Learning Bayesian Network Structure Using Genetic Algorithm with Consideration of the Node Ordering via Principal Component Analysis

‎The most challenging task in dealing with Bayesian networks is learning their structure‎. ‎Two classical approaches are often used for learning Bayesian network structure;‎ ‎Constraint-Based method and Score-and-Search-Based one‎. ‎But neither the first nor the second one are completely satisfactory‎. ‎Therefore the heuristic search such as Genetic Algorithms with a fitness score function is considered for learning Bayesian network structure‎. ‎To assure the closeness of the genetic operators‎, ‎the ordering among variables (nodes) must be determined.

‎In this paper‎, ‎we determine the  node ordering by considering the Principal Component Analysis (PCA)‎. ‎For this purpose we first determine the appropriate correlation between variables and then use the absolute value of variable's coefficients in the first component‎. ‎It means that a node X_i can only have the node X_j as a parent‎, ‎if the absolute value of   coefficient X_j in first component will be higher than X_i.  ‎We then use the Genetic Algorithm with fitness score BIC regarding the  node ordering  to construct the Bayesian Network. ‎Experimental results over well-known networks  Asia‎, ‎Alarm and Hailfinder  show that our new technique  has higher accuracy and better degree of data matching‎.  ‎In addition‎,  ‎we apply our technique to the  real data set which is related to Bank's debtor that owe over 500 million Rials to Bank Maskan (Housing Bank) in Iran‎. ‎Results also show that the proposed technique has greater modeling power than other node ordering techniques such as   Hruschka et al. (2007), Chen et al. (2008) and K2 algorithm‎.