受噪声影响的模糊样本学习理论的关键定理  

The Key Theorem of Learning Theory with Fuzzy Samples Corrupted by Noise

作　　者：哈明虎[1] 田静[2] 周彩丽[1] 李俊华[1] 

机构地区：[1]河北大学数学与计算机学院,河北保定071002 [2]河北大学质量技术监督学院,河北保定071002

出　　处：《河北大学学报（自然科学版）》2006年第6期561-564,581,共5页Journal of Hebei University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(60573069);河北省自然科学基金重点资助项目(F2004000129);河北省教育厅科学研究计划重点资助项目(2005001D);教育部科学技术研究重点项目(206012)

摘　　要：统计学习理论是一种较好的小样本统计理论,它所处理的数据是随机样本.考虑到现实世界的模糊性,把统计学习理论中的样本从随机样本扩展到模糊样本既有理论意义又有应用价值.然而目前基于模糊样本的统计学习理论的研究,总是假定所处理的样本不受噪声的影响,从而不会引起误差,但由于人为、环境等因素的影响,事实往往并非如此.基于此种考虑,本文给出了受噪声影响的模糊样本的统计学习理论的关键定理.Statistical learning theory is a small-sample statistics. The samples that can be handled by the Statistical Learning Theory are only random samples. In view of the fuzzy characteristics of real world, we transform the random samples into fuzzy random samples which has the extensively range. In the study of statistical learning theory with fuzzy random samples, samples which we deal with are supposed to be noise-free. But it is not always the case because of the influence of human or environmental factors. With a view is, this paper investigates the key theorem of statistical learning theory with fuzzy random samples corrupted by noise.

关 键 词：模糊期望风险泛函 模糊经验风险泛函 关键定理 

分 类 号：C81[社会学—统计学]