Bounding probabilistic relationships in Bayesian networks using qualitative influences: Methods and applications

International Journal of Approximate Reasoning

Volumn 36, Issue 1, 2004, Pages 31-73

  Liu, Chao Lin ^a   Wellman, Michael P ^b  

^a NATIONAL CHENGCHI UNIVERSITY   (Taiwan)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL METHODS; ENCODING (SYMBOLS); MOTION PLANNING; PROBABILITY DISTRIBUTIONS; THEOREM PROVING;

BAYESIAN NETWORKS; RANDOM VARIABLES;

RANDOM PROCESSES;

EID: 1542609594     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijar.2003.06.002     Document Type: Article

References (53)

1. Ahuja R.K., Magnanti T.L., Orlin J.B. Network Flows: Theory, Algorithms and Applications. 1993;Prentice-Hall.
2. Boddy M., Dean T.L. Deliberation scheduling for problem solving in time-constrained environments. Artificial Intelligence. 67(2):1994;245-285.
3. Boyan J.A., Littman M.L. Exact solutions to time-dependent MDPs. Advances in Neural Information Processing Systems. 13:2001;1026-1032.
4. * algorithm for the computation of fastest paths in the discrete-time dynamic networks IEEE Transactions on Intelligent Transportation Systems. 3(1):2002;60-74.
5. Chan H., Darwiche A. When do numbers really matter? Journal of Artificial Intelligence Research. 17:2002;265-287.
6. Chrisman L. Incremental conditioning of lower and upper probabilities. International Journal of Approximate Reasoning. 13(1):1995;1-25.
7. Dagum P., Luby M. Approximating probabilistic inference in Bayesian belief networks is NP-hard. Artificial Intelligence. 60(1):1993;141-153.
8. Dagum P., Luby M. An optimal approximation algorithm for Bayesian inference. Artificial Intelligence. 93(1-2):1997;1-27.
9. D'Ambrosio B. Inference in Bayesian networks. AI Magazine. 20(2):1999;21-36.
10. Deo N., Pang C. Shortest path algorithms: Taxonomy and annotation. Networks. 14:1984;275-323.
11. Dijkstra E.W. A note on two problems in connextion with graphs. Numerische Mathematik. 1:1959;269-271.
12. D.L. Draper, S. Hanks, Localized partial evaluation of belief networks, in: Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence, 1994, pp. 170-177.
13. Dreyfus S.E. An appraisal of some shortest-path algorithms. Operations Research. 17:1969;395-412.
14. M.J. Druzdzel, M. Henrion, Efficient reasoning in qualitative probabilistic networks, in: Proceedings of the Eleventh National Conference on Artificial Intelligence, 1993, pp. 548-553.
15. P.C. Fishburn, R.G. Vickson, Theoretical foundations of stochastic dominance, in: Whitmore and Findlay [53].
16. Goldszmidt M. Research issues in qualitative and abstract probability. AI Magazine. 15(4):1994;63-65.
17. M. Goldszmidt, J. Pearl, Reasoning with qualitative probabilities can be tractable, in: Proceedings of the Eighth Conference on Uncertainty in Artificial Intelligence, 1992, pp. 112-120.
18. V. Ha, P. Haddawy, Geometric foundations for interval-based probabilities, in: KR'98: Principles of Knowledge Representation and Reasoning, 1998, pp. 582-593.
19. Haddawy P. An overview of some recent developments in Bayesian problem-solving techniques. AI Magazine. 20(2):1999;11-19.
20. Hall R.W. The fastest path through a network with random time-dependent travel times. Transportation Science. 20(3):1986;182-188.
21. Heckerman D.E., Mamdani A., Wellman M.P. Real-world applications of Bayesian networks. Communications of the ACM. 38(3):1995;24-26.
22. Henrion M., Druzdzel M.J. Qualitative propagation and scenario-based approaches to explanation of probabilistic reasoning. Bonissone P., Henrion M., Kanal L., Lemmer J. Uncertainty in Artificial Intelligence 6. 1991;17-32 Elsevier.
23. E. Horvitz, Computation and Action Under Bounded Resources, PhD Thesis, Stanford University, Stanford, California, USA, 1990.
24. Jensen F.V. Bayesian Networks and Decision Graphs. 2001;Springer-Verlag, New York.
25. Jordan M.I., Ghahramani Z., Jaakkola T., Saul L.K. An introduction to variational methods for graphical models. Machine Learning. 37(2):1999;183-233.
26. Kaufman D.E., Smith R.L. Fastest paths in time-dependent networks for intelligent vehicle-highway systems applications. IVHS Journal. 1(1):1993;1-11.
27. U. Kjærulff, Reduction of computational complexity in Bayesian networks through removal of weak independences, in: Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence, 1994, pp. 374-382.
