贝叶斯网络结构学习及其应用研究
|
摘要
现实世界中存在着大量的不确定性现象，建立有效的模型是对不确定性问题正确决策的关键。针对问题领域中变量之间的不确定性关系，贝叶斯网络提供了一种紧凑、直观且有效的图形表达方式。建立高效稳定的贝叶斯网络学习算法是贝叶斯网络走向应用的关键所在，多年来，贝叶斯网络学习及其应用一直是国内外研究的热门课题。本文在对贝叶斯网络的国内外研究现状进行全面分析的基础上，针对结构学习目前所面临的收敛速度慢和可能收敛于局部最优两大主要问题，对数据完备和数据缺失两种情况下的贝叶斯网络结构学习进行了研究，并进一步地对贝叶斯网络在灵敏度分析和频繁模式挖掘中的应用进行了研究。全文主要内容如下：
1．贝叶斯网络的结构学习研究
①数据完备情况下贝叶斯网络的结构学习：研究发现MCMC方法抽样过程产生的马尔可夫链具有各态遍历性，并能保证最终收敛于平稳分布，因而具有良好的精度。 MHS是最常用的MCMC方法之一，但MHS算法抽样过程的融合性差，收敛速度较慢。本文从初始值、建议分布和对网络子结构的抽样三个方面对MHS抽样算法进行改进，提出了一种贝叶斯网络结构学习算法PCMHS，该算法同时进行多个MHS抽样，构建多条并行的收敛于Boltzmann分布的马尔可夫链。算法PCMHS首先基于节点之间的互信息，进行所有马尔可夫链的初始化，在其迭代过程中，算法PCMHS基于并行的上一代抽样的样本总体得到产生下一代个体的建议分布，并通过同时对网络中弧和子结构的抽样产生下一代个体。算法PCMHS能收敛于网络结构的平稳分布，因而具有良好的学习精度，而该算法又通过使其初始分布和建议分布近似于其平稳分布，有效地提高了抽样过程的收敛速度。在标准数据集上的实验结果也验证了算法PCMHS的学习效率和学习精度明显优于经典算法MHS和PopMCMC。
②数据缺失情况下贝叶斯网络的结构学习：针对数据缺失严重情况下，具有缺失数据的贝叶斯网络结构学习方法存在的学习效率偏低和易于陷入局部最优等问题，本文建立了一种具有缺失数据的贝叶斯网络结构学习算法BC-ISOR，该算法基于界定折叠方法从缺失数据集学习不同变量子集的概率分布，然后基于依赖分析方法进行网络结构的学习。针对属性个数不超过30的数据集，算法BC-ISOR可以通过一遍扫描数据集得到所有已经发生的实例数和可能的实例数，其对缺失数据的处理效率与数据的缺失率无关，并通过在结构学习的过程中采用启发式切割集搜索算法和在冗余边检验之前识别出所有的边的方向来降低条件独立性检验的次数和阶数，因而具有良好的学习性能。在标准数据集上的实验结果表明该算法具有良好的学习效率和学习精度。
2．贝叶斯网络的应用研究
学习贝叶斯网络的目的是基于贝叶斯网络的推理开展贝叶斯网络的应用研究。
①贝叶斯网络的灵敏度分析：贝叶斯网络的灵敏度分析基于连接树推理算法，主要包括证据重要性分析和参数灵敏度分析。Shafer-Shenoy和Hugin算法设计了两种不同的基于连接树的推理分析算法的消息传播方式，相比于Shafer-Shenoy算法，Hugin算法具有较高的推理分析效率，但在邻接树中存在零因子的情况下不能保证能够通过局部计算进行灵敏度分析，针对这一问题，本文通过在Hugin算法的消息传播过程中引入零因子标志位和零因子处理机制，提出了一种用于进行灵敏度分析的Hugin算法的改进算法R-Hugin，并从理论和实验两个方面证明了R-Hugin算法的正确性和有效性。
②基于贝叶斯网络的频繁模式发现：本文采用贝叶斯网络表示领域知识，提出一种基于领域知识的频繁项集和频繁属性集的兴趣度计算和剪枝方法BN-EJTR，其目的在于发现当前领域知识不一致的知识，以解决频繁模式挖掘所面临的有趣性和冗余问题。针对兴趣度计算过程中批量推理的需求，BN-EJTR提供了一种基于扩展邻接树消元的贝叶斯网络推理算法，用于计算大量项集在贝叶斯网络中的支持度，同时BN-EJTR提供了一种基于兴趣度阈值和拓扑有趣性的剪枝算法，实验结果表明：与同类方法相比方法BN-EJTR具有良好的时间性能，而且剪枝效果明显，分析发现经过剪枝后的频繁属性集和频繁项集相对于领域知识符合有趣性要求。
There are many types of uncertainty in the real world and building effective uncertainty modelsis crucial for making correct decisions on uncertain problems. A Bayesian network provides acompact, intuitive and effective graphical expression mode for uncertain relationships of variables inapplication domains. Efficient and reliable algorithms for structure learning are essential forBayesian network applications. Both Bayesian networks and their applications have been hotresearch topics in China and abroad in recent years. After an extensive review on related work inBayesian networks on dealing with two major problems, low convergence rates and convergence tolocal optima faced by existing structure learning algorithms, this thesis studies structure learningunder two scenarios: when the data is complete and when there are missing data items. In addition,the applications of Bayesian networks in sensitivity analysis and frequent patterns mining areinvestigated in the thesis. The main contributions of the thesis are as follows.
1. Bayesian network structure learning
①Bayesian network structure learning with complete data. Exisiting research has shown thatthe Markov Chain Monte Carlo (MCMC) is a stochastic simulation that ensures ergodicity andreaches solutions with a long term frequency equal to the Boltzmann. The Metropolis-Hastingssampler (MHS) is the most frequently used MCMC method. But the Markov chain of MHS has theproblem of poor mixing and low convergence rates. This thesis improves the MHS algorithm on itsinitial structure, proposal distribution, and sub-structure sampling, and presents an improvedalgorithm PCMHS for learning Bayesian networks. The PCMHS algorithm runs multiMetropolis-Hasting samplers simultaneously, and each sampler is a Markov chain simulating asystem converging to Boltzmann distribution. Firstly, the PCMHS algorithm, based on the mutualinformation between nodes, initializes all Markov chains. In the process of each iteration, thealgorithm, based on the population from parallel Metropolis-Hasting samplers, generates theproposed distribution for the next generation, and uses edge sampling and sub-structure sampling toproduce the individuals of the next generation. The PCMHS algorithm converges to a stabledistribution and has a better learning accuracy. In addition, PCMHS provides an initial distributionand a proposed distribution as close as possible to the stable distribution, and improves theconvergence rate significantly. The experimental results on benchmark datasets also demonstrate thatthe learning accuracy and efficiency of the PCMHS algorithm outperform state-of-the-art algorithmsMHS and PopMCMC.
②Bayesian network structure learning with missing data. Exisitng methods for learningBayesian networks from missing data have the problems of getting stuck on local optima and lowlearning efficiency in the case of a large percentage of missing data. To solve these problems, an algorithm BC-ISOR is proposed for learning Bayesian networks from datasets with missing data.BC-ISOR firstly estimates the probability distribution of a variable set from missing data based onthe Bound and Collapse method. Then, BC-ISOR learns Bayesian networks based on dependencyanalysis. When a dataset has no more than30attributes, BC-ISOR can obtain realistic instances andprobable instances through one dataset scan, and its missing data processing efficiency is irrelevantto the missing rate. In addition, through using heuristic ideas for searching cut-sets and orienting allthe edges before removing redundant edges, BC-ISOR can reduce the number and order ofconditional independence tests. So the BC-ISOR algorithm has a good learning performance.Experimental results on benchmark datasets show that BC-ISOR learns more efficiently andaccuracily than the well-known algorithm SEM.
2. Applications of Bayesian networks
①Sensitivity analysis of Bayesian networks. Sensitivity analysis of Bayesian networks is basedon a tree-join algorithm and mainly includes evidence sensitivity analysis and parameter sensitivityanalysis. The Shafer-Shenoy algorithm and the Hugin algorithm provide two different messagepropagation modes for reasoning-analysizing algorithms based on joint trees. Compared with theShafer-Shenoy algorithm, the Hugin algorithm is more efficient, but cannot guarantee sensitivityanalysis through a local calculation in the case of zero-division. To overcome the limitation of theHugin algorithm in the case of zero-division, a refined Hugin algorithm, R-Hugin, is proposed in thisthesis for sensitivity analysis, which introduces a zero-division flag and a zero-division processingmechanism in the message propagation process of the Hugin algorithm. Meanwhile, the correctnessand efficiency of the R-Hugin algorithm are validated by both theoretic analysis and experiments.
