Bayesian Network Structure Learning And Application Based On Evolutionary Algorithm

Bayesian network can efficiently model complex problems under uncertain scenarios.As one of the most effective models in the field of uncertainty representation and inference,Bayesian network has been widely applied in various fields such as industry,healthcare,and machine learning.The correct Bayesian network structure is a prerequisite and guarantee for application,while learning the network structure from data is an NP-hard problem.Although researchers have proposed many algorithms for learning the structures of Bayesian networks from data in recent years,existing methods still suffer from problems such as low accuracy,low efficiency,and poor result diversity.In this paper,these problems are addressed as follows:(1)Firstly,to address the problem that it is difficult to efficiently evaluate orderings when searching for network structures in the ordering space,this paper proposes an approximate graph guided evolutionary Bayesian network structure learning algorithm(AGEA).AGEA first constructs an undirected approximate graph based on mutual information between random variables.And then a directed approximate graph is constructed by combining an individual encoded as ordering and the undirected approximate graph to improve the efficiency of evaluating orderings.Next,in the framework of evolutionary algorithm,the optimal ordering is searched by the proposed Kendall Tau distance based crossover operator and the inverse degree based mutation operator.The experiment results on 8 Bayesian networks of different sizes demonstrate that AGEA can better balance computation efficiency and accuracy compared to other algorithms.(2)Secondly,to address the problem of low diversity of results when existing algorithms learn multiple Bayesian network structures,this paper proposes a clustering-based evolutionary diverse Bayesian network structure learning algorithm(CEDA).CEDA first obtains the candidate edge set by the χ~2 test and generates the initial population based on them.Then,bit-flip mutation is performed on the individuals,and the individuals are clustered by the proposed clustering method based on Hamming distance.After that,intracluster crossover is performed via uniform crossover operator,and inter-cluster crossover is performed via the proposed adaptive crossover operator guided by inter-cluster distance.The above process is iterated until the inter-cluster distance is less than the preset value.And the optimal individuals from each cluster are selected to form the solution set according to the rules.Experiment results on 5 Bayesian networks of different sizes demonstrate that CEDA can not only learn better network structures but also ensure result diversity.(3)Finally,to address the problem that existing cognitive diagnosis models in education cannot meet the needs of error attribution,this paper proposes an evolutionary Bayesian error attribution network(EBEAN)for implementing fine-grained cognitive di-agnosis.EBEAN uses Bayesian network as the base model and learns the structure of knowledge concept structure graph(KCSG)by the proposed segmentation-based evolutionary Bayesian network structure learning algorithm(SE-BNSL).EBEAN can auto-matically generate error attribution reports based on students’wrong responses,provide students with fine-grained diagnosis reports that reveal error paths and path weights.Experiment results on 3 different real-world datasets verify the accuracy of EBEAN cognitive diagnosis and error attribution,and the fine-grained diagnosis reports generated by EBEAN are more interpretable than those generated by existing cognitive diagnosis models.