Bucket elimination: a unifying framework for reasoning

Artificial Intelligence

Volumn 113, Issue 1, 1999, Pages 41-85

  Dechter, Rina ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMBINATORIAL MATHEMATICS; CONSTRAINT THEORY; DYNAMIC PROGRAMMING; INFERENCE ENGINES; LEARNING SYSTEMS; PROBABILISTIC LOGICS; SET THEORY;

AUTOMATED REASONING; BELIEF NETWORKS; BUCKET ELIMINATION; CONSTRAINT NETWORKS;

ARTIFICIAL INTELLIGENCE;

EID: 0033188982     PISSN: 00043702     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0004-3702(99)00059-4     Document Type: Article

References (52)

1. S. Arnborg, A. Proskourowski, Linear time algorithms for np-hard problems restricted to partial k-trees, Discrete Appl. Math.
2. S.A. Arnborg, Efficient algorithms for combinatorial problems on graphs with bounded decomposability - A survey, BIT 25 (1985) 2-23.
3. F. Bacchus, P. van Run, Dynamic variable ordering in CSPs, in: Principles and Practice of Constraints Programming (CP-95), Cassis, France, Lecture Notes in Computer Science, Vol. 976, Springer, Berlin, 1995, pp. 258-277.
4. A. Becker, D. Geiger, A sufficiently fast algorithm for finding close to optimal junction trees, in: Proc. 12th Conference on Uncertainty in Artificial Intelligence (UAI-96), 1996, pp. 81-89.
5. U. Bertele, F. Brioschi, Nonserial Dynamic Programming, Academic Press, New York, 1972.
6. S. Bistarelli, U. Montanari, F. Rossi, Semiring-based constraint satisfaction and optimization, J. ACM 44 (2) (1997) 165-201.
7. C. Boutilier, Context-specific independence in Bayesian networks, in: Proc. 12th Conference on Uncertainty in Artificial Intelligence (UAI-96), 1996, pp. 115-123.
8. C. Cannings, E.A. Thompson, H.H. Skolnick, Probability functions on complex pedigrees, Adv. Appl. Probab. 10 (1978) 26-61.
9. G.F. Cooper, Nestor: A computer-based medical diagnosis aid that integrates causal and probabilistic knowledge, Technical Report, Computer Science Department, Stanford University, Palo Alto, CA, 1984.
10. B. D'Ambrosio R.D. Shachter, B.A. Del Favero, Symbolic probabilistic inference in belief networks, in: Proc. AAAI-90, Boston, MA, 1990, pp. 126-131.
11. A. Darwiche, Conditioning methods for exact and approximate inference in causal networks, in: Proc. 11th Conference on Uncertainty in Artificial Intelligence (UAI-95), 1995, pp. 99-107.
12. M. Davis, G. Logemann, D. Loveland, A machine program for theorem proving, Comm. ACM 5 (1962) 394-397.
13. M. Davis, H. Putnam, A computing procedure for quantification theory, J. ACM 7 (3) (1960).
14. A. Dechter, R. Dechter, J. Pearl, Optimization in constraint networks, in: Influence Diagrams, Belief Nets and Decision Analysis, Wiley, New York, 1990, pp. 411-425.
15. R. Dechter, Enhancement schemes for constraint processing: Backjumping, learning and cutset decomposition, Artificial Intelligence 41 (1990) 273-312.
16. R. Dechter, Constraint networks, in: Encyclopedia of Artificial Intelligence, 1992, pp. 276-285.
17. R. Dechter, Bucket elimination: A unifying framework for probabilistic inference algorithms, in: Proc. 12th Conference on Uncertainty in Artificial Intelligence (UAI-96), 1996, pp. 211-219.
18. R. Dechter, Topological parameters for time-space tradeoffs, in: Proc. 12th Conference on Uncertainty in Artificial Intelligence (UAI-96), 1996, pp. 220-227.
19. R. Dechter, Mini-buckets: A general scheme of generating approximations in automated reasoning, in: Proc. IJCAI-97, Nagoya, Japan, 1997, pp. 1297-1302.
20. R. Dechter, Bucket elimination: A unifying framework for probabilistic inference algorithms, in: M.I. Jordan (Ed.), Learning in Graphical Models, Kluwer Academic, Dordrecht, 1998.
21. R. Dechter, D. Frost, Backtracking algorithms for constraint satisfaction problems, UCI Technical Report, 1999. Also on web page www.ics.uci.edu/~dechter.
22. R. Dechter, J. Pearl, Network-based heuristics for constraint satisfaction problems, Artificial Intelligence 34 (1987) 1-38.
23. R. Dechter, J. Pearl, Tree clustering for constraint networks, Artificial Intelligence 38 (1989) 353-366.