②Frequent pattern discovery based on Bayesian networks. Based on background knowledgerepresented as a Bayesian network, this thesis presents a BN-EJTR method for computing theinterestingness of frequent items and frequent attributes, and for pruning. BN-EJTR seeks to findinconsistent knowledge relative to the background knowledge and to resolve the problems ofun-interestingness and redundancy faced by frequent pattern mining. To deal with the demand ofbatch reasoning in Bayesian networks during computing interestingness, BN-EJTR provides areasoning algorithm based on extended junction tree elimination for computing the support of a largenumber of items in a Bayesian network. In addition, BN-EJTR is equipped with a pruningmechanism based on a threshold for topological interestingness. Experimental results demonstratethat BN-EJTR has a good time performance compared with the same classified methods, andBN-EJTR has effective pruning results. Our analysis indicates that both the pruned frequentattributes and the pruned frequent items are un-interesting with respect to the backgroundknowledge.
1．贝叶斯网络的结构学习研究
①数据完备情况下贝叶斯网络的结构学习：研究发现MCMC方法抽样过程产生的马尔可夫链具有各态遍历性，并能保证最终收敛于平稳分布，因而具有良好的精度。 MHS是最常用的MCMC方法之一，但MHS算法抽样过程的融合性差，收敛速度较慢。本文从初始值、建议分布和对网络子结构的抽样三个方面对MHS抽样算法进行改进，提出了一种贝叶斯网络结构学习算法PCMHS，该算法同时进行多个MHS抽样，构建多条并行的收敛于Boltzmann分布的马尔可夫链。算法PCMHS首先基于节点之间的互信息，进行所有马尔可夫链的初始化，在其迭代过程中，算法PCMHS基于并行的上一代抽样的样本总体得到产生下一代个体的建议分布，并通过同时对网络中弧和子结构的抽样产生下一代个体。算法PCMHS能收敛于网络结构的平稳分布，因而具有良好的学习精度，而该算法又通过使其初始分布和建议分布近似于其平稳分布，有效地提高了抽样过程的收敛速度。在标准数据集上的实验结果也验证了算法PCMHS的学习效率和学习精度明显优于经典算法MHS和PopMCMC。
②数据缺失情况下贝叶斯网络的结构学习：针对数据缺失严重情况下，具有缺失数据的贝叶斯网络结构学习方法存在的学习效率偏低和易于陷入局部最优等问题，本文建立了一种具有缺失数据的贝叶斯网络结构学习算法BC-ISOR，该算法基于界定折叠方法从缺失数据集学习不同变量子集的概率分布，然后基于依赖分析方法进行网络结构的学习。针对属性个数不超过30的数据集，算法BC-ISOR可以通过一遍扫描数据集得到所有已经发生的实例数和可能的实例数，其对缺失数据的处理效率与数据的缺失率无关，并通过在结构学习的过程中采用启发式切割集搜索算法和在冗余边检验之前识别出所有的边的方向来降低条件独立性检验的次数和阶数，因而具有良好的学习性能。在标准数据集上的实验结果表明该算法具有良好的学习效率和学习精度。
2．贝叶斯网络的应用研究
学习贝叶斯网络的目的是基于贝叶斯网络的推理开展贝叶斯网络的应用研究。
①贝叶斯网络的灵敏度分析：贝叶斯网络的灵敏度分析基于连接树推理算法，主要包括证据重要性分析和参数灵敏度分析。Shafer-Shenoy和Hugin算法设计了两种不同的基于连接树的推理分析算法的消息传播方式，相比于Shafer-Shenoy算法，Hugin算法具有较高的推理分析效率，但在邻接树中存在零因子的情况下不能保证能够通过局部计算进行灵敏度分析，针对这一问题，本文通过在Hugin算法的消息传播过程中引入零因子标志位和零因子处理机制，提出了一种用于进行灵敏度分析的Hugin算法的改进算法R-Hugin，并从理论和实验两个方面证明了R-Hugin算法的正确性和有效性。
②基于贝叶斯网络的频繁模式发现：本文采用贝叶斯网络表示领域知识，提出一种基于领域知识的频繁项集和频繁属性集的兴趣度计算和剪枝方法BN-EJTR，其目的在于发现当前领域知识不一致的知识，以解决频繁模式挖掘所面临的有趣性和冗余问题。针对兴趣度计算过程中批量推理的需求，BN-EJTR提供了一种基于扩展邻接树消元的贝叶斯网络推理算法，用于计算大量项集在贝叶斯网络中的支持度，同时BN-EJTR提供了一种基于兴趣度阈值和拓扑有趣性的剪枝算法，实验结果表明：与同类方法相比方法BN-EJTR具有良好的时间性能，而且剪枝效果明显，分析发现经过剪枝后的频繁属性集和频繁项集相对于领域知识符合有趣性要求。
There are many types of uncertainty in the real world and building effective uncertainty modelsis crucial for making correct decisions on uncertain problems. A Bayesian network provides acompact, intuitive and effective graphical expression mode for uncertain relationships of variables inapplication domains. Efficient and reliable algorithms for structure learning are essential forBayesian network applications. Both Bayesian networks and their applications have been hotresearch topics in China and abroad in recent years. After an extensive review on related work inBayesian networks on dealing with two major problems, low convergence rates and convergence tolocal optima faced by existing structure learning algorithms, this thesis studies structure learningunder two scenarios: when the data is complete and when there are missing data items. In addition,the applications of Bayesian networks in sensitivity analysis and frequent patterns mining areinvestigated in the thesis. The main contributions of the thesis are as follows.
1. Bayesian network structure learning
①Bayesian network structure learning with complete data. Exisiting research has shown thatthe Markov Chain Monte Carlo (MCMC) is a stochastic simulation that ensures ergodicity andreaches solutions with a long term frequency equal to the Boltzmann. The Metropolis-Hastingssampler (MHS) is the most frequently used MCMC method. But the Markov chain of MHS has theproblem of poor mixing and low convergence rates. This thesis improves the MHS algorithm on itsinitial structure, proposal distribution, and sub-structure sampling, and presents an improvedalgorithm PCMHS for learning Bayesian networks. The PCMHS algorithm runs multiMetropolis-Hasting samplers simultaneously, and each sampler is a Markov chain simulating asystem converging to Boltzmann distribution. Firstly, the PCMHS algorithm, based on the mutualinformation between nodes, initializes all Markov chains. In the process of each iteration, thealgorithm, based on the population from parallel Metropolis-Hasting samplers, generates theproposed distribution for the next generation, and uses edge sampling and sub-structure sampling toproduce the individuals of the next generation. The PCMHS algorithm converges to a stabledistribution and has a better learning accuracy. In addition, PCMHS provides an initial distributionand a proposed distribution as close as possible to the stable distribution, and improves theconvergence rate significantly. The experimental results on benchmark datasets also demonstrate thatthe learning accuracy and efficiency of the PCMHS algorithm outperform state-of-the-art algorithmsMHS and PopMCMC.
②Bayesian network structure learning with missing data. Exisitng methods for learningBayesian networks from missing data have the problems of getting stuck on local optima and lowlearning efficiency in the case of a large percentage of missing data. To solve these problems, an algorithm BC-ISOR is proposed for learning Bayesian networks from datasets with missing data.BC-ISOR firstly estimates the probability distribution of a variable set from missing data based onthe Bound and Collapse method. Then, BC-ISOR learns Bayesian networks based on dependencyanalysis. When a dataset has no more than30attributes, BC-ISOR can obtain realistic instances andprobable instances through one dataset scan, and its missing data processing efficiency is irrelevantto the missing rate. In addition, through using heuristic ideas for searching cut-sets and orienting allthe edges before removing redundant edges, BC-ISOR can reduce the number and order ofconditional independence tests. So the BC-ISOR algorithm has a good learning performance.Experimental results on benchmark datasets show that BC-ISOR learns more efficiently andaccuracily than the well-known algorithm SEM.
2. Applications of Bayesian networks
①Sensitivity analysis of Bayesian networks. Sensitivity analysis of Bayesian networks is basedon a tree-join algorithm and mainly includes evidence sensitivity analysis and parameter sensitivityanalysis. The Shafer-Shenoy algorithm and the Hugin algorithm provide two different messagepropagation modes for reasoning-analysizing algorithms based on joint trees. Compared with theShafer-Shenoy algorithm, the Hugin algorithm is more efficient, but cannot guarantee sensitivityanalysis through a local calculation in the case of zero-division. To overcome the limitation of theHugin algorithm in the case of zero-division, a refined Hugin algorithm, R-Hugin, is proposed in thisthesis for sensitivity analysis, which introduces a zero-division flag and a zero-division processingmechanism in the message propagation process of the Hugin algorithm. Meanwhile, the correctnessand efficiency of the R-Hugin algorithm are validated by both theoretic analysis and experiments.
