贝叶斯网络的非忠实性分布  

Unfaithful distributions with respect to Bayesian networks

作　　者：杨有龙[1] 刘蔚[1] 吴艳[1] 

机构地区：[1]西安电子科技大学理学院,西安710071

出　　处：《智能系统学报》2009年第4期335-338,共4页CAAI Transactions on Intelligent Systems

基　　金：国家自然科学基金资助项目(60574075)

摘　　要：贝叶斯网络是图论和概率论有机融合的概率图形模型,主要用于统计推理和智能数据分析.理论上通常假设由基于分布的独立关系可推出基于图结构的d-分割,即贝叶斯网络上的分布是忠实的.针对布尔域上的贝叶斯网络,研究了非忠实分布的构成,提出了贝叶斯网络上分布延拓的概念,得到忠实分布与非忠实分布的平凡延拓均是非忠实分布.Bayesian networks are a marriage between probability theory and graph theory, and thus are probabilistic graphical models. They are mainly used for statistical inference and intelligent data analysis. It is usually supposed that the network retains the d-separation criterion that characterize graph structure from the independence constraints based on distribution, that is, the distribution is a faithful distribution with respect to a Bayesian network. In this paper, some unfaithful distributions are characterized with respect to discrete Bayesian networks in a Boolean domain. It was shown that distributions trivially expanded from faithfulness or unfaithfulness are unfaithful distributions with respect to Bayesian networks.

关 键 词：贝叶斯网络 忠实性分布 图形模型 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]