人机结合的贝叶斯网建模方法研究
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摘要
贝叶斯网是20世纪80年代提出的不确定性推理方法,是用来表示变量之间连接概率的图形模式,它为因果关系提供了一种自然而有效的表达方式。贝叶斯网具备概率推理能力强、语义清晰、易于理解等技术特点,可以发现数据集中潜在的关系和模式,因此在数据挖掘中显示出独特的优越性。正是基于这一出发点,本文将贝叶斯网建模方法作为一个核心研究内容,通过系统的理论研究,为贝叶斯网的建模和实际应用提供有力的依据。
本文致力于贝叶斯网的理论和建模方法的研究,在前人工作的基础上,提出了一些新的建模思路。全文研究了如下几个问题：
(1)建模方法的研究
研究贝叶斯网的学习方法,针对机器学习方法搜索空间大,收敛速度慢的缺点,讨论如何在学习的过程中融合专家的知识,先利用专家的先验知识选择“好的”网络结构,再利用样本数据求精,修正专家知识,以加快学习速度,很好的实现了人机结合。
(2)不完备数据下的结构学习
数据缺失,是一种很正常的现象。现实训练数据集在采集时难免会因为技术等问题存在着数据记录中具体变量的具体属性值缺失的现象。
数据缺失和网络结构未知情况下学习贝叶斯网问题本身就存在重要的现实意义。如不能很好地解决,那么就说明贝叶斯网距离广泛的应用还有很大的距离。
(3)探索初始网络
在目前有关文献中关于数据缺失下学习贝叶斯网问题都会涉及到初始网络。这个初始网络到底如何给出?它在学习贝叶斯网整个过程中所扮演的角色又是如何?诸多文献并没有给出统一意见。本文通过引入知识图的作为初始网络进行研究。
(4)贝叶斯网在水文预报中的应用
研究贝叶斯网在水文预报中的应用,通过所建模型,为决策提供支持。
Bayesian networks are the method for uncertainty reasoning and knowledge representation that was advanced at the end of the 20th Century. It is a kind of probabilistic graphical model to represent the relationships between variables. It provides an effective and natural way to represent casual relationships. It is one of most effective theory models in finding the relationship and mode among the data sets because it has a strong ability for probabilistic reasoning and the characteristic of easy understanding to humans. In this paper, it focuses on the Bayesian networks modeling method, and establishes a systemic method based on the theoretical research. All of these may provide advantageous basis for construction and application of Bayesian networks.
In this dissertation I dedicate to the research of Bayesian Network's theory and the method for structure leaning。In order to enhance modeling efficiency when dealing with complex issues, it advances new thinking routes for modeling on the ground of ancestor's work. The entire thesis can be divided into four parts.
(1) Studying for constructing model
Research on Bayesian network learning, it found that machine learning methods have a large search space, at the slow pace of convergence. Discuss how to learn Bayesian network with the expert knowledge. The first step is use the knowledge of experts to choose "good" network, then Re-use sample data refinement, as amended expertise to accelerate the pace of learning, achieve Man-machine combination.
(2) Learning structure under incomplete data
Missing data is a normal phenomenon. Training data sets in real time is inevitable because of technical problems such as the existence of specific variables and specific values in the data record are missing.
In the case of lacking in data and unknowing in network structure, learning Bayesian network has important practical significance. If not well resolved, there is a lot of distance from the wide range of applications in Bayesian network.
(3) Exploring the initial network
In the current literature, learning Bayesian networks with incomplete data are related to the initial network. How is the initial network been given? Which role is the initial network in the whole process of learning Bayesian network? Literature has not given a lot of consensus. The dissertation use knowledge map as an initial network.
(4) Bayesian network in the forecasting
The dissertation research the, prediction of flood through the Bayesian network, in order to support decision-making.
