The Structural Learning Of Bayesian Network And Practice For Risk Analysis On Complex Systems

In term of complex systems,it always is hard to acquire abundant samples related to them and model them using the limited samples.Attempting to overcome the hardness,the paper proposes a Bayesian network structure learning algorithm named TT algorithm.Firstly,the paper conducts investigations on the penalties of scoring function,and reveals two attributes of penalties.The first is that with given search algorithm a penalty is applicable for only some situations.The second is that with given search algorithm,the greater penalties are usually good at learning more complex systems while the lower penalties tend to perform well in learning more simple systems.Based on these attributes and Boltzmann Entropy,a scoring function aiming at effectively learning from more complex systems is developed,named BE scoring function.And its effectiveness is demonstrated by the comparison among BE?BIC?AIC and MDL.Secondly,inspired by the mechanism of self-purification of water,the heuristic search algorithm named TT algorithm is proposed.TT is comprised of three steps.First step,a kind of constrain-based Bayesian Network structure learning algorithm is selected to learn a part of structure of a system.Second step,the remaining structure will be learnt using MIK algorithm.MIK algorithm defines the potential parents of node X as the all nodes except node X and its children.If the score for a potential parent is greatest among all scores that have been made,the potential parent is defined as the parent of node X(i.e.elitism strategy).If the score for a potential parent is not the greatest among all scores,the potential parent is defined as the parent of node X with a probability P_a,and P_a is the divide between the mutual information of node X and the potential parent and sum of mutual information of node X and each of its parents determined using elitism strategy.Third step,the Hill-Climbing method is employed to heuristically search for the entire structure.Additionally,to determine whether a score-based Bayesian network structure learning algorithm can converge to global optimum or not,two criterion are developed:parents are kept according to elitism strategy and the probability that any one of non-global optimums turns into global optimum is greater than zero.Applying TT,K2 and Hill-Climbing to learning Alarm network,and the results present that TT algorithm is able to learning a network with highest accuracy.Finally,TT algorithm is employed to learn two cases related to safety risks,and the evaluations on the outputs furtherly validate the effectiveness of TT algorithm.