全图与无带图的等价性研究
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摘要
为解决含有隐变量和选择偏差的有向无圈图在多元统计分析中处理随机变量过程时的不稳定性,以全图的稳定结构与独立模型为基础,通过全图模型的分离准则、边缘化算法与条件化算法,讨论了全图模型与其无带图分支的差异,研究了结构精简的无带图分支及其分离准则,提出在对某些特定边进行重复时,全图与无带图的分离准则是等价的。在这种情形下无带图可以克服有向无圈图的局限性。
When dealing with random variables in the process of multivariate statistical analysis,the instability of directed acyclic graphs which have hidden or selected variables will cause much inconvenience.In order to solve the problem,a series of MC graphs was introduced.Based on its stable structure and independent model,the separation criteria as well as algorithms for marginalization and conditioning of MC graphs was presented.Next the differences of the MC graph and ribbonless graph were discussed.The separation of ribbonless graph which own a simpler structure was also studied.Finally the equivalence of MC graph and ribbonless graph when repeating certain edges was proven.Through these procedures,the limitation of directed acyclic graph had been overcome.
When dealing with random variables in the process of multivariate statistical analysis,the instability of directed acyclic graphs which have hidden or selected variables will cause much inconvenience.In order to solve the problem,a series of MC graphs was introduced.Based on its stable structure and independent model,the separation criteria as well as algorithms for marginalization and conditioning of MC graphs was presented.Next the differences of the MC graph and ribbonless graph were discussed.The separation of ribbonless graph which own a simpler structure was also studied.Finally the equivalence of MC graph and ribbonless graph when repeating certain edges was proven.Through these procedures,the limitation of directed acyclic graph had been overcome.
引文
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[2] Youlong Y,Yan W.On the properties of concept classes induced by multivalued bayesian networks[J].Information Sciences,2012,184(1):155-165.
[3] Bencic F M,Zarko I P.Distributed Ledger Technology:Blockchain Compared to Directed Acyclic Graph[C]//38th IEEE International Conference on Distributed Computing Systems,Vienna,Austria,July 2-6,2018.IEEE Computer Society,2018,1569-1570.
[4] Sadeghi K.Stable mixed graphs[J/OL].[2013-12-17].https://arxiv.org/pdf/1110.4168.pdf.Bernoulli,2001,19(5B):2330-2358.
[5] Richardson T,Spirtes P.Ancestral graph markov models[J].Annals of Statistics,2002,30:962-1030.
[6] Box G E P,Hunter J S,Hunter W G.Statistics for experimenters:an introduction to design,data analysis,and model building[M].New York:Wiley series in probability and mathematical statistics,1978.
[7] Alvarez M D L,Lane D M.A Hidden Markov Model application with Gaussian Mixture emissions for fault detection and diagnosis on a simulated AUV platform[C]//OCEANS 2016MTS/IEEE Monterey,CA,USA,September 19-23,2016.OCEANS,2016,1-4.
[8] Chen S,Gao F,Liu T.Load identification based on Factorial Hidden Markov Model and online performance analysis.13th IEEE International Conference on Automation Science and Engineering,Xi’an,China,August 20-23,2017[C]//IEEE Conf CASA,2017,1249-1253.
[9] Dumont T.Context Tree Estimation in Variable Length Hidden Markov Models[J].IEEE.Trans.Information Theory,2014,60:3196-3208.
[10]Koster J T A.Marginalizing and conditioning in graphical models[J].Bernoulli,2002,8(6):817-840.
[11]Wermuth N.Probability distributions with summary graph structure[J].Bernoulli,2011,17:845-879.
[12]Ali T,Richardson R A,Spirtes P.Markov equivalence for ancestral graph[J].Annals of Statistics,2009,37:2808-2837.
[13]Kiiveri T P,Speed H,Carlin J B.Recursive causal models[J].J.Austral.Math.Soc.(Series A),1984,36:30-52.
[14]Hallonquist N.Graphical models:An extension to random graphs,trees and other objects[D].New York:University of Cornell,2017.
[15]Sadeghi K.Graphical representation of independence structure[D].Cambridge:University of Oxford,2012.