28. D. Koller, U. Lerner, D. Angelov, A general algorithm for approximate inference and its application to hybrid Bayes nets, in: Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence, 1999, pp. 324-333.
29. C.-L. Liu, Advances in applying stochastic-dominance relationships to bounding probability distributions in Bayesian networks, in: Proceedings of the IASTED International Conference on Artificial and Computational Intelligence 2002, 2002, pp. 251-256.
30. C.-L. Liu, M.P. Wellman, Incremental tradeoff resolution in qualitative probabilistic networks, in: Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence, 1998, pp. 338-345.
31. C.-L. Liu, M.P. Wellman, Using qualitative relationships for bounding probability distributions, in: Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence, 1998, pp. 346-353.
32. C.-L. Liu, M.P. Wellman, Using stochastic-dominance relationships for bounding travel times in stochastic networks, in: Proceedings of the Second International IEEE Conference on Intelligent Transportation Systems, 1999, pp. 55-60.
33. Liu C.-L., Wellman M.P. Evaluation of Bayesian networks with flexible state-space abstraction methods. International Journal of Approximate Reasoning. 30(1):2002;1-39.
34. T.P. Minka, Expectation propagation for approximate Bayesian inference, in: Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence, 2001, pp. 362-369.
35. Neapolitan R.E. Probabilistic Reasoning in Expert Systems: Theory and Algorithms. 1990;Wiley.
36. Osseiran A.C. Qualitative Bayesian networks. Information Sciences. 131(1-4):2001;87-106.
37. S. Parsons, Refining reasoning in qualitative probabilistic networks, in: Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence, 1995, pp. 427-433.
38. Parsons S. Qualitative Methods for Reasoning under Uncertainty. 2001;MIT Press.
39. Parsons S., Dohnal M. A semiqualitative approach to reasoning in probabilistic networks. Applied Artificial Intelligence. 7(3):1993;223-235.
40. Pearl J. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. 1988;Morgan Kaufmann.
41. D. Poole, Average-case analysis of a search algorithm for estimating prior and posterior probabilities in Bayesian networks with extreme probabilities, in: Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence, 1993, pp. 606-612.
42. D. Poole, Context-specific approximation in probabilistic inference, in: Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence, 1998, pp. 447-454.
43. S. Renooij, L.C. van der Gaag, Enhancing QPNs for trade-off resolution, in: Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence, 1999, pp. 559-566.
44. S. Renooij, L.C. van der Gaag, Exploiting non-monotonic influences in qualitative belief networks, in: Proceedings of the Eighth International Conference on Information Processing and Management of Uncertainty, 2000, pp. 1285-1290.
45. Renooij S., van der Gaag L.C., Parsons S. Context-specific sign-propagation in qualitative probabilistic networks. Artificial Intelligence. 140(1-2):2002;207-230.
46. S. Renooij, L.C. van der Gaag, S. Parsons, S. Green, Pivotal pruning of trade-offs in QPNs, in: Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence, 2000, pp. 515-522.
47. Shachter R.D. Probabilistic inference and influence diagrams. Operation Research. 36(4):1988;589-604.
48. R.D. Shachter, Bayes-ball: The rational pastime (for determining irrelevance and requisite information in belief networks and influence diagrams), in: Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence, 1998, pp. 480-487.
49. van Engelen R.A. Approximating Bayesian belief networks by arc removal. IEEE Transactions on Pattern Analysis and Machine Intelligence. 19(8):1997;916-920.
50. Wellman M.P. Fundamental concepts of qualitative probabilistic networks. Artificial Intelligence. 44(3):1990;257-303.
51. M.P. Wellman, Some varieties of qualitative probability, in: Proceedings of the Fifth International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, 1994, pp. 437-442.
52. M.P. Wellman, M. Ford, K. Larson, Path planning under time-dependent uncertainty, in: Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence, 1995, pp. 532-539.
53. Whitmore G.A., Findlay M.C. Stochastic Dominance: An Approach to Decision Making Under Risk. 1978;D.C. Heath and Company.