【作者】 孙晓静；

【导师】 哈明虎； 田大增；

【作者基本信息】 河北大学 ， 应用数学， 2012， 硕士

【摘要】 统计学习理论是建立在概率空间上基于实随机变量的。不确定统计学习理论是统计学习理论的拓广，它是建立在概率空间上基于实或非实随机变量，或者是建立在非概率空间上基于非实随机变量的。无论是统计学习理论，还是其拓广的不确定统计学习理论都是建立在某一种空间上(如，概率空间、可能性空间、可信性空间、Sugeno空间、不确定空间等)基于实或非实随机变量的，尚难以处理乘积空间(如，机会空间、P×P空间)上基于相应混合变量的统计学习问题。基于此，本文在机会空间和P×P空间上分别讨论了基于相应混合变量的统计学习理论基础。在机会空间和P×P空间上，首先，分别给出并证明了基于相应混合变量的学习理论的关键定理；其次，分别讨论了基于相应混合变量的学习过程一致收敛速度的界；最后分别构建了基于相应混合变量的结构风险最小化原则并讨论了收敛速率的渐近界。更多还原

【Abstract】 Statistical learning theory is based on real random variable in probability space.Uncertain statistical learning theory is an extension of the statistical learning theory, which isbased on the real or non-real random variables in probability space or based on non-randomvariables in non-probability space. Statistical learning theory and uncertain statistical learningtheory are based on real or non-real variables in a certain space (for example, probabilityspace, possibility space, credibility space, Sugeno space, uncertain space) and it is hardly todeal with the learning problems based on corresponding hybrid variables in product space(such as chance space and P×P space). Based on this, the theoretical foundations of statisticallearning theory based on corresponding hybrid variables in chance space and P×P space arediscussed. First of all, the key theorems based on corresponding hybrid variables in chancespace and P×P space are given and proved respectively; Secondly, the bounds on the rate ofuniform convergence of learning processes based on corresponding hybrid variables in chancespace and P×P space are discussed respectively. Finally, structural risk minimizationprinciples based on corresponding hybrid variables in chance space and P×P space areconstructed respectively, and the asymptotic bounds on the rate of convergence based oncorresponding hybrid variables in chance space and P×P space are presented respectively.更多还原