24. R. Dechter, I. Rish, Directional resolution: The Davis-Putnam procedure, revisited, in: Proc. Internat. Conference of the Principles of Knowledge Representation and Reasoning (KR-94), Bonn, Germany, 1994, pp. 134-145.
25. R. Dechter, P. van Beek, Local and global relational consistency, in: Principles and Practice of Constraint Programming (CP-95), Cassis, France, Lecture Notes in Computer Science, Vol. 976, Springer, Berlin, 1995, pp. 240-257.
26. R. Dechter, P. van Beek, Local and global relational consistency, Theoret. Comput. Sci. 173 (1997) 283-308.
27. Y. El-Fattah, R. Dechter, An evaluation of structural parameters for probabilistic reasoning: Results on benchmark circuits, in: Proc. 12th Conference on Uncertainty in Artificial Intelligence (UAI-96), 1996, pp. 244-251.
28. E.C. Freuder, A sufficient condition for backtrack-free search, J. ACM 29 (1) (1982) 24-32.
29. M.R. Garey, D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-completeness, W.H. Freeman, San Francisco, CA, 1979.
30. D. Geiger, T. Verma, J. Pearl, Identifying independence in Bayesian networks, Networks 20 (1990) 507-534.
31. F.V. Jensen, S.L Lauritzen, K.G. Olesen, Bayesian updating in causal probabilistic networks by local computation, Comput. Statist. Quarterly 4 (1990) 269-282.
32. U. Kjœrulff, A computational scheme for reasoning in dynamic probabilistic networks, in: Proc. 9th Conference on Uncertainty in Artificial Intelligence (UAI-93), 1993, pp. 121-149.
33. J.-L. Lassez, M. Mahler, On Fourier's algorithm for linear constraints, J. Automat. Reason. 9 (1992).
34. S.L. Lauritzen, D.J. Spiegelhalter, Local computation with probabilities on graphical structures and their application to expert systems, J. Roy. Statist. Soc., Ser. B 50 (2) (1988) 157-224.
35. Z. Li, B. D'Ambrosio, Efficient inference in bayes networks as a combinatorial optimization problem, internat. J. Approx. Reason. 11 (1994) 1-58.
36. L.G. Mitten, Composition principles for the synthesis of optimal multistage processes, Oper. Res. 12 610-619.
37. J. Pearl, Probabilistic Reasoning in Intelligent Systems, Morgan Kaufmann, San Mateo, CA, 1988.
38. Y. Peng, J.A. Reggia, Plausability of diagnostic hypothesis, in: Proc. AAAI-86, Philadelphia, PA, 1986, pp. 140-145.
39. Y. Peng, J.A. Reggia, A connectionist model for diagnostic problem solving, IEEE Trans. Systems Man Cybernet. (1989).
40. D. Poole, Probabilistic partial evaluation: Exploiting structure in probabilistic inference, in: Proc. IJCAI-97, Nagoya, Japan, 1997.
41. I. Rish, R. Dechter, To guess or to think? hybrid algorithms for SAT, in: Principles of Constraint Programming (CP-96), Cambridge, MA, 1996, pp. 555-556.
42. E. Santos, On the generation of alternative explanations with implications for belief revision, in: Proc. 7th Conference on Uncertainty in Artificial Intelligence (UAI-91), 1991, pp. 339-347.
43. E. Santos, S.E. Shimony, E. Williams, Hybrid algorithms for approximate belief updating in Bayes nets, Internat. J. Approx. Reason. 12 (2-3) 191-216.
44. L.K. Saul, M.I. Jordan, Learning in boltzmann trees, Neural Computation 6 (1994) 1173-1183.
45. R.D. Shachter, An ordered examination of influence diagrams, Networks 20 (1990) 535-563.
46. R.D. Shachter, Evaluating influence diagrams, Oper. Res. 34 (1986).
47. R.D. Shachter, Probabilistic inference and influence diagrams, Oper. Res. 36 (1988).
48. P.P. Shenoy, Valuation-based systems for Bayesian decision analysis, Oper. Res. 40 (1992) 463-484.
49. S.E. Shimony, E. Charniak, A new algorithm for finding map assignments to belief networks, in: P. Bonissone, M. Henrion, L. Kanal, J. Lemmer (Eds.), Uncertainty in Artificial Intelligence, Vol. 6, Elsevier, Amsterdam, 1991, pp. 185-193.
50. K. Shoiket, D. Geiger, A practical algorithm for finding optimal triangulation, in: Proc. Fourteenth National Conference on Artificial Intelligence (AAAI-97), Providence, RI, 1997, pp. 185-190.
51. J.A. Tatman, R.D. Shachter, Dynamic programming and influence diagrams, IEEE Trans. Systems Man Cybernet. (1990) 365-379.
52. N.L. Zhang, D. Poole, Exploiting causal independence in Bayesian network inference, J. Artificial Intelligence Res. (1996).