本文致力于贝叶斯网的理论和建模方法的研究,在前人工作的基础上,提出了一些新的建模思路。全文研究了如下几个问题：
(1)建模方法的研究
研究贝叶斯网的学习方法,针对机器学习方法搜索空间大,收敛速度慢的缺点,讨论如何在学习的过程中融合专家的知识,先利用专家的先验知识选择“好的”网络结构,再利用样本数据求精,修正专家知识,以加快学习速度,很好的实现了人机结合。
(2)不完备数据下的结构学习
数据缺失,是一种很正常的现象。现实训练数据集在采集时难免会因为技术等问题存在着数据记录中具体变量的具体属性值缺失的现象。
数据缺失和网络结构未知情况下学习贝叶斯网问题本身就存在重要的现实意义。如不能很好地解决,那么就说明贝叶斯网距离广泛的应用还有很大的距离。
(3)探索初始网络
在目前有关文献中关于数据缺失下学习贝叶斯网问题都会涉及到初始网络。这个初始网络到底如何给出?它在学习贝叶斯网整个过程中所扮演的角色又是如何?诸多文献并没有给出统一意见。本文通过引入知识图的作为初始网络进行研究。
(4)贝叶斯网在水文预报中的应用
研究贝叶斯网在水文预报中的应用,通过所建模型,为决策提供支持。
Bayesian networks are the method for uncertainty reasoning and knowledge representation that was advanced at the end of the 20th Century. It is a kind of probabilistic graphical model to represent the relationships between variables. It provides an effective and natural way to represent casual relationships. It is one of most effective theory models in finding the relationship and mode among the data sets because it has a strong ability for probabilistic reasoning and the characteristic of easy understanding to humans. In this paper, it focuses on the Bayesian networks modeling method, and establishes a systemic method based on the theoretical research. All of these may provide advantageous basis for construction and application of Bayesian networks.
In this dissertation I dedicate to the research of Bayesian Network's theory and the method for structure leaning。In order to enhance modeling efficiency when dealing with complex issues, it advances new thinking routes for modeling on the ground of ancestor's work. The entire thesis can be divided into four parts.
(1) Studying for constructing model
Research on Bayesian network learning, it found that machine learning methods have a large search space, at the slow pace of convergence. Discuss how to learn Bayesian network with the expert knowledge. The first step is use the knowledge of experts to choose "good" network, then Re-use sample data refinement, as amended expertise to accelerate the pace of learning, achieve Man-machine combination.
(2) Learning structure under incomplete data
Missing data is a normal phenomenon. Training data sets in real time is inevitable because of technical problems such as the existence of specific variables and specific values in the data record are missing.
In the case of lacking in data and unknowing in network structure, learning Bayesian network has important practical significance. If not well resolved, there is a lot of distance from the wide range of applications in Bayesian network.
(3) Exploring the initial network
In the current literature, learning Bayesian networks with incomplete data are related to the initial network. How is the initial network been given? Which role is the initial network in the whole process of learning Bayesian network? Literature has not given a lot of consensus. The dissertation use knowledge map as an initial network.
(4) Bayesian network in the forecasting
The dissertation research the, prediction of flood through the Bayesian network, in order to support decision-making.
引文
[1]徐计.基于贝叶斯网络的数据挖掘研究[D].天津：师范大学,2008
[2]马壮,杨善林,胡小建.贝叶斯网结构学习的研究现状及发展趋势[J].合肥：工业大学学报,2005,8
[3]Chow C K, Liu C N. Approximating discrete probability distributions with dependence trees[J]. IEEE Transactions on Information Theory,1968,14(3):462-467
[4]Pearl J. Probabilistic reasoning in intelligent systems:networks of plausible inference[M]. San Mateo, California:Morgan Kaufmann Publishers,1988:117-133
[5]Sampath Srinivas, Stuart Russell, Alice Agogino. Automated construction of sparse Bayesian networks from unstructured probabilistic models and domain information[C]. Proceedings of the Fifth Annual Conference on Uncertainty in Artificial Intelligence, Amsterdam, North Holland,1990:295-308
[6]Wermuth N, Lauritzen S. Graphical and recursive models for contingency tables[J]. Biometrika,1983,70(3):537-552
