基于链图模型的变量消除算法
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摘要
链图模型是一种同时存在有向边和无向边,但不存在有向圈的概率图模型,为变量之间复杂的关系提供了有力的框架。在链图模型中,基于贝叶斯网络中边缘分布的变量消除算法,根据链图模型的独立性,利用因子分解的方法,将算法推广到链图模型中,得到基于链图模型的变量消除算法。
The chain graph is a probabilistic graphical model with both directed edge and undirected edge,but without directed cycles.It provides a robust framework for complex relationships between variables.In the chain graph model,The variable elimination algorithm based on the Bayesian network,and calculates marginal distribution,depends on the independence of the chain graph model,and uses the method of factorization.Finally,the algorithm extends to the chain graph model,and then the variable elimination algorithm of the chain graph model is obtained.
The chain graph is a probabilistic graphical model with both directed edge and undirected edge,but without directed cycles.It provides a robust framework for complex relationships between variables.In the chain graph model,The variable elimination algorithm based on the Bayesian network,and calculates marginal distribution,depends on the independence of the chain graph model,and uses the method of factorization.Finally,the algorithm extends to the chain graph model,and then the variable elimination algorithm of the chain graph model is obtained.
引文
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[2]Zhang L,Ji Q.A Bayesian Network Model for Automatic and Interactive Image Segmentation[J].IEEE Transactions on Image Processing,2011,20(9):2582-2593.
[3]Bouckaert R R,Studeny'M.Chain graphs:Semantics and expressiveness[M].Froidevaux C,Kohlas J.Symbolic and Quantitative Approaches to Reasoning and Uncertainty.Berlin:Springer-verlag,1995:69-76.
[4]孟宪勇.图模型基础理论研究[D].沈阳:东北师范大学,2012.
[5]刘建伟,黎海恩,罗雄麟.概率图模型表示理论[J].计算机科学,2014,41(9):1-17.
[6]Frydenberg M.The Chain Graph Markov Property[J].Scandinavian Journal of Statistics,1990,17(4):333-353.
[7]Drton M.Discrete chain graph models[J].Bernoulli,2009,15(3):736-753.
[8]Studeny M,Bouckaert R R.On Chain Graph Models for Description of Conditional Independence Structures[J].Annals of Statistics,1998,26(4):1434-1495.
[9]Pena J M.Factorization,Inference and Parameter Learning in Discrete AMP Chain Graphs[M].Godo L.Symbolic and Quantitative Approaches to Reasoning with Uncertainty.Heidelberg:Springer International Publishing,2015:335-345.
[10]Pe1a J M.Unifying DAGs and UGs[EB/OL].[2018-03-01].https://arxiv.org/abs/1708.08722.
[11]Gottard A,Grilli L,Rampichini C.A Multilevel Chain Graph Model for the Analysis of Graduates’Employment[M].Fabbris L.Effectiveness of University Education in Italy.Heidelberg:Physica-Verlag HD,2007:169-181.
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[13]Dechter R.Bucket Elimination:A Unifying Framework for Probabilistic Inference[J].Constraints,1996,2(1):51-55.
[14]Cozman F G.Generalizing Variable Elimination in Bayesian Networks[C]//Workshop on Probabilistic Reasoning in Artificial Intelligence.Atibaia,2000:27-32.