②Frequent pattern discovery based on Bayesian networks. Based on background knowledgerepresented as a Bayesian network, this thesis presents a BN-EJTR method for computing theinterestingness of frequent items and frequent attributes, and for pruning. BN-EJTR seeks to findinconsistent knowledge relative to the background knowledge and to resolve the problems ofun-interestingness and redundancy faced by frequent pattern mining. To deal with the demand ofbatch reasoning in Bayesian networks during computing interestingness, BN-EJTR provides areasoning algorithm based on extended junction tree elimination for computing the support of a largenumber of items in a Bayesian network. In addition, BN-EJTR is equipped with a pruningmechanism based on a threshold for topological interestingness. Experimental results demonstratethat BN-EJTR has a good time performance compared with the same classified methods, andBN-EJTR has effective pruning results. Our analysis indicates that both the pruned frequentattributes and the pruned frequent items are un-interesting with respect to the backgroundknowledge.
引文
[1] T.R.Bayes. An Essay toward Solving a Problem in the Doctrine of Chances. PhilosophicalTransactions of the Royal Soeiety.1763,53:370-418.
[2] H.Jeffries. An Invariant Form for the Prior Probability in Estimation Problems. Pro. Roy. Soc.AA.1946,186:453-461.
[3] J.Pearl. Probabilistic Reasoning in Intelligent Systems: Network of Plausible Inference.Morgan Kaufinann,1988:1-86
[4] D.Geiger and T.Verma. D-Separation: From Theorems to Algorithms. In: Proceedings of the5th Workshop on Uncertainty in Artificial Intelligence. Windsor, Ontario,1989,118-125.
[5] J.Pearl. Propagation and Structuring in Belief Networks. Artificial Intelligence,1986,29(3):241-288.
[6] H.J.Suermondt and G. F. Cooper. Probabilistic Inference in Multiply Connect Belief NetworksUsing Loop Cutsets. International Journal of Approximate Reasoning,1990.
[7] F.J.Diez. Local Conditioning in Bayesian Networks. Cognitive Systems Laboratory,Department of Computer Science, UCLA,1992.
[8] R.D.Shachter, S.K.Anderson, and P. Szolovits. Global Conditioning for Probabilistic Inferencein Belief Networks. In: Proceedings of the Uncertainty in Artificial Intelligence Conference,SanFranci sco. CA: Morgan Kaufmann,1994,514-522.
[9] A.Darwiche. Conditioning methods for exact and Approximate Inference in Causal Networks.In: Proceedings of the11th Annual Conference on Uncertainty in Artificial Intelligence.Montreal: Morgan Kauffman,1995.
[10] A. Darwiche. Recursive conditioning. Artificial Intelligence,2001,125(1-2):5-41.
[11] S.L.Lauritzen and D.J.Spiegelhalter. Local Computations with Probabilities on GraphicalStructures and Their Applications to Expert Systems. In: Proceedings of the Royal StatisticalSociety.1988, B(50),154-227.
[12] P.Shenoy and G.Shafer. Axioms for Probability and Belief-function Propagation. Uncertaintyin AI,1990,4:169-198.
[13] F.V.Jensen, S.Lauritzen, and K.Olesen. Bayesian Updating in Causal Probabilistic Networksby Local Computation. Computational Statistics Quarterly,1990(4):269-282.
[14] A.L.Madsen and F.V. Jensen. Lazy Propagation in Junction Trees. In: Proceedings of theFourteenth Conference on Uncertainty in Artificial Intelligence. Morgan Kaufmann,1998,362-369.
[15] R.D.Shachter, D.B.Ambrosio, and B.D.DelFavero. Symbolic Probabilistic Inference in BeliefNetworks. In: Proceedings of the Eighth National Conference on Artificial Intelligence. Boston:MIT,1990,126-131.
[16] N.L.Zhang and D.Poole. A Simple Approach to Bayesian network Computations. In:Proceedings of the10th Canadian Conference on Artificial Intelligence.1994,171-178.
[17] R.Dechter. Bucket elimination: a Unifying Framework for Probabilistic Inference. In:Proceedings of the12th Conference on Uncertainty in Artificial Intelligence. Portland, Oregon,1996,211-219.
[18] K.Kask, R.Dechter, J.Larrosa, et al. Bucket-tree Elimination for Automated Reasoning.Artificial Intelligence,2001(125):91-131.
[19] R.D.Shachter. Evidence Absorption and Propagation through Evidence Reversals.Uncertaintyin Artificial Intelligence,1990(5):173-190.
[20] Y.W.C.Adrian and C.Boutilier. Structured Arc Reversal and Simulation of DynamicProbabilistic Networks. In: Proceedings of the13th Conference on Uncertainty in ArtificialIntelligence.1997.
[21] A.Darwiche. A Differential Approach to Inference in Bayesian. In: Proceedings of the6thConference on Uncertainty in Artificial Intelligence. San Francisco: Morgan Kaufmann,2000.
[22] B.Boris. An Extension of the Differential Approach for Bayesian Network Inference toDynamic Bayesian Networks. International Journal of Intelligent Systems,2004,19(8):727-748.
[23] P.Dagum, R.Karp, M.Luby, et al. An Optimal Algorithm for Monte Carlo estimation. In:Proceedings of the6th IEEE Symposium on Foundations of Computer Science, Portland,Oregon:1995,142-149.
[24] M.Henrion. Propagating Uncertainty in Bayesian Networks by Probabilistic LogicSampling.Uncertainty in Artificial Intelligence,1988(2):149-163.
[25] R.Fung and K.C.Chang. Weighting and Integrating Evidence for Stochastic Simulation inBayesian Networks. Uncertainty in Artificial Intelligence,1989(5):209-219.
[26] R.D.Shachter and M.A.Peot. Simulation Approaches to General Probabilistic Inference onBelief Networks. In: Proceedings of the Conference on Uncertainty in Artificial Intelligence.1990.
[27] S.Geman and D.Geman. Stochastic Relaxation, Gibbs Distribution and the BayesianRestoration of Images. IEEE Transactions on Pattern Analysis and Machine Intelligence,1984,6(6):721-741.
[28] R.M.Chavez and G.F.Cooper. A Randomized Approximation Algorithm for ProbabilisticInference on Bayesian Belief Networks.Networks,1990:661-685.
[29] D.Draper. Localized partial evaluation of Bayesian belief networks. Seattle: University ofWashington.1995.
[30] E.Horvitz, H.J.Suermondt, and G.F.Cooper. Bounded Conditional: Flexible Inference forDecisions under Scarce Resources. In: Proceedings of the5th Conference on Uncertainty inArtificial Intelligence. Windsor, Ontario,1989,182-193.
[31] M.P.Wellman and C.L.Liu. State-space Abstraction for Anytime Evaluation of ProbabilisticNetworks.Uncertainty in Artificial Intelligence,1994:567-574.
[32] T.S.Jaakkola and M.Jordan. Variational Probabilistic Inference and the QMR-DT Network.Journal of Artificial Intelligence Research,1999,10:291-322.
[33] D.Poole. Context-specific Approximation in Probabilistic Inference. In: Proceedings of the14th Conference on Uncertainty in Artificial Intelligence.1998.
[34] S.Sarkar. Using Tree-decomposable Structures to Approximate Belief Networks. In:Proceedings of the9th Conference on Uncertainty in Artificial Intelligence. Washington, DC:Morgan Kaufmann,1993.
[35] K.P.Murphy, Y.Weiss, and M.Jordan. Loopy Belief Propagation for Approximate Inference: anEmpirical Study. In: Proceedings of the15th Conference Uncertainty in Artificial Intelligence.1999,467-475.
[36] S.Tatikonda and M.Jordan. Loopy Belief Propagation and Gibbs Measures. Uncertainty inArtificial Intelligence,2002.
[37] E.Herskovits. Computer-based Probabilistic-Network Construction.USA: Stanford University,1991.
[38] R.R.Bouckaert. A Stratified Simulation Scheme for Inference in Bayesian Belief Networks. In:Proceedings of the10th Conference Uncertainty in Artificial Intelligence.1994.110-117.
[39] D.Chickering, D.Geiger, and D.Heckerman. Learning Bayesian Networks: Search Methodsand Experimental Results. In: Proceedings of the5th conference on Artificial Intelligence andStatistics. IEEE Press,1995,112-128.
[40] J.Suzuki. A Construction of Bayesian Networks from Databases Based on an MDL Principle.In: Proceedings of the9th Conference on Uncertainty in Artificial Intelligence. WashingtonD.C.1996,266-273.
[41] P.Larranaga. Structure Learning of Bayesian Networks by Genetic Algorithms: a PerformanceAnalysis of Control Parameters. IEEE Transactions on Pattern Analysis and MachineIntelligence,1996,18b(9):912-926.
[42] P.Larranaga. Searching for the Best Ordering in the Structure Learning of Bayesian Netwroks.IEEE Transactions on System, Man and Cybermetics,1996,26(4):487-493.
[43] M.L.Wong, S.Y.Lee, and K.S.Leung. A Hybrid Approach to Discover Bayesian Networks fromDatabases Using Evolutionary Programming. In: Proceedings on International ConferenceData Mining.2002,498-505.