[7]R.M.Fung, S.L.Crawford. Constructor:a system for the induction of probabilistic models[C]. Proceedings of the Seventh National Conference on Artificial Intelligence, Boston, MA,1990:762-769
[8]Cooper G F, Herskovits E A. Bayesian method for the induction of probabilistic networks from data[J]. Machine Learning,1992,9(4):309-347
[9]Remco R. Bouckaert. A stratified simulation scheme for inference in Bayesian belief networks[C]. Proceedings of the Tenth Annual Conference on Uncertainty in Artificial Intelligence, Seattle, WA,1994:110-117
[10]Suzuki J. Learning Bayesian belief networks based on the MDL principle:an efficient algorithm using the branch and bound technique[C]. Proceedings of the International Conference on Machine Learning, Bally, Italy,1996:463-470
[11]Lam W, Bacchus F. Learning Bayesian belief networks:an approach based on the MDL principle[J]. Computational Intelligence,1994,10(3):269-293
[12]David Heckerman, Dan Geiger and David M. Chickering. Learning Bayesian Networks:The Combination of Knowledge and Statistical Data[J]. Machine Learning, 1995,25(3):197-243
[13]David Heckerman. A Bayesian approach for learning causal networks[C]. Proceedings of Eleventh Conference on Uncertainty in Artificial Intelligence, San Francisco,1995:285-295
[14]N. Friedman, M. Goldszmidt. Learning Bayesian networks with local structure[C]. Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence, Portland, Oregon,1996:252-262
[15]刘大有,王飞,卢奕南,薛万欣,王松听.基于遗传算法的Bayesian网络结构学习研究[J].计算机研究与发展,2001：38(8)
[16]Singh M, Valtorta M. Construction of Bayesian network structures form data: a brief survey and an efficient algorithm[J]. International Journal of Approximate Reasoning,1995,12(2):111-131
[17]董立岩.贝叶斯网络应用基础研究[D].吉林：吉林大学,2008
[18]Cooper. Probabilistic inference using belief network is NP-hard[J]. Artificial Intelligence,1990(42):393-405
[19]D. Paul and L. Michael. Approximating Probabilistic Inference in Bayesian Belief Network is NP-hand[J]. Artificial Intelligence,1993,60(1):141-153
[20]M.P.Wellman, J.S.Breese, and R.P.Goldman. From knowledge bases to decision model[J]. The Knowledge Engineering Review,1992,7(1):35-53
[21]胡笑旋.贝叶斯网建模技术及其在决策中的应用[D].合肥：工业大学,2006
[22]赵海丰.关联规则挖掘及贝叶斯网表示研究[D].重庆：重庆大学,2007
[23]张连文,郭海鹏.贝叶斯网引论[M].科学出版社,2006
[24]Mitchell T. Machine Learning [M].New York:The McGraw-Hill Companies, Inc,1997:184～199
[25]冀俊忠,刘椿年,沙志强.贝叶斯网模型的学习、推理和应用[J].计算机工程与应用,2003.5
[26]刘大有等,知识系统中的不确定性和模糊性处理的数值方法[J].吉林大学出版社,2000
[27]R Dechter. Bucket elimination:A unifying framework for reasoning[J]. Artificial Intelligence,1999,113(1/2):41-85
[28]N. L. Zhang, D. Poole. Exploiting causal independence in Bayesian network inference[J]. Journal of Artificial Intelligence Research,1996:301-328
[29]F. G. Cozman. Generalizing variable elimination in Bayesian networks[J]. Proceedings of the BERAMIA/SBIA Workshops,2000:21-26
[30]Ann Becker and Dan Geiger, Approximate Algorithms for the Loop Cutset Problem[J]. Proceedings of 10th Uncertainty in Artificial Intelligence,1994
[31]R.Shachter, B.D'Ambrosio, and B.DelFavero. Symbolic probabilistic inference in belief networks[C]. In proceedings Eighth National Conference on AI, AAAI,1990:126-131
[32]R. Dechter, Bucket elemination:A unifying framework for probabilistic inference[C]. Proc. of thel2th Conference on Uncertainty in Artificial Intelligence, Morgan Kaufmann, San Francisco,1996:211-219
[33]Amesty P, DavisT, Duff I. An approximate minimum degree ordering algorithm [J]. AIAM Journal of Matrix Analysis and Aplications,1996,17(4): 886-905
[34]CorcoranAL, Wainwright R L LibGA. A user-friendly workbench for order-based genetic algorithm research[J]. In Proc,1993
