噪声影响的机会空间上学习理论的关键定理  

Key Theorem of Learning Theory with Samples Corrupted by Noise on Chance Space

作　　者：崔玮[1] 杜二玲[1] CUI Wei;DU Er-ling(China University of Geosciences Great Wall College Basic Teaching Depart ment,Baoding 071000,China)

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

出　　处：《模糊系统与数学》2018年第4期169-173,共5页Fuzzy Systems and Mathematics

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,引入了机会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,提出并证明了机会空间上样本受噪声影响的学习理论关键定理。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 ran- dom 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 chance 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 chance space and based on random samples corrupted by noise.

关 键 词：机会空间 噪声 经验风险最小化原则 关键定理 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]