[44] D.Madigan, A.E. Raftery, J.C. York, et al. Strategies for Graphical Model Selection, In: P.Cheeseman, R.W. Oldford (Eds.), Selecting Models from Data: Artificial Intelligence andStatistics.Springer, Berlin,1994,4.
[45] N.Friedman and D.Koller. Being Bayesian about Network Structure: A Bayesian Approach toStructure Discovery in Bayesian Networks. Machine Learning,2003,50:95-126.
[46] B. Ellis and W. Wong. Sampling Bayesian Networks quickly. In: Interface, Pasadena:2006.
[47] D.M.Chickering and D.Geiger. Learning Bayesian Networks: Search Methods andExperimental Results. In: Proceedings of5th Conference on Artificial Intelligence andStatistics.1995.112-128.
[48] M.Koivisto and K. Sood. Exact Bayesian Structure Discovery in Bayesian Networks. MachineLearning Research,2004,5:549-573.
[49] N.Wermuth and S.Lauritzen. Graphical and Recursive Models for Contingency tables.Biometrika,1983,70(1):537-552.
[50] C.Spirtes, P.Glymour, and R.Scheines. Causality from Probability. Evolving Knowledge inNatural Science and Artificial Intelligence. London: Piman,1990:181-199.
[51] P.Spirtes, C.Glymour, and R.Scheines. An Algorithm for Fast Recovery of Sparse CausalGraphs. Social Science Computer Review,1991,9(1):62-72.
[52] J.Cheng and R.Greiner. Learning Bayesian Networks from Data: an Information Theory basedApproach. Artificial Intelligence,2002,137(1-2):43-90.
[53] M.Singh and M.Valtorta. Construction of Bayesian Network Structures form Data: a BriefSurvey and an Efficient Algorithm. International Journal of Approximate Reasoning,1995,12(2):111-131.
[54] X.W.Chen,G. Anantha, and X.T. Lin. Improving Bayesian Network Structure Learning withMutual Information-Based Node Order in the K2Algorithm. IEEE Transactions on Knowledgeand Data Engineering,2008,20(5):628-640.
[55] M.L.Wong and K.S.Leung. An Efficient Data Mining Method for Learning Bayesian NetworksUsing an Evolutionary Algorithm-based Hybrid Approach. IEEE Transactions on EvolutionaryComputation,2004,8:378-404.
[56] I.Tsamardinos, E.Brown, and C.F.Aleferis. The Max-min Hill-climbing Bayesian NetworkStructure Learning algorithm. Machine Learning,2006,65(1):31-78.
[57] A.Statnikov, I.Tsamardinos, and C.F.Aliferis. An Algorithm for Generation of LargeBayesian Networks. Vanderbilt University,2003, TR-03-01.
[58] P.C. Pinto, A.Nagele, M.Deiori, et al. Learning of Bayesian Networks by a Local DiscoveryAnt Colony Algorithm. IEEE World Congress on Computational Intelligence. Hong Kong:China,2008,2741-2748.
[59] N.Friedman. Leaming Belief Networks in the Presence of Missing Values and Hiddenvariables. In: Proeeedings of the14th International Conference on Machine Learning. MorganKaufinann, Nashville, Tennessee, USA,1997,125-133.
[60] N.Friedman. The Bayesian Struetural EM Algoritbm. In: Proeeedings of the14th Conferenceon Uncertainty in Artificial Intelligenee. Morgan Kaufinann, Madison, Wiseonsin,USA.1998,129-138.
[61] J.W.Myers, K.B.Laskey, T.S.Levitt. Learning Bayesian Networks from Incomplete Data withStochastic Search Algorithms. In: Proeeedings of the15th Conference on Uncertainty inArtificial Intelligence. MorganKaufmann, Stockholm, Sweden.1999,476-485.
[62] K.B.Laskey and J.W. Myers. Population Markov Chain Monte Carlo. Machine Learning,2003,50,175-196.
[63] D.Chickering, D.Heckerman and C.Meek Large-sample learning of Bayesian Networks isNP-Hard. Machine Learning Research,2004,5,1287-1330.
[64] G.Cooper. Computational Complexity of Probabilistic Inference Using Bayesian BeliefNetwork. Artificial Intelligence,1990,42:393-405
[65] P.Dagum and R.M.Chavez. Approximating Probabilistic Inference in Bayesian BeliefNetworks. IEEE Transactions on Pattern Analysis and MachineIntelligence,1993,15(3):246-255
[66] www.onparenting.msn.com
[67] P.J.F.Lucas. Expert Knowledge and Its Role in Learning Bayesian Networks in Medicine: AnAppraisal. In: Proceedings of the8th Conference on AI in Medicine in European. Springer,Cascais, Portugal.2001,156-166.
[68] A.Onisko, P.J.F.Lucas, and M.J.Druzdzel. Comparison of Rule-Based and Bayesian NetworkApproaches in Medical Diagnostic Systems. In: Proceedings of the8th conference on AI inMedicine in European. Springer, Cascais, Portugal.2001,283-292.
[69] M.J.Sillanpaa and J.Corander. Model Choice in Gene Mapping: What and Why. Trends Genet,2002,18(6):301-307.
[70] M, Andronescu, A. Condon, H Hoos, et al.Efficient parameter estimation for RNA secondarystructure prediction, Bioinformatics2007
[71] N.Friedman. Inferring Cellular Networks Using Probabilistic Graphical Models. Science,2004,303:799-805.
[72] A.Hartemink, D.Gifford, T.Jaakkola, et al. Bayesian Methods for Elucidating GeneticRegulatory Networks. IEEE Intelligent Systems,2002,17(2):37-43.
[73] A. Jaimovich, G. Elidan, H.Margalit, et al. Towards an integrated protein-protein interactionnetwork: a relational Markov network approach. Journal of computational biology,2006,6,13(2):145-64.
[74] A.Raval, Z.Ghahramani, and D.L.Wild. A Bayesian Network Model for Protein Fold andRemote Homologue Recognition. Bioinformatics.2002,18(6):788-801.
[75] S.Geman and K.Kochanek Dynamic Programming and the Graphical Representation ofError-correcting Codes. IEEE Transactions on Information Theory,2001,47(2):549-568.
[76] A.Krause and C.Guestrin. Near-optimal Nonmyopic Value of Information in Graphical Models.In: Proceedings of the21th Conference in Uncertainty in Artificial Intelligence. AAAI Press,Edinburgh, Scotland.2005,324-331.
[77] M.A.Rodrigues, Y. Liu, L.Bottaci, et al. Learning and Diagnosis in Manufacturing ProcessesThrough an Executable Bayesian Network. In: Proceedings of the13th InternationalConference on Industrial and Engineering Applications of Artificial Intelligence and ExpertSystems. Springer, New Orleans, Louisiana, USA,2000,390-395.
[78] B.McCabe. Belief Networks for Engineering Applications. International Journal of TechnologyManagement,2001,21(3-4):257-270.
[79] P.Giudici. Bayesian Data Mining with Application to Benchmarking and Credit Scoring.Application Stochastic Model Business.2001,17(1):69-81.
[80] J.Gemela. Financial Analysis Using Bayesian Networks. Application Stochastic ModelBusiness.2001,17(1):57-67.
[81] G.Socher, G.Sagerer, and P.Perona. Bayesian Reasoning on Qualitative Descriptions fromImages and Speech. Image Vision Compution.2000,18(2):155-172.
[82] T.V.Pham, M.Wowing, and A.W.M.Smeulders. Face Detection by Aggregated BayesianNetwork Classifiers. Pattern Recognition Letters,2002,23(4):451-461.
[83] D.A.Wooff, M.Goldstein, and F.P.A.Coolen. Bayesian Graphical Models for Software Testing.IEEE Software Engineering,2002,28(5):510-525.
[84]宫秀军，刘少辉，史忠植.一种增量贝叶斯分类模型.计算机学报，2002,25(6):645-650.
[85]宫秀军，史忠植.基于贝叶斯潜在语义分析的半监督web挖掘.软件学报,2002，13(8)：1508-1514.
[86]李伟生,王宝树.实现规划识别的一种贝叶斯网络.西安电子科技大学学报(自然科学版),2002，29(6):741-744.
[87]霍利民，朱永利，范高峰等.一种基于贝叶斯的电力系统可靠性评估新方法.电力系统自动化，2002，27(5):36-40.
[88]李俭川，胡莺庆等.基于贝叶斯网络的智能故障诊断方法.中国惯性技术学报，2002，10(4):24-28.
[89]邓勇，施文康，陈良州.基于模型诊断的贝叶斯解释及应用.上海交通大学学报,2003，37(1):5-8.
[90]汪荣贵. bayes网络理论及其在目标检测中应用研究[博士学位论文].合肥工业大学,2004.
[91]雷耀山,史定华,王翼飞.基因调控网络的生物信息学研究.自然杂志.2004,26(1):7-12.
