Abstract
This paper shows how an efficient and parallel algorithm for inference in Bayesian Networks (BNs) can be built and implemented combining sparse matrix factorization methods with variable elimination algorithms for BNs. This entails a complete separation between a first symbolic phase, and a second numerical phase.
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References
Colla, E.C.: Aplicação de Técnicas de Fatoração de Matrizes Esparsas para Inferência em Redes Bayesianas. Ms.S. Thesis, MAC-IME-USP, Institute of Mathematics and Statistics, University of São Paulo (2007)
Cozman, F.G.: Generalizing variable elimination in Bayesian networks. IBERAMIA-SBIA, Workshop proceedings. São Paulo, Tec. Art, pp. 27–32 (2000)
Mandani, A., Heckerman, D., Wellman, M.P.: Real-world applications of Bayesian networks. Comm. of the ACM 38(3), 24–26 (1995)
Dechter, R.: Bucket elimination: An unifying framework for probabilistic inference. In: 12th UAI proceedings, pp. 211–219. Morgan Kaufmann Publishers, San Francisco (1996)
George, A., Gilbert, J.R., Liu, J.W.H. (eds.): Graph Theory and Sparse Matrix Computation. Springer, NY (1993)
Jensen, F.V.: An introduction to Bayesian networks. Springer, NY (1996)
Lauritzen, S.L., Spiegelhalter, D.J.: Local computations with probabilities on graphical structures and their application to expert systems. J. Royal Statistical Soc., B 50(2), 157–224 (1988)
Pearl, J.: Probabilistic reasoning in intelligent systems: Networks of plausive inference. Morgan Kaufmann, San Francisco (1988)
Pissanetzky, S.: Sparse matrix technology. Academic Press, New York (1984)
Shachter, R.: Bayes-ball: The rational pastime (for determining irrelevance and requisite information in belief networks and influence diagrams). In: 14th UAI proceedings, pp. 480–487. Morgan Kaufmann, San Francisco (1998)
Stern, J.M.: Simulated Annealing with a Temperature Dependent Penalty Function. ORSA Journal on Computing 4, 311–319 (1992)
Stern, J.M.: Esparsidade, Estrutura, Estabilidade e Escalonamento em Álgebra Linear Computacional. IX Escola de Computação. UFPE, Recife (1994)
Stern, J.M.: Decoupling, Sparsity, Randomization, and Objective Bayesian Inference. Cybernetics and Human Knowing 15(2), 49–68 (2008a)
Stern, J.M.: Cognitive Constructivism and the Epistemic Significance of Sharp Statistical Hypotheses. Tutorial book for MaxEnt, The 28th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, July 06-11, Boracéia, São Paulo, Brazil (2008b)
Stern, J.M., Vavasis, S.A.: Nested Dissection for Sparse Nullspace Bases. SIAM Journal on Matrix Analysis and Applications 14(3), 766–775 (1993)
Stern, J.M., Vavasis, S.A.: Active Set Algorithms for Problems in Block Angular Form. Computational and Applied Mathemathics 12(3), 199–226 (1994)
van der Vorst, H.A., van Dooren, P. (eds.): Parallel Algorithms for Numerical Linear Algebra. North-Holland, Amsterdam (1990)
Zhang, N.L., Poole: Exploiting casual independence in Bayesian network inference. Journal of Artificial Intelligence Research, 301–328 (1996)
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© 2009 Springer-Verlag Berlin Heidelberg
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Stern, J.M., Colla, E.C. (2009). Factorization of Sparse Bayesian Networks. In: Nakamatsu, K., Phillips-Wren, G., Jain, L.C., Howlett, R.J. (eds) New Advances in Intelligent Decision Technologies. Studies in Computational Intelligence, vol 199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00909-9_27
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DOI: https://doi.org/10.1007/978-3-642-00909-9_27
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