可信性空间上基于复模糊变量的学习过程一致收敛速度的界  

The bounds on the rate of uniform convergence of learning process based on complex fuzzy variable on credibility space

作　　者：田景峰[1] 张植明[2] 

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

出　　处：《华北电力大学学报（自然科学版）》2009年第5期106-112,共7页Journal of North China Electric Power University：Natural Science Edition

基　　金：国家自然科学基金资助项目(60773062);教育部科学技术研究重点项目(206012);华北电力大学校内科研基金(200911033);河北省自然科学基金(2008000633)

摘　　要：在统计学习理论中关于经验风险和实际风险的关系的重要结论被称为推广性的界,它是分析学习机器性能和发展新的学习算法的重要基础。学习过程一致收敛速度的界是推广性的界的重要组成部分。给出并证明了可信性测度空间上基于复模糊变量的一些性质,在此基础上给出并证明了可信性测度空间上基于复模糊变量的一致收敛速度的界。为系统建立可信性空间上复统计学习理论奠定了理论基础。In the statistical learning theory, the important conclusions about the relation between the empirical risk and practical risk are expressed in the form of the bounds of generalization. They become essential when analyzing the capacity of learning machines and developing new learning algorithms. The bounds on the rates of uniform convergence of learning process are important components of the bounds of generalization. Some properties of complex fuzzy variable were presented on credibility measure space. According to these properties, the bounds on the rates of uniform convergence of learning process based on complex fuzzy variable on credibility measure space were given and proven. The investigations lay essential theoretical foundations for the systematic and comprehensive development of the complex statistical learning theory on credibility space.

关 键 词：统计学习理论 一致收敛速度的界 可信性测度空间 复模糊变量 复统计学习理论 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程] O234[自动化与计算机技术—控制科学与工程]