[35]Lauritzen, S. L., and Spiegelhalter, D. J., Local computations with probabilities on graphical structures and their application to expert systems[J]. Journal of the Royal Statistical Society B,1988:157-224
[36]Jensen, F.V, Madsen, A.L., LAZY propagation:A junction tree inference algorithm based on lazy evaluation[J]. Articial Intelligence,1999:113,203-245
[37]Cecil Huang and Adnan Darwiche. Inference in belief networks:A procedural guide[J]. International Journal of Approximate Reasoning,1996:225-263
[38]田凤占,张宏伟,陆玉昌,石纯一.多模块贝叶斯网中推理的简化.计算机研究与发展[J].2003：1230-1237
[39]Skaanning C, Jensen F V. Printer Troubleshooting Using Bayesian Networks[J]. Industrial and Engineering Application of Artificial Intelligence and Expert Systems, New Orleans, USA,2000
[40]刘启元,张聪,沈一栋.信度网近似推理算法[J].计算机科学,2001,28
[41]Tomas Hrycej, Gibbs Sampling in Bayesian Networks[J].Arrificial Intelligence,46(1990):351-363
[42]Neal R M. Probabilistic inference using Markov chain Monte Carlo methods[J]. Department of Computer Science, University of Toronto,1993
[43]Pearl J. Addendum:Evidential Reasoning using stochastic simulation of causal models[J]. Artificial Intelligence,1987,33
[44]C. Jensen, A. Kong, and U. Kjaerul.Blocking gibbs sampling in very large probabilistic expert systems. International Journal of Human Computer Studies[J]. Special Issue on Real-World Applications of Uncertain Reasoning.,1995:647-666
[45]Dagum P, Luby M. An Optimal Approximation for Bayesian Inference[J]. Artificial Intelligence,1993,60:141-153
[46]Fung R, Chang K-C. Weighting and integration evidence for stochastic simulation in Bayesian networks[J]. In:Uncertainty in Artificial Intelligence 5, Elsevier, Amsterdam, The Netherlands,1990:209-219
[47]David Poole, Probabilitic Conflicts in a Search algorithm for estimating postrior probabilities in Bayesian Networks[J].Artificial Intelligence,88(1996):69-100
[48]Neil M, Fenton N, Nielsen L. Building large-scale Bayesian networks[J]. The Knowledge Engineering Review,2000
[49]Heckerman D, Geiger D, Chickering D M. Learning Bayesian networks:the combination of knowledge and statistical data[J]. Machine Learning,1995
[50]M. Singh. Learning Bayesian Networks from Incomplete Data[J]. In AAAI97, 1997:27-31
[51]N. Friedman. Learning Belief Networks in the Presence of Missing Values and Hidden Variables[C]. In Proc.14th International Conference on Machine Learning, Morgan Kaufmann,1997:125-133
[52]A. Dempster, N. Laird, and D. Rubin. Maximum Likelihood from Incomplete Data via the EM Algorithm[J]. Journal of the Royal Statistical Society,1977,39(1): 1-38
[53]G.J. Mclachlan and T. Krishnan. The EM Algorithm and Extensions[J]. Wiley Series in Probability and Satistics,1997
[54]廖学清.数据缺失下学习贝叶斯网的研究[D].苏州：苏州大学,2007
[55]贾海洋.贝叶斯网学习若干问题研究[D].吉林：吉林大学,2007
[56]D.Spiegelhalter, S.Lauritzen. Sequential updating of conditional probabilities on directed graphical structures[J].Networks,1990, vol.20:579-605
[57]R.Little, D.Rubin, Statical Analysis with Missing Data[J].New York:John Willey & Sons,1987
[58]童立,马远良.设计模式在基于组件的框架设计中的应用[J].计算机工程与应用,(17)2002：123-124
[59]Valerie Issarny, Luc Bellissard, Michel Riveill, etc. Component-Based Programming of Distributed Applications[J]. Lecture Notes in Computer Science, Vol.1752,2000:328-349
[60]J.Cheng, R.Greniner, J.Kelly, D.Bell, W.R.Liu. Learing Bayesian networks from data:An information-theory based approach[J]. Artificial Intellifence,2002, vol.137:43-90
[61]J.Rissanen, Stochastic Complexity in Statistical Inquiry[J].River Edge, NJ:World Scientific,1989
[2]马壮,杨善林,胡小建.贝叶斯网结构学习的研究现状及发展趋势[J].合肥：工业大学学报,2005,8
[3]Chow C K, Liu C N. Approximating discrete probability distributions with dependence trees[J]. IEEE Transactions on Information Theory,1968,14(3):462-467
[4]Pearl J. Probabilistic reasoning in intelligent systems:networks of plausible inference[M]. San Mateo, California:Morgan Kaufmann Publishers,1988:117-133
