jmlr jmlr2005 jmlr2005-51 jmlr2005-51-reference knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Robert G. Cowell
Abstract: This paper describes a scheme for local computation in conditional Gaussian Bayesian networks that combines the approach of Lauritzen and Jensen (2001) with some elements of Shachter and Kenley (1989). Message passing takes place on an elimination tree structure rather than the more compact (and usual) junction tree of cliques. This yields a local computation scheme in which all calculations involving the continuous variables are performed by manipulating univariate regressions, and hence matrix operations are avoided. Keywords: Bayesian networks, conditional Gaussian distributions, propagation algorithm, elimination tree
A. Becker and D. Geiger. A sufficiently fast algorithm for finding close to optimal clique trees. Artificial Intelligence Journal, 2001. R. G. Cowell. Decision networks: a new formulation for multistage decision problems. Research Report 132, Department of Statistical Science, University College London, London, United Kingdom, 1994. R. G. Cowell, S. L. Lauritzen, and J. Mortera. Identification and separation of DNA mixtures using peak area information. Cass Statistical Science Research Report 25, City University London, 2004. R. G. Cowell, A. P. Dawid, S. L. Lauritzen, and D. J. Spiegelhalter. Probabilistic Networks and Expert Systems. Springer–Verlag, 1999. A. P. Dawid. Applications of a general propagation algorithm for probabilistic expert systems. Statistics and Computing, 2:25–36, 1992. U. Kjærulff. Graph triangulation — algorithms giving small total state space. Technical Report R 90-09, Aalborg university, Denmark, 1990. P. Larra˜ aga, C. M. H. Kuijpers, M. Poza, and R. H. Murga. Decomposing Bayesian networks: n triangulation of the moral graph with genetic algorithms. Statistics and Computing, pages 19–34, 1997. S. L. Lauritzen. Propagation of probabilities, means and variances in mixed graphical association models. Journal of the American Statistical Association, 87:1098–1108, 1992. S. L. Lauritzen. Graphical Models. Oxford, United Kingdom, 1996. 1549 C OWELL S. L. Lauritzen and N. Wermuth. Mixed interaction models. Technical Report R 84-8, Institute for Electronic Systems, Aalborg University, 1984. S. L. Lauritzen and N. Wermuth. Graphical models for associations between variables, some of which are qualitative and some quantitative. Annals of Statistics, 17:31–57, 1989. S. L. Lauritzen and F. Jensen. Stable local computation with conditional Gaussian distributions. Statistics and Computing, 11:191–203, 2001. S. L. Lauritzen and D. J. Spiegelhalter. Local computations with probabilities on graphical structures and their application to expert systems (with discussion). Journal of the Royal Statistical Society, Series B, 50:157–224, 1988. H.-G. Leimer. Triangulated graphs with marked vertices. Annals of Discrete Mathematics, 41: 311–324, 1989. A. L. Madsen and F. V. Jensen. Lazy propagation in junction trees. In G. F. Cooper and S. Moral, editors, Proceedings of the 14th Annual Conference on Uncertainty in Artificial Intelligence, pages 362–369, San Francisco, California, 1998. Morgan Kaufmann, San Francisco, California. K. G. Olesen and A. Madsen. Maximal prime subgraph decomposition of Bayesian networks. IEEE Transactions on Systems, Man, and Cybernetics, Part B, 32(21–31), 2002. J. Pearl. Probabilistic Inference in Intelligent Systems. Morgan Kaufmann, San Mateo, California, San Mateo, California, 1988. C. Raphael. Bayesian networks with degenerate Gaussian distributions. Methodology and Computing in Applied Probability, 5(2):235–263, 2003. R. D. Shachter and C. Kenley. Gaussian influence diagrams. Management Science, 35:527–550, 1989. R. D. Shachter, S. K. Andersen, and K. L. Poh. Directed reduction algorithms and decomposable graphs. In In Proceedings of the Sixth Conference on Uncertainty in Artificial Intelligence, July 27-29, Cambridge, MA, pages 237–244, New York, NY, 1990. Elsevier Science Publishing Company, Inc. R. E. Tarjan and M. Yannakakis. Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs. 13:566–579, 1984. M. Yannakakis. Computing the minimum fill-in is NP-complete. SIAM Journal on Algebraic and Discrete Methods, 2:77–79, 1981. 1550