Inference in hybrid Bayesian networks with mixtures of truncated exponentials

International Journal of Approximate Reasoning

Volumn 41, Issue 3, 2006, Pages 257-286

  Cobb, Barry R ^a   Shenoy, Prakash P ^b  

^a VIRGINIA MILITARY INSTITUTE   (United States)

^b UNIVERSITY OF KANSAS   (United States)

Author keywords

Conditional linear Gaussian models; Hybrid Bayesian networks; Mixtures of truncated exponentials; Shenoy Shafer architecture

Indexed keywords

APPROXIMATION THEORY; GRAPH THEORY; MATHEMATICAL MODELS; PROBABILITY DENSITY FUNCTION;

CONDITIONAL LINEAR GAUSSIAN MODELS; HYBRID BAYESIAN NETWORKS; MIXTURES OF TRUNCATED EXPONENTIALS; SHENOY-SHAFER ARCHITECTURE;

FORMAL LOGIC;

EID: 33644863766     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijar.2005.06.002     Document Type: Article

References (26)

1. J. Binder, D. Koller, S.J. Russell, and K. Kanazawa Adaptive probabilistic networks with hidden variables Mach. Learn. J. 29 2-3 1997 213 244
2. K.C. Chang, Z. Tian, Efficient inference for mixed Bayesian networks, Proceedings of the 5th ISIF/IEEE International Conference on Information Fusion, 2002, pp. 512-519.
3. B.R. Cobb, R. Rumí, P.P. Shenoy, Approximating probability density functions with mixtures of truncated exponentials, Proceedings of the Tenth Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU-04), 2004, pp. 429-436. Available from: < http://lark.cc.ku.edu/~pshenoy/Papers/IPMU04.pdf>.
4. B.R. Cobb, and P.P. Shenoy Nonlinear deterministic relationships in Bayesian networks L. Godo Symbolic and Quantitative Approaches to Reasoning with Uncertainty, Lecture Notes in Artificial Intelligence vol. 3571 2005 Springer-Verlag Heidelberg 27 38
5. B.R. Cobb, P.P. Shenoy, Hybrid Bayesian networks with linear deterministic variables, in: F. Bacchus, T. Jaakkola (Eds.), Uncertainty in Artificial Intelligence, vol. 21, in press.
6. R.G. Cowell, A.P. Dawid, S.L. Lauritzen, and D.J. Spiegelhalter Probabilistic Networks and Expert Systems 1999 Springer New York
7. S. Davies, and A. Moore Interpolating conditional density trees A. Darwiche N. Friedman Uncertainty in Artificial Intelligence vol. 18 2002 Morgan Kaufmann San Francisco, CA 119 127
8. R. Demirer, P.P. Shenoy, Sequential valuation networks and asymmetric decision problems, Eur. J. Oper. Res., in press.
9. M.I. Jordan, and R.A. Jacobs Hierarchical mixtures of experts and the EM algorithm Neural Comput. 6 1994 181 214
10. D. Koller, U. Lerner, and D. Anguelov A general algorithm for approximate inference and its application to hybrid Bayes nets K.B. Laskey H. Prade Uncertainty in Artificial Intelligence vol. 15 1999 Morgan Kaufmann San Francisco, CA 324 333
11. A.V. Kozlov, and D. Koller Nonuniform dynamic discretization in hybrid networks D. Geiger P.P. Shenoy Uncertainty in Artificial Intelligence vol. 13 1997 Morgan Kaufmann San Francisco, CA 314 325
12. S.L. Lauritzen Propagation of probabilities, means and variances in mixed graphical association models J. Am. Stat. Assoc. 87 1992 1098 1108
13. S.L. Lauritzen, and F. Jensen Stable local computation with conditional Gaussian distributions Stat. Comput. 11 2001 191 203
14. S.L. Lauritzen, and D.J. Spiegelhalter Local computations with probabilities on graphical structures and their application to expert systems J. Roy. Stat. Soc. B. 50 2 1988 157 224
15. U. Lerner, and R. Parr Inference in hybrid networks: theoretical limits and practical algorithms J. Breese D. Koller Uncertainty in Artificial Intelligence vol. 17 2001 Morgan Kaufmann San Francisco, CA 310 318
16. U. Lerner, E. Segal, and D. Koller Exact inference in networks with discrete children of continuous parents J. Breese D. Koller Uncertainty in Artificial Intelligence vol. 17 2001 Morgan Kaufmann San Francisco, CA 319 328
17. P. McCullagh, and J.A. Nelder Generalized Linear Models 1983 Chapman and Hall London
18. S. Moral, R. Rumí, and A. Salmerón Mixtures of truncated exponentials in hybrid Bayesian networks P. Besnard S. Benferhart Symbolic and Quantitative Approaches to Reasoning under Uncertainty, Lecture Notes in Artificial Intelligence vol. 2143 2001 Springer-Verlag Heidelberg 156 167
19. S. Moral, R. Rumí, A. Salmerón, Estimating mixtures of truncated exponentials from data, in: J.A. Gamez, A. Salmerón (Eds.), Proceedings of the First European Workshop on Probabilistic Graphical Models (PGM-02), Cuenca, Spain, 2002, pp. 135-143.
20. S. Moral, R. Rumí, and A. Salmerón Approximating conditional MTE distributions by means of mixed trees T.D. Nielsen N.L. Zhang Symbolic and Quantitative Approaches to Reasoning under Uncertainty, Lecture Notes in Artificial Intelligence vol. 2711 2003 Springer-Verlag Heidelberg 173 183
21. K. Murphy A variational approximation for Bayesian networks with discrete and continuous latent variables K.B. Laskey H. Prade Uncertainty in Artificial Intelligence vol. 15 1999 Morgan Kaufmann San Francicso, CA 457 466
22. V. Romero, R. Rumí, A. Salmerón, Structural learning of Bayesian networks with mixtures of truncated exponentials, in: P. Lucas (Ed.), Proceedings of the Second European Workshop on Probabilistic Graphical Models (PGM-04), Leiden, Netherlands, 2004, pp. 177-184.
23. R. Rumí, Modelos De Redes Bayesianas Con Variables Discretas Y Continuas, Doctoral Thesis, Universidad de Almería, Departamento de Estadística Y Matemática Aplicada, Almería, Spain, 2003.
24. P.P. Shenoy Binary join trees for computing marginals in the Shenoy-Shafer architecture Int. J. Approx. Reason. 17 2-3 1997 239 263
25. P.P. Shenoy, and G. Shafer Axioms for probability and belief function propagation R.D. Shachter T.S. Levitt J.F. Lemmer L.N. Kanal Uncertainty in Artificial Intelligence vol. 4 1990 North-Holland Amsterdam 169 198
26. D.J. Spiegelhalter, A.P. Dawid, S.L. Lauritzen, and R.G. Cowell Bayesian analysis in expert systems Stat. Sci. 8 3 1993 219 283