高维数据下的贝叶斯网络结构学习  

Bayesian Network Structure Learning under High Dimensional Data

作　　者：杨雨萌 黄琼华 汪四水[1] YANG Yu-meng;HUANG Qiong-hua;WANG Si-shui(School of Mathematical Sciences,Soochow University.Jiangsu Suzhou 215000,China)

机构地区：[1]苏州大学数学科学学院

出　　处：《数理统计与管理》2019年第6期1014-1025,共12页Journal of Applied Statistics and Management

基　　金：“十三五”江苏省重点学科统计学项目(GD10700117)

摘　　要：贝叶斯网络模型作为一种传统有效的大数据图模型,因其具有因果和概率性语义等特点受到学者们的广泛研究。为了解决基于高维数据构建贝叶斯网络的难题,本文提出了一种适用于高维数据的贝叶斯网络结构学习算法-LTB算法,该算法由Lasso、Tabu Search算法和BIC结合。首先,运用Lasso降低协变量的维数,筛选出与目标变量关系密切的协变量将作为贝叶斯网络的顶点。然后,选择Tabu Search作为元启发式算法,选择BIC作为计算得分的方法,两者结合构建全局最优的贝叶斯网络结构。实证分析表明,LTB算法应用于上证综指影响因素的研究,既可以获得上证综指与其影响因素间的因果关系,也可以利用条件概率得到上证综指影响因素间的组合方式。As a traditional and effective big data graph model,Bayesian network model has been extensively studied by scholars because of its causal and probabilistic semantics.In order to solve the problem of constructing Bayesian network based on high-dimensional data,this paper proposes a novel Bayesian network structure learning algorithm-LTB algorithm which is suitable for high-dimensional data.The algorithm is combined with Lasso,Tabu Search algorithm and BIC.First,by using Lasso to reduce the dimension of covariates,we can find out that the covariates closely related to the target variables will be the vertices of the Bayesian network.Then,TS is selected as the meta-heuristic algorithm and BIC is selected as the method to calculate the score.The two are combined to construct the globally optimal Bayesian network structure.Empirical analysis shows that the LTB algorithm applied to the research on the influencing factors of Shanghai Composite Index can not only obtain the causal relationship between Shanghai Composite Index and its influencing factors but also use the conditional probability to get the combination mode of influencing factors of Shanghai Composite Index.

关 键 词：贝叶斯网络 Lasso Tabu SEARCH BIC 上证综指 

分 类 号：O212[理学—概率论与数理统计]