Bayes Risk Consistency of Large Margin Binary Classification Methods - A Survey

In this paper we survey the Bayes Risk Consistency of various Large Margin Binary Classifiers. Many classification algorithms minimize a tractable convex surrogate φ of the 0-1 loss function. For e.g. the SVM (Support Vector Machine) and AdaBoost, which minimize the hinge loss and the exponential loss respectively. By imposing some sort of regularization conditions, it is possible to demonstrate the Bayes-risk consistency of methods based on minimizing the convex surrogate of the intractable 0-1 loss function. We have surveyed four papers which present such results in the binary classification setting, namely [BJM04], [Jia00], [Zha04] and [LV04].