## Statistical Behavior and Consistency of Classification Methods based on Convex Risk Minimization (2001)

Citations: | 113 - 6 self |

### BibTeX

@MISC{Zhang01statisticalbehavior,

author = {Tong Zhang},

title = {Statistical Behavior and Consistency of Classification Methods based on Convex Risk Minimization},

year = {2001}

}

### Years of Citing Articles

### OpenURL

### Abstract

We study how close the optimal Bayes error rate can be approximately reached using a classification algorithm that computes a classifier by minimizing a convex upper bound of the classification error function. The measurement of closeness is characterized by the loss function used in the estimation. We show that such a classification scheme can be generally regarded as a (non maximum-likelihood) conditional in-class probability estimate, and we use this analysis to compare various convex loss functions that have appeared in the literature. Furthermore, the theoretical insight allows us to design good loss functions with desirable properties. Another aspect of our analysis is to demonstrate the consistency of certain classification methods using convex risk minimization.