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Issue No.07 - July (2012 vol.24)
pp: 1306-1312
M. Neil , Sch. of Electron. Eng. & Comput. Sci., Queen Mary Univ. of London, London, UK
Reducing the computational complexity of inference in Bayesian Networks (BNs) is a key challenge. Current algorithms for inference convert a BN to a junction tree structure made up of clusters of the BN nodes and the resulting complexity is time exponential in the size of a cluster. The need to reduce the complexity is especially acute where the BN contains continuous nodes. We propose a new method for optimizing the calculation of Conditional Probability Tables (CPTs) involving continuous nodes, approximated in Hybrid Bayesian Networks (HBNs), using an approximation algorithm called dynamic discretization. We present an optimized solution to this problem involving binary factorization of the arithmetical expressions declared to generate the CPTs for continuous nodes for deterministic functions and statistical distributions. The proposed algorithm is implemented and tested in a commercial Hybrid Bayesian Network software package and the results of the empirical evaluation show significant performance improvement over unfactorized models.
tree data structures, approximation theory, belief networks, computational complexity, pattern clustering, software packages, statistical distributions, unfactorized models, conditional probability tables, binary factorization, computational complexity, junction tree structure, BN nodes, time exponential complexity, cluster size, CPT, approximation algorithm, dynamic discretization, arithmetical expressions, deterministic functions, statistical distributions, hybrid Bayesian network software package, Clustering algorithms, Algorithm design and analysis, Heuristic algorithms, Inference algorithms, Approximation algorithms, Bayesian methods, Junctions, dynamic discretization., Bayesian networks, binary factorization
M. Neil, "Optimizing the Calculation of Conditional Probability Tables in Hybrid Bayesian Networks Using Binary Factorization", IEEE Transactions on Knowledge & Data Engineering, vol.24, no. 7, pp. 1306-1312, July 2012, doi:10.1109/TKDE.2011.87
[1] J. Pearl, Probabilistic Reasoning in Intelligent Systems: Network of Plausible Inference. Morgan Kaufmann Publishers, 1988.
[2] D.J. Speigelhalter and R.J. Cowell, "Learning in Probabilistic Expert Systems," Bayesian Statistics, vol. 4, pp. 447-465, 1992.
[3] M. Neil, N.E. Fenton, S. Forey, and R. Harris, "Using Bayesian Belief Networks to Predict the Reliability of Military Vehicles," Computing and Control Eng. J., vol. 12, no. 1, pp. 11-20, 2001.
[4] M. Neil, M. Tailor, D. Marquez, N. Fenton, and P. Hearty, "Modelling Dependable Systems Using Hybrid Bayesian Networks," Reliability Eng. and System Safety, vol. 93, no. 7, pp. 933-939, , July 2008.
[5] M. Neil, N. Fenton, and M. Tailor, "Using Bayesian Networks to Model Expected and Unexpected Operational Losses," Risk Analysis J., vol. 25, pp. 963-972, Aug. 2005.
[6] R.J. Cowell, R.J. Verral, and Y.K. Yoon, "Modelling Operational Risk with Bayesian Networks," The J. Risk and Insurance, vol. 74, no. 4, pp 795-827, 2006.
[7] F.V. Jensen, An Introduction to Bayesian Networks. UCL Press, 1996.
[8] S.L. Lauritzen and D.J. Spiegelhalter, "Local Computations with Probabilities on Graphical Structures and Their Application to Expert Systems (with Discussion)," J. Royal Statistical Soc. Series B, vol. 50, no 2, pp. 157-224, 1988.
[9], 2010.
[10] M. Neil, N.M. Nielson, F. Fenton, and X. Nielson, "Building Large-Scale Bayesian Networks," The Knowledge Eng. Rev., vol. 15, no. 3, pp. 257-284, 2000.
[11] P. Shenoy and G. Shafer, "Propagating Belief Functions with Local Computations," IEEE Expert, vol. E-1, no. 3, pp. 43-52, Sept. 1986.
[12] F. Jensen, S.L. Lauritzen, and K. Olesen, "Bayesian Updating in Recursive Graphical Models by Local Computations," Computational Statistics Quarterly, vol. 4, pp. 260-282, 1990.
[13] M. Neil, M. Tailor, and D. Marquez, "Inference in Bayesian Networks Using Dynamic Discretization," Statistics and Computing, vol. 17, no. 3, pp. 219-233, Sept. 2007.
[14] B. Das, "Generating Conditional Probabilities for Bayesian Networks: Easing the Knowledge Acquisition Problem," Computing Research Repository, vol. cs.AI/0411034,, 2004.
[15] A. Choi, H. Chan, and A. Darwiche, "On Bayesian Network Approximation by Edge Deletion," Proc. 21st Conf. Uncertainly in Artificial Intelligence, 2005.
[16] N. Fenton, M. Neil, and J. Gabaiiero, "Using Ranked Nodes to Model Qualitative Judgments in Bayesian Networks," IEEE Trans. Knowledge and Data Eng., vol. 19, no. 10, pp. 1420-1432, Oct. 2007.
[17] N. Zhang and D. Poole, "Exploiting Causal Independence in Bayesian Network Inference," J. Artificial Intelligence Research, vol. 5, pp. 301-328, 1996.
[18] F. Jensen, Bayesian Networks and Decision Graphs. Springer Verlag, 2007.
[19] B. Cobb and P. Shenoy, "Operations for Inference in Continuous Bayesian Networks with Linear Deterministic Variables," Int'l. J. Approximate Reasoning, vol. 42, nos. 1/2, pp. 21-36, 2006.
[20] B. Cobb and P. Shenoy, "Inference in Hybrid Bayesian Networks with Mixtures of Truncated Exponentials," Int'l J. Approximate Reasoning, vol. 41, pp. 257-286, 2006, doi:10.1016/j.ijar.2005.06.002.
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