[92]徐肖江.从功能基因组数据重建基因调控网络[博士学位论文].中国科学院上海生命科学研究院生物化学与细胞生物学研究所,2005.
[93] D. Geiger, T.Verma, and J.Pearl. Identifying Independence in Bayesian Networks. Networks,1990,20:507-534.
[94] F.V. Jensen. Bayesian Networks and Decision. Statistics for Engineering and InformationScience Series, Springer Verlag,2001.
[95] G.F.Cooper and E. Herskovits. A Bayesian Method for the Induction of Probabilistic Networksfrom Data. Machine Learning,1992,9:309-347.
[96] G.F.Cooper and E. Herskovits. A Bayesian Method for Constructing Bayesian Belief Networksfrom Databases. In: Proceedings of the7th Annual Conference on Uncertainty in ArtificialIntelligence. Morgan Kaufmann, Los Angeles, CA, USA.1991,86-94.
[97] D.Heckerman, D.Geiger, and D.M.Chickering. Learning Bayesian Networks: the Combinationof Knowledge and Statistical Data. Machine Learning.1995,20(3):197-243.
[98] C. Andrieu, N.D. Freitas, A. Doucet, et al. An introduction to MCMC for Machine Learning.Machine Learning,2003,50:5-43.
[99] C.Robert, G. Casella. Monte Carlo statistical methods.2nd edition, Springer,2004.
[100] W. Gilks, S. Richardson and D.Spiegelhalter. Markov Chain Monte Carlo Methods in Practice.CRC Press,1996.
[101] D. Madigan and J. York. Bayesian Graphical Models for Discrete Data. InternationalStatistical Review,1995,63:215-232.
[102] P.Giudici and R.Castelo. Improving Markov Chain Monte Carlo Model Search for DataMining. Machine Learning,2003,50(1-2):127-158.
[103] C.K. Chow and C. N. Liu. Approximating Discrete Probability Distributions with DependenceTrees. IEEE Transactions on Information Theory,1968,14(3):462-467.
[104] S.L.Lauritzen. The EM Algorithm for Graphical Association Models with Missing Data.Computational Statistics and Data Analysis,1995,19:191–201.
[105] M.Ramoni and P. Sebastiani. Parameter Estimation in Bayesian Networks form IncompleteDatabases. KMI-TR-57,1997,11.
[106]胡学钢,胡春玲.一种基于依赖分析的贝叶斯网络结构学习算法.模式识别与人工智能,2006,19(4):445-449.
[107] V. Lepar and P. P. Shenoy. A Comparison of Lauritzen-Spiegelhalter, Hugin and Shenoy-ShaferArchitectures for Computing Marginals of Probability Distributions. In: Proceedings of the14th Conference on Uncertainty in Artificial Intelligence. California: Morgan Kaufmann,1998.328-337
[108] F.V.Jensen and T.D.Nielsen. Bayesian Networks and Decision Graphs.2nd ed., New York:Springer-Verleg,2007,109-166.
[109] A.Darwiche. A Differential Approach to Inference in Bayesian Networks. Journal of the ACM,2003,50(5):280-305
[110] F.V. Jensen and F.Jensen. Optimal Junction Trees. In: Proceedings of the10th Conference onUncertainty in Artificial Intelligence. Seattle, Washington, USA,1994,360-366.
[111] A.Becker and D.Geiger. A Sufficiently Fast Algorithm for Finding Close to Optimal JunctionTrees. In: Proceedings of the12th Conference on Uncertainty in Artificial Intelligence.Portland, Oregon, USA,1996:81-89
[112] K.Kask, R.Dechter, J Larrosa, et al. Unifying Tree Decompositions for Reasoning in GraphicalModels. Artificial Intelligence,2005,166(1-2):165-193
[113] R Mateescu, K Kask, V Gogate. Join-Graph Propagation Algorithms, Artificial Intelligence,2010(37):279-328
[114] J. Park and A.Darwiche. A Differential Semantics for Jointree Algorithms. Technical ReportD-118. Los Angeles:Computer Science Department, UCLA,2002.
[115] V.Lepar. Performance of Architectures for Local Computations in Bayesian Networks. Ph.D.thesis, University of Fribourg, Institute of Informatics.1999
[116] J.W.Han, H.Cheng, D. Xin, et al. Frequent pattern mining: current status and future directions.Data Mining Knowledge Discovery,2007,15(1):55-86.
[117] H.Zhang, B.Padmanabhan, and A.Tuzhilin. On the Discovery of Significant StatisticalQuantitative Rules. In: Proceedings of the10th ACM-SIGKDD International Confenerce onKnowledge Discovery and Data Mining. New York: ACM Press,2004,374-383.
[118] H.Cheng, X.F.Yan, and J.W.Han. Discriminative Frequent Pattern Analysis for EffectiveClassification. In: Proceedings of the23rd International Confenerce on Data Engineering. LosAlamitos, CA, USA: IEEE Computer Society Press,2007,716-725.
[119] H.X.Wang, W.Wang, J.Yang, et al. Clustering by Pattern Similarity in Large Data Sets. In:Proceedings of the28th ACM-SIGMOD International Confenerce on Management of Data.New York: ACM Press,2002,394-405.
[120] K.Mcgarry. A Survey of Interestingness Measures for Knowledge Discovery. KnowledgeEngineering Review,2005,20(1):39-61.
[121] S.Jaroszewicz and D.A. Simovici. Pruning Redundant Association Rules Using MaximumEntropy Principle. In: Proceedings of the6th Pacific-Asia Conference. on KnowledgeDiscovery and Data Mining. LNCS2336, Heidelberg: Springer-Verlag,2002.135-147.
[122] M.J.Zaki. Generating Non-Redundant Association Rules. In: Proceedings of the6thACM-SIGKDD Int’l Conf. on Knowledge Discovery and Data Mining. New York: ACM Press,2000,34-43.
[123]黄名选,严小卫,张师超.基于矩阵加权关联规则挖掘的伪相关反馈查询扩展.软件学报,2009,20(7):1854-1865.
[124] H.Yao and H.J. Hamilton. Mining Itemset Utilities from Transaction Databases. Data&Knowledge Engineering,2006,59(3):603-626.
[125] J.Blanchard, F.Guillet, R.Gras, et al. Using Information-Theoretic Measures to AssessAssociation Rule Interestingness. In: Proceedings of the5th International Confenerce on DataMining. Washington, DC: IEEE Computer Society,2005.66-73.
[126] D.R.Carvalho, A.A.Freitas, and N.Ebecken. Evaluating the Correlation between ObjectiveRule Interestingness Measures and Real Human Interest. In: Proceedings of the9th EuropeanConference on Principles of Data Mining and Knowledge Discovery. LNCS3721, Heidelberg:Springer-Verlag,2005.453-461.
[127] M.Ohsaki, S.Kitaguchi, K.Okamoto, et al. Evaluation of Rule Interestingness Measures with aClinical Dataset on Hepatitis. In: Proc. of the8th European Conf. on Principles of Data Miningand Knowledge Discovery. LNCS3202, Heidelberg: Springer-Verlag,2004.362-373.
[128] B.Padmanabhan and A.Tuzhilin. Small is Beautiful: Discovering the Minimal Set ofUnexpected Patterns. In: Proceedings of the6th ACM-SIGKDD International Confenerce onKnowledge Discovery and Data Mining. New York: ACM Press,2000.54-63.
[129] B.Padmanabhan and A.Tuzhilin. On Characterization and Discovery of Minimal UnexpectedPatterns in Rule Discovery. IEEE Transaction Knowledge Data Engineer,2006,18(2):202-216.
[130]丁贵涛.基于贝叶斯网络的数据挖掘方法及其基因表达分析应用[硕士学位论文].南开大学,2004.
[131] S.Jaroszewicz and D.A.Simovici. Interestingness of Frequent Itemsets Using BayesianNetworks as Background Knowledge. In: Proceedings of the10th ACM-SIGKDDInternational Confenerce on Knowledge Discovery and Data Mining. New York: ACM Press,2004.178-186.
[132] R.Malhas and Z.A.Aghbari. Fast Discovery of Interesting Patterns based on Bayesian NetworkBackground Knowledge. University of Sharjah Journal of Pure&Applied Sciences,2007,4(3):29-46.
[133] S.Jaroszewicz and T. Scheffer. Fast Discovery of Unexpected Patterns in Data Relative to aBayesian Network. In: Proceedings of the11th ACM SIGKDD International Confenerce onKnowledge Discovery and Data Mining. New York: ACM Press,2005.118-127.
[134] S. Jaroszewicz, T. Scheffer, and D.A.Simovici. Scalable Pattern Mining with BayesianNetworks as Background Knowledge. Data Mining and Knowledge Discovery,2008,18(1):56-100.
[135] R. Agrawal, T. Imielinski, and A. Swami. Mining Association Rules between Sets of Items inLarge Databases. In: Proceedings of the18th ACM-SIGMOD International Confenerce onManagement of Data. New York: ACM Press,1993.207-216.
