Bayesian Network Structure Learning Algorithm Based On HFC And Recursive Decomposition

Bayesian network is a graph model structure combining probability theory and graph theory.It is widely used in many fields such as financial analysis,artificial intelligence and fault detection because of its advantages in uncertain knowledge representation and reasoning.The construction of Bayesian network structure is the basis of parameter learning and Bayesian inference.As Bayesian network structure learning is proved to be an NP problem.Thus,it has certain theoretical and practical value to research on effective Bayesian network structure learning algorithms.In this paper,the Bayesian network structure learning problem is deeply studied.The hierarchical fair competition model is applied to Bayesian network structure learning.At the same time,the idea of recursive decomposition is combined to solve the structure learning problem of complex Bayesian networks.The main work of this paper can be summarized as follows.First of all,this paper introduces the basic concepts related to Bayesian networks,as well as the mathematical model of Bayesian networks,and elaborates on the three basic methods of Bayesian network structure learning.Then,for the problem that the structure learning method based on search-andscoring is easy to fall into the local optimum,a structure learning method based on HFC(Hierarchical Fair Competition)model is proposed.Based on the idea of multigroup model and fitness density function,the algorithm improves the standard genetic algorithm.Firstly,according to the individual fitness value,the population is divided into different levels,and then evolutionary operations are carried out independently within the hierarchy,and migration operations are carried out between different levels to ensure the fairness of evolution and the diversity of the population.At the same time,random operators are added to the lowest-level population to continuously expand the search range and accelerate convergence.Finally,the effectiveness and computational speed advantage of the algorithm are proved by experiments.Finally,for the time complexity problem of structural learning of Bayesian networks with many nodes,a structural learning method based on HFC model and recursive decomposition is proposed.Firstly,the algorithm uses the chi-square test to judge the correlation of nodes and construct an undirected independent graph.Secondly,based on the idea of recursive decomposition,the minimum-weight vertex separators algorithm is applied to decompose the undirected independent graph into two subnetworks,and then the sub-network is decomposed into smaller sub-networks,which are continuously recursively decomposed until the sub-network cannot be decomposed.Then,based on the HFC model,the sub-network structure is learned separately.Finally,all the sub-networks are synthesized into a complete Bayesian network according to the V-structure invariant criterion.The experimental simulation proves the efficiency of the structure learning method based on HFC model and recursive decomposition for Bayesian network structure learning problems with large number of nodes.