贝叶斯网络诱导的内积空间  

Inner Product Spaces for Bayesian Networks

作　　者：白旭英[1,2] 杨有龙[1] 

机构地区：[1]西安电子科技大学理学院,陕西西安710071 [2]西北农林科技大学理学院,陕西杨凌712100

出　　处：《电子科技》2009年第7期1-4,8,共5页Electronic Science and Technology

基　　金：国家自然科学基金资助项目(60574075)

摘　　要：概率模型和核函数相结合的方法是学习系统的热点研究领域,贝叶斯网络是重要的一类概率图形模型。文中主要讨论了变量取值在布尔域上的两类分类任务,重点讨论了几个常见贝叶斯网络诱导的内积空间的最低维数,为解决一些常见的分类问题提供了理论依据。文中通过分析概念类的VC维来确定其欧几里德维数的下界,VC维还可用于估计贝叶斯网络概念类的复杂性和判断概念类的分类性能。There has been a remarkable interest in learning systems that combine the key advantages of probabilistic models and kernel functions. Bayesian networks are one of the major probabilistic graphical models. We focus on two-label classification tasks over the Boolean domain. Emphasis is put on the lowest dimension of inner product spaces induced by several common cases of Bayesian networks, which serves as a theoretical foundation for the solution of common problems. The lower bounds are obtained by analyzing the VC dimension of the concept class associated with the Bayesian network. VC dimension can also be used to estimate the complexity of the concept class induced by Bayesian networks and judge the performance of the classification of the concept class.

关 键 词：贝叶斯网络 内积空间 线性排列 VC维数 欧几里德维数 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]