摘要
进一步讨论了拟概率的一些性质,给出了拟概率空间上的拟随机变量及其分布函数、期望和方差的概念及若干性质;证明了拟概率空间上的Markov不等式、Chebyshev不等式和Khinchine大数定律;给出并证明了拟概率空间上学习理论的关键定理和学习过程一致收敛速度的界,把概率空间上的学习理论的关键定理和学习过程一致收敛速度的界推广到了拟概率空间,为系统地建立拟概率上的统计学习理论与构建支持向量机奠定了理论基础.
Some properties of quasi-probability are further discussed. The definitions and properties of quasi-random variable and its distribution function, expected value and variance are then presented. Markov inequality, Chebyshev＇s inequality and the Khinchine＇s law of large numbers on quasi-probability spaces are also proved. Then the key theorem of learning theory on quasiprobability spaces is proved, and the bounds on the rate of uniform convergence of learning process on quasi-probability spaces are constructed. The investigations will help lay essential theoretical foundations for the systematic and comprehensive development of the quasi-statistical learning theory.
出处
《计算机学报》
EI
CSCD
北大核心
2008年第3期476-485,共10页
Chinese Journal of Computers
基金
国家自然科学基金(60573069,60574077,60773062)
教育部科学技术研究重点项目计划(206012)
河北省自然科学基金(F2004000129)
河北省教育厅科研计划重点项目(2005001D)资助
关键词
拟概率
期望风险泛函
经验风险泛函
关键定理
一致收敛速度的界
quasi-probability
empirical risk functional
expected risk functional
key theorem
bounds on the rate of uniform convergence
