基于双重粗糙样本的统计学习理论的理论基础  

The Theoretical Foundations of Statistical Learning Theory of Birough Samples

作　　者：张植明[1] 田景峰[2] 

机构地区：[1]河北大学数学与计算机学院,保定071002 [2]华北电力大学科技学院,保定071051

出　　处：《应用数学学报》2009年第4期608-619,共12页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(60773062);教育部科学技术研究重点项目(206012);河北省自然科学基金(2008000633);河北省教育厅科研计划重点项目(2005001D)资助项目

摘　　要：本文介绍双重粗糙理论的基本内容;提出双重粗糙经验风险泛函,双重粗糙期望风险泛函,双重粗糙经验风险最小化原则等概念;最后证明基于双重粗糙样本的统计学习理论的关键定理并讨论学习过程一致收敛速度的界。为系统建立基于不确定样本的统计学习理论并构建相应的支持向量机奠定了理论基础。In this paper, firstly birough theory is introduced. Secondly some concepts such as birough empirical risk functional, birough expected risk functional and birough empirical risk minimization principle are proposed. Finally the key theorem of statistical learning theory based on birough samples is proved, and the bounds on the rate of uniform convergence of learning process are discussed. The investigations will help lay essential theoretical foundations for the systematic and comprehensive development of statistical learning theory and support vector machine based on uncertain samples.

关 键 词：双重粗糙样本 双重粗糙经验风险最小化原则 关键定理 一致收敛速度的界 

分 类 号：O29[理学—应用数学] O234[理学—数学]