[136] S.G. B ttcher and C.Dethlefsen. Deal: a Package for Learning Bayesian Networks. http://www.jstatsoft.org/v08/i20/paper
[137] P. Myllymaki, T. Silander, H. Tirri, et al. B-course: A Web-Based Tool for Bayesian and CausalData Analysis. International Journal on Artificial Intelligence Tools,2002,11(3):369-387.
[2] H.Jeffries. An Invariant Form for the Prior Probability in Estimation Problems. Pro. Roy. Soc.AA.1946,186:453-461.
[3] J.Pearl. Probabilistic Reasoning in Intelligent Systems: Network of Plausible Inference.Morgan Kaufinann,1988:1-86
[4] D.Geiger and T.Verma. D-Separation: From Theorems to Algorithms. In: Proceedings of the5th Workshop on Uncertainty in Artificial Intelligence. Windsor, Ontario,1989,118-125.
[5] J.Pearl. Propagation and Structuring in Belief Networks. Artificial Intelligence,1986,29(3):241-288.
[6] H.J.Suermondt and G. F. Cooper. Probabilistic Inference in Multiply Connect Belief NetworksUsing Loop Cutsets. International Journal of Approximate Reasoning,1990.
[7] F.J.Diez. Local Conditioning in Bayesian Networks. Cognitive Systems Laboratory,Department of Computer Science, UCLA,1992.
[8] R.D.Shachter, S.K.Anderson, and P. Szolovits. Global Conditioning for Probabilistic Inferencein Belief Networks. In: Proceedings of the Uncertainty in Artificial Intelligence Conference,SanFranci sco. CA: Morgan Kaufmann,1994,514-522.
[9] A.Darwiche. Conditioning methods for exact and Approximate Inference in Causal Networks.In: Proceedings of the11th Annual Conference on Uncertainty in Artificial Intelligence.Montreal: Morgan Kauffman,1995.
[10] A. Darwiche. Recursive conditioning. Artificial Intelligence,2001,125(1-2):5-41.
[11] S.L.Lauritzen and D.J.Spiegelhalter. Local Computations with Probabilities on GraphicalStructures and Their Applications to Expert Systems. In: Proceedings of the Royal StatisticalSociety.1988, B(50),154-227.
[12] P.Shenoy and G.Shafer. Axioms for Probability and Belief-function Propagation. Uncertaintyin AI,1990,4:169-198.
[13] F.V.Jensen, S.Lauritzen, and K.Olesen. Bayesian Updating in Causal Probabilistic Networksby Local Computation. Computational Statistics Quarterly,1990(4):269-282.
[14] A.L.Madsen and F.V. Jensen. Lazy Propagation in Junction Trees. In: Proceedings of theFourteenth Conference on Uncertainty in Artificial Intelligence. Morgan Kaufmann,1998,362-369.
[15] R.D.Shachter, D.B.Ambrosio, and B.D.DelFavero. Symbolic Probabilistic Inference in BeliefNetworks. In: Proceedings of the Eighth National Conference on Artificial Intelligence. Boston:MIT,1990,126-131.
[16] N.L.Zhang and D.Poole. A Simple Approach to Bayesian network Computations. In:Proceedings of the10th Canadian Conference on Artificial Intelligence.1994,171-178.
[17] R.Dechter. Bucket elimination: a Unifying Framework for Probabilistic Inference. In:Proceedings of the12th Conference on Uncertainty in Artificial Intelligence. Portland, Oregon,1996,211-219.
[18] K.Kask, R.Dechter, J.Larrosa, et al. Bucket-tree Elimination for Automated Reasoning.Artificial Intelligence,2001(125):91-131.
[19] R.D.Shachter. Evidence Absorption and Propagation through Evidence Reversals.Uncertaintyin Artificial Intelligence,1990(5):173-190.
[20] Y.W.C.Adrian and C.Boutilier. Structured Arc Reversal and Simulation of DynamicProbabilistic Networks. In: Proceedings of the13th Conference on Uncertainty in ArtificialIntelligence.1997.
[21] A.Darwiche. A Differential Approach to Inference in Bayesian. In: Proceedings of the6thConference on Uncertainty in Artificial Intelligence. San Francisco: Morgan Kaufmann,2000.
[22] B.Boris. An Extension of the Differential Approach for Bayesian Network Inference toDynamic Bayesian Networks. International Journal of Intelligent Systems,2004,19(8):727-748.
[23] P.Dagum, R.Karp, M.Luby, et al. An Optimal Algorithm for Monte Carlo estimation. In:Proceedings of the6th IEEE Symposium on Foundations of Computer Science, Portland,Oregon:1995,142-149.
[24] M.Henrion. Propagating Uncertainty in Bayesian Networks by Probabilistic LogicSampling.Uncertainty in Artificial Intelligence,1988(2):149-163.
[25] R.Fung and K.C.Chang. Weighting and Integrating Evidence for Stochastic Simulation inBayesian Networks. Uncertainty in Artificial Intelligence,1989(5):209-219.
[26] R.D.Shachter and M.A.Peot. Simulation Approaches to General Probabilistic Inference onBelief Networks. In: Proceedings of the Conference on Uncertainty in Artificial Intelligence.1990.
[27] S.Geman and D.Geman. Stochastic Relaxation, Gibbs Distribution and the BayesianRestoration of Images. IEEE Transactions on Pattern Analysis and Machine Intelligence,1984,6(6):721-741.
[28] R.M.Chavez and G.F.Cooper. A Randomized Approximation Algorithm for ProbabilisticInference on Bayesian Belief Networks.Networks,1990:661-685.
[29] D.Draper. Localized partial evaluation of Bayesian belief networks. Seattle: University ofWashington.1995.
[30] E.Horvitz, H.J.Suermondt, and G.F.Cooper. Bounded Conditional: Flexible Inference forDecisions under Scarce Resources. In: Proceedings of the5th Conference on Uncertainty inArtificial Intelligence. Windsor, Ontario,1989,182-193.
[31] M.P.Wellman and C.L.Liu. State-space Abstraction for Anytime Evaluation of ProbabilisticNetworks.Uncertainty in Artificial Intelligence,1994:567-574.
[32] T.S.Jaakkola and M.Jordan. Variational Probabilistic Inference and the QMR-DT Network.Journal of Artificial Intelligence Research,1999,10:291-322.
[33] D.Poole. Context-specific Approximation in Probabilistic Inference. In: Proceedings of the14th Conference on Uncertainty in Artificial Intelligence.1998.
[34] S.Sarkar. Using Tree-decomposable Structures to Approximate Belief Networks. In:Proceedings of the9th Conference on Uncertainty in Artificial Intelligence. Washington, DC:Morgan Kaufmann,1993.
[35] K.P.Murphy, Y.Weiss, and M.Jordan. Loopy Belief Propagation for Approximate Inference: anEmpirical Study. In: Proceedings of the15th Conference Uncertainty in Artificial Intelligence.1999,467-475.
[36] S.Tatikonda and M.Jordan. Loopy Belief Propagation and Gibbs Measures. Uncertainty inArtificial Intelligence,2002.
[37] E.Herskovits. Computer-based Probabilistic-Network Construction.USA: Stanford University,1991.
[38] R.R.Bouckaert. A Stratified Simulation Scheme for Inference in Bayesian Belief Networks. In:Proceedings of the10th Conference Uncertainty in Artificial Intelligence.1994.110-117.
[39] D.Chickering, D.Geiger, and D.Heckerman. Learning Bayesian Networks: Search Methodsand Experimental Results. In: Proceedings of the5th conference on Artificial Intelligence andStatistics. IEEE Press,1995,112-128.
[40] J.Suzuki. A Construction of Bayesian Networks from Databases Based on an MDL Principle.In: Proceedings of the9th Conference on Uncertainty in Artificial Intelligence. WashingtonD.C.1996,266-273.
[41] P.Larranaga. Structure Learning of Bayesian Networks by Genetic Algorithms: a PerformanceAnalysis of Control Parameters. IEEE Transactions on Pattern Analysis and MachineIntelligence,1996,18b(9):912-926.
[42] P.Larranaga. Searching for the Best Ordering in the Structure Learning of Bayesian Netwroks.IEEE Transactions on System, Man and Cybermetics,1996,26(4):487-493.
[43] M.L.Wong, S.Y.Lee, and K.S.Leung. A Hybrid Approach to Discover Bayesian Networks fromDatabases Using Evolutionary Programming. In: Proceedings on International ConferenceData Mining.2002,498-505.
[44] D.Madigan, A.E. Raftery, J.C. York, et al. Strategies for Graphical Model Selection, In: P.Cheeseman, R.W. Oldford (Eds.), Selecting Models from Data: Artificial Intelligence andStatistics.Springer, Berlin,1994,4.
[45] N.Friedman and D.Koller. Being Bayesian about Network Structure: A Bayesian Approach toStructure Discovery in Bayesian Networks. Machine Learning,2003,50:95-126.
