若干基于模糊随机样本的SLT定理  

Several Theorems of Slt Based on Fuzzy-stochastic Samples

作　　者：何其慧[1] 高巍[2] 王翠翠[3] 毛军军[3] 

机构地区：[1]安徽经济管理学院基础部,安徽合肥230059 [2]安徽财经大学统计与应用数学学院,安徽蚌埠233030 [3]安徽大学数学科学学院,安徽合肥230601

出　　处：《数学的实践与认识》2012年第24期245-252,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(61073117);安徽省高等学校青年基金(2011SQRL186);安徽大学研究生创新项目(yfc100017)

摘　　要：基于模糊随机样本空间,提出了模糊随机期望风险泛函,模糊随机经验风险泛函和模糊随机经验风险泛函最小化原则等概念;基于模糊随机变量及其期望,讨论了相关概率不等式;最后证明了基于模糊随机样本统计学习理论的关键定理并研究了学习过程一致收敛速度的界等问题.Some concepts such as fuzzy-stochastic expected risk functional, fuzzy-stochastic empirical risk functional and fuzzy-stochastic empirical risk minimization principle had been proposed based on fuzzy-stochastic sample space; Some relevant probability inequalities had been discussed on fuzzy-stochastic variable and expectation; Finally, the key theorem of sta- tistical learning theory based on fuzzy-stochastic samples was proved, and problems such as the bounds on the rate of uniform convergence of learning process were investigated.

关 键 词：模糊随机样本 风险泛函 关键定理 一致收敛速度的界 

分 类 号：O212.2[理学—概率论与数理统计]