计算机工程与应用 ›› 2009, Vol. 45 ›› Issue (7): 59-64.DOI: 10.3778/j.issn.1002-8331.2009.07.019

• 研究、探讨 • 上一篇    下一篇

Sugeno测度空间基于复样本的统计学习理论

张植明1,田景峰2   

  1. 1.河北大学 数学与计算机学院,河北 保定 071002
    2.华北电力大学 科技学院,河北 保定 071051
  • 收稿日期:2008-01-17 修回日期:2008-03-31 出版日期:2009-03-01 发布日期:2009-03-01
  • 通讯作者: 张植明

Statistical learning theory of complex samples on Sugeno measure space

ZHANG Zhi-ming1,TIAN Jing-feng2   

  1. 1.College of Mathematics and Computer Sciences,Hebei University,Baoding,Hebei 071002,China
    2.College of Science and Technology,North China Electric Power University,Baoding,Hebei 071051,China
  • Received:2008-01-17 Revised:2008-03-31 Online:2009-03-01 Published:2009-03-01
  • Contact: ZHANG Zhi-ming

摘要: 引入复gλ随机变量、准范数的定义,给出了复gλ随机变量的期望和方差的概念及若干性质;证明了基于复gλ随机变量的马尔可夫不等式、契比雪夫不等式和辛钦大数定律;提出了Sugeno测度空间中复经验风险泛函、复期望风险泛函以及复经验风险最小化原则严格一致性等定义;证明并构建了基于复gλ随机样本的统计学习理论的关键定理和学习过程一致收敛速度的界,为系统建立基于复gλ随机样本的统计学习理论奠定了理论基础。

关键词: Sugeno测度空间, 准范数, 复经验风险最小化原则, 关键定理, 收敛速度的界

Abstract: Firstly,the definitions of complex gλ random variable and primary norm are introduced.Next the concepts and some properties of the mathematical expectation and variance of complex gλ random variables are provided.Secondly,for complex gλ random variables,a number of fundamental concepts such as e.g.,Markov’s inequalities,Chebyshev’s inequalities and a Khinchine’s law of large numbers are discussed.Finally,the definitions of the complex empirical risk functional,the complex expected risk functional and complex empirical risk minimization principle on Sugeno measure space are proposed.Then the key theorem of learning theory based on complex gλ random samples is proved,and the bounds on the rate of uniform convergence of learning process are constructed.The investigations help lay essential theoretical foundations for the systematic and comprehensive development of the statistical learning theory of complex gλ random samples.

Key words: Sugeno measure space, primary norm, complex empirical risk minimization principle, the key theorem, the bounds on the rate of convergence