Classification with Gaussians and convex loss Ⅱ:improving error bounds by noise conditions  

作　　者：XIANG DaoHong 

机构地区：[1]Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China

出　　处：《Science China Mathematics》2011年第1期165-171,共7页中国科学：数学（英文版）

摘　　要：We continue our study on classification learning algorithms generated by Tikhonov regularization schemes associated with Gaussian kernels and general convex loss functions. Our main purpose of this paper is to improve error bounds by presenting a new comparison theorem associated with general convex loss functions and Tsybakov noise conditions. Some concrete examples are provided to illustrate the improved learning rates which demonstrate the effect of various loss functions for learning algorithms. In our analysis, the convexity of the loss functions plays a central role.We continue our study on classification learning algorithms generated by Tikhonov regularization schemes associated with Gaussian kernels and general convex loss functions. Our main purpose of this paper is to improve error bounds by presenting a new comparison theorem associated with general convex loss functions and Tsybakov noise conditions. Some concrete examples are provided to illustrate the improved learning rates which demonstrate the effect of various loss functions for learning algorithms. In our analysis, the convexity of the loss functions plays a central role.

关 键 词：reproducing kernel Hilbert space binary classification general convex loss Tsybakov noise condition Sobolev space 

分 类 号：O211.67[理学—概率论与数理统计] TP311.13[理学—数学]