[46] B. Ellis and W. Wong. Sampling Bayesian Networks quickly. In: Interface, Pasadena:2006.
[47] D.M.Chickering and D.Geiger. Learning Bayesian Networks: Search Methods andExperimental Results. In: Proceedings of5th Conference on Artificial Intelligence andStatistics.1995.112-128.
[48] M.Koivisto and K. Sood. Exact Bayesian Structure Discovery in Bayesian Networks. MachineLearning Research,2004,5:549-573.
[49] N.Wermuth and S.Lauritzen. Graphical and Recursive Models for Contingency tables.Biometrika,1983,70(1):537-552.
[50] C.Spirtes, P.Glymour, and R.Scheines. Causality from Probability. Evolving Knowledge inNatural Science and Artificial Intelligence. London: Piman,1990:181-199.
[51] P.Spirtes, C.Glymour, and R.Scheines. An Algorithm for Fast Recovery of Sparse CausalGraphs. Social Science Computer Review,1991,9(1):62-72.
[52] J.Cheng and R.Greiner. Learning Bayesian Networks from Data: an Information Theory basedApproach. Artificial Intelligence,2002,137(1-2):43-90.
[53] M.Singh and M.Valtorta. Construction of Bayesian Network Structures form Data: a BriefSurvey and an Efficient Algorithm. International Journal of Approximate Reasoning,1995,12(2):111-131.
[54] X.W.Chen,G. Anantha, and X.T. Lin. Improving Bayesian Network Structure Learning withMutual Information-Based Node Order in the K2Algorithm. IEEE Transactions on Knowledgeand Data Engineering,2008,20(5):628-640.
[55] M.L.Wong and K.S.Leung. An Efficient Data Mining Method for Learning Bayesian NetworksUsing an Evolutionary Algorithm-based Hybrid Approach. IEEE Transactions on EvolutionaryComputation,2004,8:378-404.
[56] I.Tsamardinos, E.Brown, and C.F.Aleferis. The Max-min Hill-climbing Bayesian NetworkStructure Learning algorithm. Machine Learning,2006,65(1):31-78.
[57] A.Statnikov, I.Tsamardinos, and C.F.Aliferis. An Algorithm for Generation of LargeBayesian Networks. Vanderbilt University,2003, TR-03-01.
[58] P.C. Pinto, A.Nagele, M.Deiori, et al. Learning of Bayesian Networks by a Local DiscoveryAnt Colony Algorithm. IEEE World Congress on Computational Intelligence. Hong Kong:China,2008,2741-2748.
[59] N.Friedman. Leaming Belief Networks in the Presence of Missing Values and Hiddenvariables. In: Proeeedings of the14th International Conference on Machine Learning. MorganKaufinann, Nashville, Tennessee, USA,1997,125-133.
[60] N.Friedman. The Bayesian Struetural EM Algoritbm. In: Proeeedings of the14th Conferenceon Uncertainty in Artificial Intelligenee. Morgan Kaufinann, Madison, Wiseonsin,USA.1998,129-138.
[61] J.W.Myers, K.B.Laskey, T.S.Levitt. Learning Bayesian Networks from Incomplete Data withStochastic Search Algorithms. In: Proeeedings of the15th Conference on Uncertainty inArtificial Intelligence. MorganKaufmann, Stockholm, Sweden.1999,476-485.
[62] K.B.Laskey and J.W. Myers. Population Markov Chain Monte Carlo. Machine Learning,2003,50,175-196.
[63] D.Chickering, D.Heckerman and C.Meek Large-sample learning of Bayesian Networks isNP-Hard. Machine Learning Research,2004,5,1287-1330.
[64] G.Cooper. Computational Complexity of Probabilistic Inference Using Bayesian BeliefNetwork. Artificial Intelligence,1990,42:393-405
[65] P.Dagum and R.M.Chavez. Approximating Probabilistic Inference in Bayesian BeliefNetworks. IEEE Transactions on Pattern Analysis and MachineIntelligence,1993,15(3):246-255
[66] www.onparenting.msn.com
[67] P.J.F.Lucas. Expert Knowledge and Its Role in Learning Bayesian Networks in Medicine: AnAppraisal. In: Proceedings of the8th Conference on AI in Medicine in European. Springer,Cascais, Portugal.2001,156-166.
[68] A.Onisko, P.J.F.Lucas, and M.J.Druzdzel. Comparison of Rule-Based and Bayesian NetworkApproaches in Medical Diagnostic Systems. In: Proceedings of the8th conference on AI inMedicine in European. Springer, Cascais, Portugal.2001,283-292.
[69] M.J.Sillanpaa and J.Corander. Model Choice in Gene Mapping: What and Why. Trends Genet,2002,18(6):301-307.
[70] M, Andronescu, A. Condon, H Hoos, et al.Efficient parameter estimation for RNA secondarystructure prediction, Bioinformatics2007
[71] N.Friedman. Inferring Cellular Networks Using Probabilistic Graphical Models. Science,2004,303:799-805.
[72] A.Hartemink, D.Gifford, T.Jaakkola, et al. Bayesian Methods for Elucidating GeneticRegulatory Networks. IEEE Intelligent Systems,2002,17(2):37-43.
[73] A. Jaimovich, G. Elidan, H.Margalit, et al. Towards an integrated protein-protein interactionnetwork: a relational Markov network approach. Journal of computational biology,2006,6,13(2):145-64.
[74] A.Raval, Z.Ghahramani, and D.L.Wild. A Bayesian Network Model for Protein Fold andRemote Homologue Recognition. Bioinformatics.2002,18(6):788-801.
[75] S.Geman and K.Kochanek Dynamic Programming and the Graphical Representation ofError-correcting Codes. IEEE Transactions on Information Theory,2001,47(2):549-568.
[76] A.Krause and C.Guestrin. Near-optimal Nonmyopic Value of Information in Graphical Models.In: Proceedings of the21th Conference in Uncertainty in Artificial Intelligence. AAAI Press,Edinburgh, Scotland.2005,324-331.
[77] M.A.Rodrigues, Y. Liu, L.Bottaci, et al. Learning and Diagnosis in Manufacturing ProcessesThrough an Executable Bayesian Network. In: Proceedings of the13th InternationalConference on Industrial and Engineering Applications of Artificial Intelligence and ExpertSystems. Springer, New Orleans, Louisiana, USA,2000,390-395.
[78] B.McCabe. Belief Networks for Engineering Applications. International Journal of TechnologyManagement,2001,21(3-4):257-270.
[79] P.Giudici. Bayesian Data Mining with Application to Benchmarking and Credit Scoring.Application Stochastic Model Business.2001,17(1):69-81.
[80] J.Gemela. Financial Analysis Using Bayesian Networks. Application Stochastic ModelBusiness.2001,17(1):57-67.
[81] G.Socher, G.Sagerer, and P.Perona. Bayesian Reasoning on Qualitative Descriptions fromImages and Speech. Image Vision Compution.2000,18(2):155-172.
[82] T.V.Pham, M.Wowing, and A.W.M.Smeulders. Face Detection by Aggregated BayesianNetwork Classifiers. Pattern Recognition Letters,2002,23(4):451-461.
[83] D.A.Wooff, M.Goldstein, and F.P.A.Coolen. Bayesian Graphical Models for Software Testing.IEEE Software Engineering,2002,28(5):510-525.
[84]宫秀军，刘少辉，史忠植.一种增量贝叶斯分类模型.计算机学报，2002,25(6):645-650.
[85]宫秀军，史忠植.基于贝叶斯潜在语义分析的半监督web挖掘.软件学报,2002，13(8)：1508-1514.
[86]李伟生,王宝树.实现规划识别的一种贝叶斯网络.西安电子科技大学学报(自然科学版),2002，29(6):741-744.
[87]霍利民，朱永利，范高峰等.一种基于贝叶斯的电力系统可靠性评估新方法.电力系统自动化，2002，27(5):36-40.
[88]李俭川，胡莺庆等.基于贝叶斯网络的智能故障诊断方法.中国惯性技术学报，2002，10(4):24-28.
[89]邓勇，施文康，陈良州.基于模型诊断的贝叶斯解释及应用.上海交通大学学报,2003，37(1):5-8.
[90]汪荣贵. bayes网络理论及其在目标检测中应用研究[博士学位论文].合肥工业大学,2004.
[91]雷耀山,史定华,王翼飞.基因调控网络的生物信息学研究.自然杂志.2004,26(1):7-12.
[92]徐肖江.从功能基因组数据重建基因调控网络[博士学位论文].中国科学院上海生命科学研究院生物化学与细胞生物学研究所,2005.
[93] D. Geiger, T.Verma, and J.Pearl. Identifying Independence in Bayesian Networks. Networks,1990,20:507-534.
[94] F.V. Jensen. Bayesian Networks and Decision. Statistics for Engineering and InformationScience Series, Springer Verlag,2001.
