受噪声影响的复拟随机样本的STL关键定理  

Key theorem of statistical learning theory with complex quasi-random samples corrupted by noise

作　　者：杜二玲[1] 李俊华[2] 

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]河北大学数学与信息科学学院,河北保定071002

出　　处：《河北大学学报（自然科学版）》2015年第5期449-452,共4页Journal of Hebei University(Natural Science Edition)

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)

摘　　要：引入了拟概率空间上复拟随机样本受噪声影响的复经验风险泛函、复期望风险泛函、复经验风险最小化原则以及严格一致性的定义,提出并证明了拟概率空间上复拟随机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的复拟随机样本的统计学习理论奠定了基础.Some new concepts, such as complex empirical risk functional, complex expected risk func- tional, complex empirical risk minimization principle, and strict consistency built on quasi-probability space and based on complex quasi-random samples corrupted by noise are introduced. The key theorem of learning theory is given and proved on quasi-probability space and based on complex quasi-random samples corrupted by noise. The investigations will help lay essential theoretical foundations for the systematic and comprehensive development of the complex quasi-random samples corrupted by noise.

关 键 词：复拟随机样本 噪声 复经验风险最小化原则 关键定理 

分 类 号：O29[理学—应用数学] TP181[理学—数学]