【作者】 辛国福；

【导师】 杨有龙；

【作者基本信息】 西安电子科技大学 ， 应用数学， 2011， 硕士

【摘要】 贝叶斯网络是概率论和图论有机融合的概率图形模型,已被广泛应用于人工智能、统计学习、因果识别等领域.如何有效地分析数据中的因果关系进行因果推断是数据分析中的研究热点问题.本文针对贝叶斯网络中的因果推断展开研究,主要工作有:首先,分析了描述贝叶斯网络中独立关系的d-分割和ud-分割的内在关系,得到d-分割是ud-分割的充分不必要条件,给出了d-分割和ud-分割同时成立的条件,利用分层排序可以得到一个贝叶斯网络的拓扑序,而且对于某些特殊的贝叶斯网络可以很方便的得到d-分割和ud-分割集来识别因果效应.其次,研究因果图模型中变量间的因果效应的识别和估计问题,并对前门准则和后门准则之间的关系进行了分析.最后,描述了SGS和PC结构学习算法,对它们的稳定性和复杂性进行了分析.在分析结构学习算法CI和FCI的基础上,通过一个构建的网络说明FCI算法存在缺陷,并对FCI算法进行了改进.更多还原

【Abstract】 Bayesian networks (BNs) are a marriage between probability theory and graphtheory, and thus are probabilistic graphical models. They are widely used in artificialintelligence, statistics learning and identifiability for causal effect. How to efficientanalyzing the relationship among nodes and then to causal reasoning is a central issuein dada analysis. This paper deals with causal reasoning in BNs, the main task is asfollows:Firstly, the relationship between d-separation and ud-separation which are twoimportant graph criteria in BNs is discussed in detail. The condition that directionalseparation is the sufficient condition for the unidirectional separation is obtained. Wepropose one condition that both directional separation and unidirectional separationhold. By using layer sorting the nodes of a Bayesian network, we can get a Bayesiannetwork’s topological sequence and find d-separation and ud-separation sets to indentifydirect causal effect quickly.What’s more, we use causal model to research the identifiability for causal effectamong nodes. The relationship between front-door and back-door criterion is analyzed.In addition, two structure learning algorithms for causal discovery are introduced,the correctness complexity and stability of SGS and PC are analyzed. It is proved by aspecially constructed network to show that the FCI algorithm is defected based on theanalysis of CI and FCI, a remedy of this algorithm is proposed.更多还原