[95] G.F.Cooper and E. Herskovits. A Bayesian Method for the Induction of Probabilistic Networksfrom Data. Machine Learning,1992,9:309-347.
[96] G.F.Cooper and E. Herskovits. A Bayesian Method for Constructing Bayesian Belief Networksfrom Databases. In: Proceedings of the7th Annual Conference on Uncertainty in ArtificialIntelligence. Morgan Kaufmann, Los Angeles, CA, USA.1991,86-94.
[97] D.Heckerman, D.Geiger, and D.M.Chickering. Learning Bayesian Networks: the Combinationof Knowledge and Statistical Data. Machine Learning.1995,20(3):197-243.
[98] C. Andrieu, N.D. Freitas, A. Doucet, et al. An introduction to MCMC for Machine Learning.Machine Learning,2003,50:5-43.
[99] C.Robert, G. Casella. Monte Carlo statistical methods.2nd edition, Springer,2004.
[100] W. Gilks, S. Richardson and D.Spiegelhalter. Markov Chain Monte Carlo Methods in Practice.CRC Press,1996.
[101] D. Madigan and J. York. Bayesian Graphical Models for Discrete Data. InternationalStatistical Review,1995,63:215-232.
[102] P.Giudici and R.Castelo. Improving Markov Chain Monte Carlo Model Search for DataMining. Machine Learning,2003,50(1-2):127-158.
[103] C.K. Chow and C. N. Liu. Approximating Discrete Probability Distributions with DependenceTrees. IEEE Transactions on Information Theory,1968,14(3):462-467.
[104] S.L.Lauritzen. The EM Algorithm for Graphical Association Models with Missing Data.Computational Statistics and Data Analysis,1995,19:191–201.
[105] M.Ramoni and P. Sebastiani. Parameter Estimation in Bayesian Networks form IncompleteDatabases. KMI-TR-57,1997,11.
[106]胡学钢,胡春玲.一种基于依赖分析的贝叶斯网络结构学习算法.模式识别与人工智能,2006,19(4):445-449.
[107] V. Lepar and P. P. Shenoy. A Comparison of Lauritzen-Spiegelhalter, Hugin and Shenoy-ShaferArchitectures for Computing Marginals of Probability Distributions. In: Proceedings of the14th Conference on Uncertainty in Artificial Intelligence. California: Morgan Kaufmann,1998.328-337
[108] F.V.Jensen and T.D.Nielsen. Bayesian Networks and Decision Graphs.2nd ed., New York:Springer-Verleg,2007,109-166.
[109] A.Darwiche. A Differential Approach to Inference in Bayesian Networks. Journal of the ACM,2003,50(5):280-305
[110] F.V. Jensen and F.Jensen. Optimal Junction Trees. In: Proceedings of the10th Conference onUncertainty in Artificial Intelligence. Seattle, Washington, USA,1994,360-366.
[111] A.Becker and D.Geiger. A Sufficiently Fast Algorithm for Finding Close to Optimal JunctionTrees. In: Proceedings of the12th Conference on Uncertainty in Artificial Intelligence.Portland, Oregon, USA,1996:81-89
[112] K.Kask, R.Dechter, J Larrosa, et al. Unifying Tree Decompositions for Reasoning in GraphicalModels. Artificial Intelligence,2005,166(1-2):165-193
[113] R Mateescu, K Kask, V Gogate. Join-Graph Propagation Algorithms, Artificial Intelligence,2010(37):279-328
[114] J. Park and A.Darwiche. A Differential Semantics for Jointree Algorithms. Technical ReportD-118. Los Angeles:Computer Science Department, UCLA,2002.
[115] V.Lepar. Performance of Architectures for Local Computations in Bayesian Networks. Ph.D.thesis, University of Fribourg, Institute of Informatics.1999
[116] J.W.Han, H.Cheng, D. Xin, et al. Frequent pattern mining: current status and future directions.Data Mining Knowledge Discovery,2007,15(1):55-86.
[117] H.Zhang, B.Padmanabhan, and A.Tuzhilin. On the Discovery of Significant StatisticalQuantitative Rules. In: Proceedings of the10th ACM-SIGKDD International Confenerce onKnowledge Discovery and Data Mining. New York: ACM Press,2004,374-383.
[118] H.Cheng, X.F.Yan, and J.W.Han. Discriminative Frequent Pattern Analysis for EffectiveClassification. In: Proceedings of the23rd International Confenerce on Data Engineering. LosAlamitos, CA, USA: IEEE Computer Society Press,2007,716-725.
[119] H.X.Wang, W.Wang, J.Yang, et al. Clustering by Pattern Similarity in Large Data Sets. In:Proceedings of the28th ACM-SIGMOD International Confenerce on Management of Data.New York: ACM Press,2002,394-405.
[120] K.Mcgarry. A Survey of Interestingness Measures for Knowledge Discovery. KnowledgeEngineering Review,2005,20(1):39-61.
[121] S.Jaroszewicz and D.A. Simovici. Pruning Redundant Association Rules Using MaximumEntropy Principle. In: Proceedings of the6th Pacific-Asia Conference. on KnowledgeDiscovery and Data Mining. LNCS2336, Heidelberg: Springer-Verlag,2002.135-147.
[122] M.J.Zaki. Generating Non-Redundant Association Rules. In: Proceedings of the6thACM-SIGKDD Int’l Conf. on Knowledge Discovery and Data Mining. New York: ACM Press,2000,34-43.
[123]黄名选,严小卫,张师超.基于矩阵加权关联规则挖掘的伪相关反馈查询扩展.软件学报,2009,20(7):1854-1865.
[124] H.Yao and H.J. Hamilton. Mining Itemset Utilities from Transaction Databases. Data&Knowledge Engineering,2006,59(3):603-626.
[125] J.Blanchard, F.Guillet, R.Gras, et al. Using Information-Theoretic Measures to AssessAssociation Rule Interestingness. In: Proceedings of the5th International Confenerce on DataMining. Washington, DC: IEEE Computer Society,2005.66-73.
[126] D.R.Carvalho, A.A.Freitas, and N.Ebecken. Evaluating the Correlation between ObjectiveRule Interestingness Measures and Real Human Interest. In: Proceedings of the9th EuropeanConference on Principles of Data Mining and Knowledge Discovery. LNCS3721, Heidelberg:Springer-Verlag,2005.453-461.
[127] M.Ohsaki, S.Kitaguchi, K.Okamoto, et al. Evaluation of Rule Interestingness Measures with aClinical Dataset on Hepatitis. In: Proc. of the8th European Conf. on Principles of Data Miningand Knowledge Discovery. LNCS3202, Heidelberg: Springer-Verlag,2004.362-373.
[128] B.Padmanabhan and A.Tuzhilin. Small is Beautiful: Discovering the Minimal Set ofUnexpected Patterns. In: Proceedings of the6th ACM-SIGKDD International Confenerce onKnowledge Discovery and Data Mining. New York: ACM Press,2000.54-63.
[129] B.Padmanabhan and A.Tuzhilin. On Characterization and Discovery of Minimal UnexpectedPatterns in Rule Discovery. IEEE Transaction Knowledge Data Engineer,2006,18(2):202-216.
[130]丁贵涛.基于贝叶斯网络的数据挖掘方法及其基因表达分析应用[硕士学位论文].南开大学,2004.
[131] S.Jaroszewicz and D.A.Simovici. Interestingness of Frequent Itemsets Using BayesianNetworks as Background Knowledge. In: Proceedings of the10th ACM-SIGKDDInternational Confenerce on Knowledge Discovery and Data Mining. New York: ACM Press,2004.178-186.
[132] R.Malhas and Z.A.Aghbari. Fast Discovery of Interesting Patterns based on Bayesian NetworkBackground Knowledge. University of Sharjah Journal of Pure&Applied Sciences,2007,4(3):29-46.
[133] S.Jaroszewicz and T. Scheffer. Fast Discovery of Unexpected Patterns in Data Relative to aBayesian Network. In: Proceedings of the11th ACM SIGKDD International Confenerce onKnowledge Discovery and Data Mining. New York: ACM Press,2005.118-127.
[134] S. Jaroszewicz, T. Scheffer, and D.A.Simovici. Scalable Pattern Mining with BayesianNetworks as Background Knowledge. Data Mining and Knowledge Discovery,2008,18(1):56-100.
[135] R. Agrawal, T. Imielinski, and A. Swami. Mining Association Rules between Sets of Items inLarge Databases. In: Proceedings of the18th ACM-SIGMOD International Confenerce onManagement of Data. New York: ACM Press,1993.207-216.
[136] S.G. B ttcher and C.Dethlefsen. Deal: a Package for Learning Bayesian Networks. http://www.jstatsoft.org/v08/i20/paper
[137] P. Myllymaki, T. Silander, H. Tirri, et al. B-course: A Web-Based Tool for Bayesian and CausalData Analysis. International Journal on Artificial Intelligence Tools,2002,11(3):369-387.