Inference in hybrid Bayesian networks with deterministic variables

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5590 LNAI, Issue , 2009, Pages 46-58

  Shenoy, Prakash P ^a   West, James C ^a  

^a UNIVERSITY OF KANSAS   (United States)

Author keywords

Deterministic variables; Dirac delta functions; Hybrid Bayesian networks; Shenoy Shafer architecture

Indexed keywords

CONDITIONAL DISTRIBUTION; DETERMINISTIC FUNCTIONS; DETERMINISTIC VARIABLES; DIRAC DELTA FUNCTION; DIRAC DELTA FUNCTIONS; HYBRID BAYESIAN NETWORKS; ILLUSTRATIVE EXAMPLES; JOINT DENSITIES; LARGE CLASS; NON-EXISTENCE; SHENOY-SHAFER ARCHITECTURE;

ARCHITECTURAL DESIGN; DISTRIBUTED PARAMETER NETWORKS; HYBRID SENSORS; IMAGE RETRIEVAL; INFERENCE ENGINES; INTELLIGENT NETWORKS; SOUND REPRODUCTION;

BAYESIAN NETWORKS;

EID: 69049092880     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-02906-6_6     Document Type: Conference Paper

References (29)

1. Cinicioglu, E.N., Shenoy, P.P.: Arc Reversals in Hybrid Bayesian Networks with Deterministic Variables. Int. J. Approx. Reas. 50(5), 763-777 (2009)
2. Cobb, B.R., Shenoy, P.P.: Hybrid Bayesian Networks with Linear Deterministic Variables. In: Bacchus, F., Jaakkola, T. (eds.) UAI 2005, pp. 136-144. AUAI Publishers, Corvallis (2005)
3. Cobb, B.R., Shenoy, P.P.: Nonlinear Deterministic Relationships in Bayesian networks. In: Godo, L. (ed.) ECSQARU 2005. LNCS, vol. 3571, pp. 27-38. Springer, Heidelberg (2005)
4. Cobb, B.R., Shenoy, P.P.: Decision Making with Hybrid Influence Diagrams Using Mixtures of Truncated Exponentials. Eur. J. Oper. Res. 186(1), 261-275 (2008)
5. Cobb, B.R., Shenoy, P.P., Rumi, R.: Approximating Probability Density Functions in Hybrid Bayesian Networks with Mixtures of Truncated Exponentials. Stat. & Comp. 16(3), 293-308 (2006)
6. Dirac, P.A.M.: The Physical Interpretation of the Quantum Dynamics. Proc. Royal Soc. London. Series A 113(765), 621-641 (1927)
7. Dirac, P.A.M.: The Principles of Quantum Mechanics, 4th edn. Oxford Univ. Press, London (1958)
8. Hoskins, R.F.: Generalised Functions. Ellis Horwood, Chichester (1979)
9. Howard, R.A., Matheson, J.E.: Influence Diagrams. In: Howard, R.A., Matheson, J.E. (eds.) The Principles and Applications of Decision Analysis, vol. 2, pp. 719-762. Strategic Decisions Group, Menlo Park (1984)
10. Kanwal, R.P.: Generalized Functions: Theory and Technique, 2nd edn. Birkhäuser, Boston (1998)
11. Kenley, C.R.: Influence Diagram Models with Continuous Variables. PhD thesis, Dept. of Engg.-Econ. Sys. Stanford University, Stanford (1986)
12. Khuri, A.I.: Applications of Dirac's Delta Function in Statistics. Int. J. Math. Edu. in Sci. & Tech. 32(2), 185-195 (2004)
13. Lauritzen, S.L., Spiegelhalter, D.J.: Local Computations with Probabilities on Graphical Structures and their Application to Expert Systems. J. Royal Stat. Soc. B 50(2), 157-224 (1988)
14. Lauritzen, S.L., Jensen, F.: Stable Local Computation with Conditional Gaussian Distributions. Stat. & Comp. 11, 191-203 (2001)
15. Lerner, U.N.: Hybrid Bayesian Networks for Reasoning About Complex Systems. PhD thesis, Dept. of Comp. Sci. Stanford University, Stanford (2002)
16. Moral, S., Rumi, R., Salmeron, A.: Mixtures of Truncated Exponentials in Hybrid Bayesian Networks. In: Benferhat, S., Besnard, P. (eds.) ECSQARU 2001. LNCS (LNAI), vol. 2143, pp. 156-167. Springer, Heidelberg (2001)
17. Murphy, K.: A Variational Approximation for Bayesian Networks with Discrete and Continuous Latent Variables. In: Laskey, K.B., Prade, H. (eds.) UAI 1999, pp. 457-466. Morgan Kaufmann, San Francisco (1999)
18. Olmsted, S.M.: On Representing and Solving Decision Problems. PhD thesis, Dept. of Engg.-Econ. Sys. Stanford University, Stanford (1983)
19. Pearl, J.: Fusion, Propagation and Structuring in Belief Networks. Art. Int. 29, 241-288 (1986)
20. Poland III, W.B.: Decision Analysis with Continuous and Discrete Variables: A Mixture Distribution Approach. PhD thesis, Dept. of Engg.-Econ. Sys., Stanford University, Stanford (1994)
21. Saichev, A.I., WoyczyŃski, W.A.: Distributions in the Physical and Engineering Sciences, vol. 1. Birkhäuser, Boston (1997)
22. Shachter, R.D.: Evaluating Influence Diagrams. Oper. Res. 34(6), 871-882 (1986)
23. Shachter, R.D., Kenley, C.R.: Gaussian Influence Diagrams. Mgmt. Sci. 35(5), 527-550 (1989)
24. Shenoy, P.P.: Valuation-Based Systems for Bayesian Decision Analysis. Oper. Res. 40(3), 463-484 (1992)
25. Shenoy, P.P.: A New Method for Representing and Solving Bayesian Decision Problems. In: Hand, D.J. (ed.) Artificial Intelligence Frontiers in Statistics: AI and Statistics III, pp. 119-138. Chapman & Hall, London (1993)
26. Shenoy, P.P.: Inference in Hybrid Bayesian Networks Using Mixtures of Gaussians. In: Dechter, R., Richardson, T. (eds.) UAI 2006, pp. 428-436. AUAI Press, Corvallis (2006)
27. Shenoy, P.P., Shafer, G.: Axioms for Probability and Belief-Function Propagation. In: Shachter, R.D., Levitt, T.S., Lemmer, J.F., Kanal, L.N. (eds.) UAI 1988, vol. 4, pp. 169-198. North-Holland, Amsterdam (1990)
28. Shenoy, P.P., West, J.C.: Inference in Hybrid Bayesian Networks with Deterministic Variables. Working Paper No. 318. School of Business, University of Kansas (2009)
29. Shenoy, P.P., West, J.C.: Inference in Hybrid Bayesian Networks with Mixtures of Polynomials. Working Paper No. 321. School of Business, University of Kansas (2009)