Abstract：In this paper,a local Gibbs sampling inference algorithm of Bayesian networks (S-LGSI) is proposed. Firstly,the S-LGSI algorithm precisely decomposes Bayesian networks based on the analytic idea of junction tree algorithm. Secondly,the suitable local model is chosen by the query node and the evidence node. Then,Gibbs sampling inference algorithm for local network model is utilized. Compared with other current approximate sampling algorithms,the S-LGSI algorithm significantly reduces the calculation dimension. The sampling inference in the local model avoids the statistics of joint sample series and greatly reduces the calculation dimension. The proposed algorithm guarantees the inference precision,as the local model contains important information about the query node. Algorithm analysis and experimental results on Alarm network show S-LGSI significantly reduces the complexity and improves the inference precision. The proposed algorithm has strong practicability,because the inference results of S-LGSI algorithm are basically consistent with the real situation on the Shanghai Stock Exchange network.
[1] Daly R,Qing S,Aithen S. Learning Bayesian Networks: Approaches and Issues. The Knowledge Engineering Review,2011,26(2): 99-127 [2] Takaishi T. Bayesian Inference of Stochastic Volatility Model by Hybrid Monte Carlo.Journal of Circuits,Systems and Computers,2009,18(8): 1381-1396 [3] Jin K H,Wu Dan,Wu Libing. On Designing Approximate Inference Algorithms for Multiply Sectioned Bayesian Networks // Proc of the IEEE International Conference on Granular Computing. Nanchang,China,2009: 294-299 [4] Neal R M. Probabilistic Inference Using Markov Chain Monte Carlo Methods. Technique Report,CRGTR 93-1. Toronto,Canada: University of Toronto,1993 [5] Yu Binbing. A Bayesian MCMC Approach to Survival Analysis with Doubly-Censored Data. Computational Statistics and Data Analysis,2010,54(8): 1921-1929 [6] Geman S,Geman D. Stochastic Relaxation,Gibbs Distributions,and the Bayesian Restoration of Images. IEEE Trans on Pattern Analysis and Machine Intelligence,1984,6(6): 721-741 [7] Yao Hongliang,Wang Hao,Zhang Yousheng,et al. Research on Multi-Agent Dynamic Influence Diagrams and Its Approximate Inference Algorithm. Chinese Journal of Computers,2008,31(2): 236-244(in Chinese) (姚宏亮,王 浩,张佑生,等.多Agent 动态影响图及其一种近似推理算法研究.计算机学报,2008,31(2): 236-244) [8] Huang C. Inference in Belief Networks: A Procedural Guide. International Journal of Approximate Reasoning,1996,15(3): 225-263 [9] Wu Dan,Tania N M,Jin K H. Heuristic Assignment of CPDs for Probabilistic Inference in Junction Trees // Proc of the 21st IEEE International Conference on Tools with Artificial Intelligence. Newark,USA,2009: 581-588 [10] Kevin G,Michael C H. Conditioning Graphs: Practical Structures for Inference in Bayesian Networks // Proc of the 18th Australian Joint Conference on Artificial Intelligence. Sydney,Australia,2005: 49-59 [11] Yao Hongliang,Wang Hao,Zhang Yousheng,et al. An Extensional Junction Tree Approximate Inference Algorithm for Dynamic Influence Diagrams // Proc of the International Conference on Neural Networks and Brain. Beijing,China,2005,I: 396-400 [12] Strens M J A.Evolutionary MCMC Sampling and Optimization in Discrete Spaces // Proc of the 20th International Conference on Machine Learning. Washington,USA,2003: 736-743 [13] Zhou Bo. Markov Chain Monte Carlo Random Testing // Proc of the AST/UCMA/ISA/CAN Conference on Advances in Computer Science and Information Technology. Miyazaki,Japan,2010: 447-456 [14] Cheng J,David B,Liu W R. Learning Bayesian Networks from Data: An Efficient Approach Based on Information Theory. Artificial Intelligence,2002,137(1/2): 43-90 [15] Eaton D,Murphy K. Exact Bayesian Structure Learning from Uncertain Interventions. AI Statistics,2007,24(1): 107-114 [16] Collie M J,Dowe D L,Fitzgibbon L J. Stock Market Simulation and Inference Technique // Proc of the 5th International Conference on Hybrid Intelligent Systems. Atlanta,USA,2005: 534-538 [17] Boginski V,Butenko S. Statistical Analysis of Financial Networks. Computational Statistics Data Analysis,2005,48(2): 431-443 [18] Zhang Yunyun,Shen Wei. Stock Yield Forecast Based on LS-SVM in Bayesian Inference // Proc of the International Conference on Future Computer and Communication. Wuhan,China,2009: 8-11
2013, Vol. 26 