[5]Sampath Srinivas, Stuart Russell, Alice Agogino. Automated construction of sparse Bayesian networks from unstructured probabilistic models and domain information[C]. Proceedings of the Fifth Annual Conference on Uncertainty in Artificial Intelligence, Amsterdam, North Holland,1990:295-308
[6]Wermuth N, Lauritzen S. Graphical and recursive models for contingency tables[J]. Biometrika,1983,70(3):537-552
[7]R.M.Fung, S.L.Crawford. Constructor:a system for the induction of probabilistic models[C]. Proceedings of the Seventh National Conference on Artificial Intelligence, Boston, MA,1990:762-769
[8]Cooper G F, Herskovits E A. Bayesian method for the induction of probabilistic networks from data[J]. Machine Learning,1992,9(4):309-347
[9]Remco R. Bouckaert. A stratified simulation scheme for inference in Bayesian belief networks[C]. Proceedings of the Tenth Annual Conference on Uncertainty in Artificial Intelligence, Seattle, WA,1994:110-117
[10]Suzuki J. Learning Bayesian belief networks based on the MDL principle:an efficient algorithm using the branch and bound technique[C]. Proceedings of the International Conference on Machine Learning, Bally, Italy,1996:463-470
[11]Lam W, Bacchus F. Learning Bayesian belief networks:an approach based on the MDL principle[J]. Computational Intelligence,1994,10(3):269-293
[12]David Heckerman, Dan Geiger and David M. Chickering. Learning Bayesian Networks:The Combination of Knowledge and Statistical Data[J]. Machine Learning, 1995,25(3):197-243
[13]David Heckerman. A Bayesian approach for learning causal networks[C]. Proceedings of Eleventh Conference on Uncertainty in Artificial Intelligence, San Francisco,1995:285-295
[14]N. Friedman, M. Goldszmidt. Learning Bayesian networks with local structure[C]. Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence, Portland, Oregon,1996:252-262
[15]刘大有,王飞,卢奕南,薛万欣,王松听.基于遗传算法的Bayesian网络结构学习研究[J].计算机研究与发展,2001：38(8)
[16]Singh M, Valtorta M. Construction of Bayesian network structures form data: a brief survey and an efficient algorithm[J]. International Journal of Approximate Reasoning,1995,12(2):111-131
[17]董立岩.贝叶斯网络应用基础研究[D].吉林：吉林大学,2008
[18]Cooper. Probabilistic inference using belief network is NP-hard[J]. Artificial Intelligence,1990(42):393-405
[19]D. Paul and L. Michael. Approximating Probabilistic Inference in Bayesian Belief Network is NP-hand[J]. Artificial Intelligence,1993,60(1):141-153
[20]M.P.Wellman, J.S.Breese, and R.P.Goldman. From knowledge bases to decision model[J]. The Knowledge Engineering Review,1992,7(1):35-53
[21]胡笑旋.贝叶斯网建模技术及其在决策中的应用[D].合肥：工业大学,2006
[22]赵海丰.关联规则挖掘及贝叶斯网表示研究[D].重庆：重庆大学,2007
[23]张连文,郭海鹏.贝叶斯网引论[M].科学出版社,2006
[24]Mitchell T. Machine Learning [M].New York:The McGraw-Hill Companies, Inc,1997:184～199
[25]冀俊忠,刘椿年,沙志强.贝叶斯网模型的学习、推理和应用[J].计算机工程与应用,2003.5
[26]刘大有等,知识系统中的不确定性和模糊性处理的数值方法[J].吉林大学出版社,2000
[27]R Dechter. Bucket elimination:A unifying framework for reasoning[J]. Artificial Intelligence,1999,113(1/2):41-85
[28]N. L. Zhang, D. Poole. Exploiting causal independence in Bayesian network inference[J]. Journal of Artificial Intelligence Research,1996:301-328
[29]F. G. Cozman. Generalizing variable elimination in Bayesian networks[J]. Proceedings of the BERAMIA/SBIA Workshops,2000:21-26
[30]Ann Becker and Dan Geiger, Approximate Algorithms for the Loop Cutset Problem[J]. Proceedings of 10th Uncertainty in Artificial Intelligence,1994
[31]R.Shachter, B.D'Ambrosio, and B.DelFavero. Symbolic probabilistic inference in belief networks[C]. In proceedings Eighth National Conference on AI, AAAI,1990:126-131
[32]R. Dechter, Bucket elemination:A unifying framework for probabilistic inference[C]. Proc. of thel2th Conference on Uncertainty in Artificial Intelligence, Morgan Kaufmann, San Francisco,1996:211-219
