论文信息 - On the Consistency of Multiclass Classification Methods

On the Consistency of Multiclass Classification Methods

Binary classification is a well studied special case of the classification problem. Statistical properties of binary classifiers, such as consistency, have been investigated in a variety of settings. Binary classification methods can be generalized in many ways to handle multiple classes. It turns out that one can lose consistency in generalizing a binary classification method to deal with multiple classes. We study a rich family of multiclass methods and provide a necessary and sufficient condition for their consistency. We illustrate our approach by applying it to some multiclass methods proposed in the literature.

Ambuj Tewari | Peter L. Bartlett | P. Bartlett | Ambuj Tewari

[1] J. Lamperti. ON CONVERGENCE OF STOCHASTIC PROCESSES , 1962 .

[2] 丸山徹. Convex Analysisの二,三の進展について , 1977 .

[3] Jason Weston,et al. Multi-Class Support Vector Machines , 1998 .

[4] Kristin P. Bennett,et al. Multicategory Classification by Support Vector Machines , 1999, Comput. Optim. Appl..

[5] Koby Crammer,et al. On the Algorithmic Implementation of Multiclass Kernel-based Vector Machines , 2002, J. Mach. Learn. Res..

[6] Michael I. Jordan,et al. Large Margin Classifiers: Convex Loss, Low Noise, and Convergence Rates , 2003, NIPS.

[7] Wenxin Jiang. Process consistency for AdaBoost , 2003 .

[8] Tong Zhang. Statistical behavior and consistency of classification methods based on convex risk minimization , 2003 .

[9] G. Lugosi,et al. On the Bayes-risk consistency of regularized boosting methods , 2003 .

[10] Yi Lin. Multicategory Support Vector Machines, Theory, and Application to the Classification of . . . , 2003 .

[11] Tong Zhang,et al. An Infinity-sample Theory for Multi-category Large Margin Classification , 2003, NIPS.

[12] Tong Zhang,et al. Statistical Analysis of Some Multi-Category Large Margin Classification Methods , 2004, J. Mach. Learn. Res..

[13] Ingo Steinwart,et al. Consistency of support vector machines and other regularized kernel classifiers , 2005, IEEE Transactions on Information Theory.