Causal Reasoning In Bayesian Networks

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.