The Annals of Statistics
- Ann. Statist.
- Volume 32, Number 1 (2004), 56-85.
Statistical behavior and consistency of classification methods based on convex risk minimization
We study how closely 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 (nonmaximum-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. This study sheds light on the good performance of some recently proposed linear classification methods including boosting and support vector machines. It also shows their limitations and suggests possible improvements.
Ann. Statist. Volume 32, Number 1 (2004), 56-85.
First available in Project Euclid: 12 March 2004
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Zhang, Tong. Statistical behavior and consistency of classification methods based on convex risk minimization. Ann. Statist. 32 (2004), no. 1, 56--85. doi:10.1214/aos/1079120130. http://projecteuclid.org/euclid.aos/1079120130.