of binary large margin classification. We establish conditions that guarantee the consistency of classifiers obtained in the risk minimization framework with respect to the classification error. Examples are provided for four specific forms of the general formulation, which extend a number of known methods. Using these examples, we show that some risk minimization formulations can also be used to obtain conditional probability estimates for the underlying problem. Such conditional probability information can be useful for statistical inferencing tasks beyond classification.