相容的贝叶斯学习及其后验分布的渐近正态性  

THE ASYMPTOTIC NORMALITY OF POSTERIOR IN BAYESIAN LEARNING

作　　者：胡振宇[1] 林士敏[2] 陆玉昌[3] 

机构地区：[1]中国科学院软件研究所,北京100080 [2]广西师范大学数学与计算机科学学院,广西桂林541004 [3]清华大学计算机科学与技术系,北京100084

出　　处：《广西师范大学学报（自然科学版）》2004年第1期43-46,共4页Journal of Guangxi Normal University:Natural Science Edition

基　　金：清华大学智能技术与系统国家重点实验室开放课题资助项目(99002)

摘　　要：从计算学习理论的角度研究贝叶斯学习的相容性和后验分布的渐近正态性,给出了贝叶斯学习的正则条件,证明了在这些条件下贝叶斯学习不仅是相容的,而且后验分布是渐近正态的.由于正态分布计算相对简单,该结果为指派恰当有效的先验分布、寻找简化贝叶斯学习计算的方法提供了理论依据,给出的正则条件比Heyde与Johnstone的5个条件更为简化,便于应用.This paper studies the consistency and asymptotic normality of posterior in Bayesian learning.It presents a set of regular conditions for Bayesian learning,and proves that under these conditions Bayesian learning has not only consistency but also has normal distribution of posterior asymptotically.Because the computing of normal distribution is relatively simple,the results in this paper provide a theoretic basis for assessing resultful prior and methods to reduce the computing in Bayesian learning.The regular conditions presented in this paper are simpler than the 5 conditions given by Heyde and Johnstone,and more suitable for application.

关 键 词：机器学习 贝叶斯学习 相容性 渐近正态性 数据采掘 后验分布 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]