拟概率空间上样本受噪声影响的SLT关键定理  

Key Theorem of Learning Theory with Samples Corrupted by Noise on Quasi-probability Space

作　　者：杜二玲[1] 王英新[2] 李俊华[3] 

机构地区：[1]中国地质大学长城学院基础课教学部,河北保定071000 [2]承德石油高等专科学校社科与数理部,河北承德067000 [3]河北大学数学与信息科学学院,河北保定071002

出　　处：《模糊系统与数学》2015年第6期119-123,共5页Fuzzy Systems and Mathematics

基　　金：河北省教育厅科研项目(QN20131055);河北省高等学校科学技术研究项目(Z2013038);中国地质大学长城学院科研项目(ZDCYK014017)

摘　　要：概率空间上基于随机样本的统计学习理论被公认为是解决小样本学习问题的最佳理论,但它难以处理非概率空间上基于受噪声影响的随机样本学习问题。基于此,引入了拟概率空间上样本受噪声影响的经验风险泛函、期望风险泛函、经验风险最小化原则严格一致性的定义,提出并证明了拟概率空间上样本受噪声影响的学习理论关键定理,为系统建立拟概率空间上基于噪声影响下的随机样本的统计学习理论奠定了基础。Statistical learning theory based on the random sample is considered as the best theory for solving the small sample learning problems on probability spaces. But it is difficult to deal with random samples learning problems when samples are corrupted by noise on non-probability spaces. In consideration of these facts, some new concepts, such as empirical risk functional, expected risk functional, and strict consistency of the empirical risk minimization principle built on quasi-probability space and based on random samples corrupted by noise, are introduced in this paper. The key theorem of learning theory is given and proved on quasi-probability space and based on random samples corrupted by noise. The investigations will help lay essential theoretical foundations for the systematic and comprehensive develooment of the random samples corrupted by noise.

关 键 词：拟概率空间 噪声 经验风险最小化原则 关键定理 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]