[33]Amesty P, DavisT, Duff I. An approximate minimum degree ordering algorithm [J]. AIAM Journal of Matrix Analysis and Aplications,1996,17(4): 886-905
[34]CorcoranAL, Wainwright R L LibGA. A user-friendly workbench for order-based genetic algorithm research[J]. In Proc,1993
[35]Lauritzen, S. L., and Spiegelhalter, D. J., Local computations with probabilities on graphical structures and their application to expert systems[J]. Journal of the Royal Statistical Society B,1988:157-224
[36]Jensen, F.V, Madsen, A.L., LAZY propagation:A junction tree inference algorithm based on lazy evaluation[J]. Articial Intelligence,1999:113,203-245
[37]Cecil Huang and Adnan Darwiche. Inference in belief networks:A procedural guide[J]. International Journal of Approximate Reasoning,1996:225-263
[38]田凤占,张宏伟,陆玉昌,石纯一.多模块贝叶斯网中推理的简化.计算机研究与发展[J].2003：1230-1237
[39]Skaanning C, Jensen F V. Printer Troubleshooting Using Bayesian Networks[J]. Industrial and Engineering Application of Artificial Intelligence and Expert Systems, New Orleans, USA,2000
[40]刘启元,张聪,沈一栋.信度网近似推理算法[J].计算机科学,2001,28
[41]Tomas Hrycej, Gibbs Sampling in Bayesian Networks[J].Arrificial Intelligence,46(1990):351-363
[42]Neal R M. Probabilistic inference using Markov chain Monte Carlo methods[J]. Department of Computer Science, University of Toronto,1993
[43]Pearl J. Addendum:Evidential Reasoning using stochastic simulation of causal models[J]. Artificial Intelligence,1987,33
[44]C. Jensen, A. Kong, and U. Kjaerul.Blocking gibbs sampling in very large probabilistic expert systems. International Journal of Human Computer Studies[J]. Special Issue on Real-World Applications of Uncertain Reasoning.,1995:647-666
[45]Dagum P, Luby M. An Optimal Approximation for Bayesian Inference[J]. Artificial Intelligence,1993,60:141-153
[46]Fung R, Chang K-C. Weighting and integration evidence for stochastic simulation in Bayesian networks[J]. In:Uncertainty in Artificial Intelligence 5, Elsevier, Amsterdam, The Netherlands,1990:209-219
[47]David Poole, Probabilitic Conflicts in a Search algorithm for estimating postrior probabilities in Bayesian Networks[J].Artificial Intelligence,88(1996):69-100
[48]Neil M, Fenton N, Nielsen L. Building large-scale Bayesian networks[J]. The Knowledge Engineering Review,2000
[49]Heckerman D, Geiger D, Chickering D M. Learning Bayesian networks:the combination of knowledge and statistical data[J]. Machine Learning,1995
[50]M. Singh. Learning Bayesian Networks from Incomplete Data[J]. In AAAI97, 1997:27-31
[51]N. Friedman. Learning Belief Networks in the Presence of Missing Values and Hidden Variables[C]. In Proc.14th International Conference on Machine Learning, Morgan Kaufmann,1997:125-133
[52]A. Dempster, N. Laird, and D. Rubin. Maximum Likelihood from Incomplete Data via the EM Algorithm[J]. Journal of the Royal Statistical Society,1977,39(1): 1-38
[53]G.J. Mclachlan and T. Krishnan. The EM Algorithm and Extensions[J]. Wiley Series in Probability and Satistics,1997
[54]廖学清.数据缺失下学习贝叶斯网的研究[D].苏州：苏州大学,2007
[55]贾海洋.贝叶斯网学习若干问题研究[D].吉林：吉林大学,2007
[56]D.Spiegelhalter, S.Lauritzen. Sequential updating of conditional probabilities on directed graphical structures[J].Networks,1990, vol.20:579-605
[57]R.Little, D.Rubin, Statical Analysis with Missing Data[J].New York:John Willey & Sons,1987
[58]童立,马远良.设计模式在基于组件的框架设计中的应用[J].计算机工程与应用,(17)2002：123-124
[59]Valerie Issarny, Luc Bellissard, Michel Riveill, etc. Component-Based Programming of Distributed Applications[J]. Lecture Notes in Computer Science, Vol.1752,2000:328-349
[60]J.Cheng, R.Greniner, J.Kelly, D.Bell, W.R.Liu. Learing Bayesian networks from data:An information-theory based approach[J]. Artificial Intellifence,2002, vol.137:43-90
[61]J.Rissanen, Stochastic Complexity in Statistical Inquiry[J].River Edge, NJ:World Scientific,1989