An optimal approximation algorithm for Bayesian inference

Artificial Intelligence

Volumn 93, Issue 1-2, 1997, Pages 1-27

  Dagum, Paul ^a   Luby, Michael ^b  

^a STANFORD UNIVERSITY SCHOOL OF MEDICINE   (United States)

^b INTERNATIONAL COMPUTER SCIENCE INSTITUTE   (United States)

Author keywords

Approximation; Bayesian inference; Belief networks

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; ARTIFICIAL INTELLIGENCE; COMPUTATIONAL COMPLEXITY; PROBABILITY;

BAYESIAN INFERENCE; BELIEF NETWORKS;

INFERENCE ENGINES;

EID: 0031170063     PISSN: 00043702     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0004-3702(97)00013-1     Document Type: Article

References (35)

1. Special Issue on Probability Forecasting, Internat. J. Forecasting 11 (1995).
2. Special Issue on Real-World Applications of Uncertain Reasoning, Comm. ACM 38 (1995).
3. R. Chavez and G.F. Cooper, An empirical evaluation of a randomized algorithm for probabilistic inference, in: M. Henrion, R.D. Shachter, L.N. Kanal and J.F. Lemmer, eds., Uncertainty in Artificial Intelligence 5 (Elsevier, Amsterdam, 1990) 191-207.
4. R. Chavez and G.F. Cooper, A randomized approximation algorithm for probabilistic inference on Bayesian belief networks, Networks 20 (1990) 661-685.
5. G.F. Cooper, NESTOR: a computer-based medical diagnostic aid that integrates causal and probabilistic knowledge, Ph.D. Thesis, Medical Computer Science Group, Stanford University, Stanford, CA (1984).
6. G.F. Cooper, The computational complexity of probabilistic inference using Bayesian belief networks, Artificial Intelligence 42 (1990) 393-405.
7. P. Dagum and R.M. Chavez, Approximating probabilistic inference in Bayesian belief networks, IEEE Trans. Pattern Analysis and Machine Intell. 15 (1993) 246-255.
8. P. Dagum and E. Horvitz, A Bayesian analysis of simulation algorithms for inference in belief networks, Networks 23 (1993) 499-516.
9. P. Dagum, R. Karp, M. Luby and S. Ross, An optimal algorithm for Monte Carlo estimation, in: Proceedings 36th IEEE Symposium on Foundations of Computer Science, Milwaukee, WI (1995) 142-149.
10. P. Dagum and M. Luby, Approximating probabilistic inference in Bayesian belief networks is NP-hard, Artificial Intelligence 60 (1993) 141-153.
11. B. D'Ambrosio, Incremental probabilistic inference, in: Proceedings 9th Conference on Uncertainty in Artificial Intelligence, Washington, DC (Association for Uncertainty in Artificial Intelligence, 1993) 301-308.
12. G. Even, O. Goldreich, M. Luby, N. Nisan and B. Velickovic, Approximations of general independent distributions, in: Proceedings 24th IEEE Annual Symposium on Theory of Computing (1992).
13. R. Fung and K.-C. Chang, Weighing and integrating evidence for stochastic simulation in Bayesian networks, in: M. Henrion, R.D. Shachter, L.N. Kanal and J.F. Lemmer, eds., Uncertainty in Artificial Intelligence 5 (Elsevier, Amsterdam, 1990) 209-219.
14. R. Fung and B. Del Favero, Backward simulation in Bayesian networks, in: Proceedings 10th Conference on Uncertainty in Artificial Intelligence, Seattle, WA (American Association for Artificial Intelligence, 1994) 227-234.
15. M. Henrion, Propagating uncertainty in Bayesian networks by probabilistic logic sampling, in: J.F. Lemmer and L.N. Kanal, eds., Uncertainty in Artificial Intelligence 2 (North-Holland, Amsterdam, 1988) 149-163.
16. M. Henrion, Search-based methods to bound diagnostic probabilities in very large belief nets, in: Proceedings 7th Workshop on Uncertainty in Artificial Intelligence, University of Los Angeles, Los Angeles, CA (1991).
17. E. Horvitz, H.J. Suermondt and G.F. Cooper, Bounded conditioning: flexible inference for decisions under scarce resources, in: Proceedings 1989 Workshop on Uncertainty in Artificial Intelligence, Windsor, Ont. (1989) 182-193.
18. K. Huang and M. Henrion, Efficient search-based inference for noisy-OR belief networks: TopEpsilon, in: Proceedings 12th Conference on Uncertainty in Artificial Intelligence, Portland, OR (American Association for Artificial Intelligence, 1996) 325-331.
19. F.V. Jensen, S.L. Lauritzen and K.G. Olesen, Bayesian updating in causal probabilistic networks by local computations, Comput. Statist. Quarterly 4 (1990) 269-282.
20. R. Karp, M. Luby and N. Madras, Monte-Carlo approximation algorithms for enumeration problems, J. Algorithms 10 (1989) 429-448.
21. S.L. Lauritzen and D. Spiegelhalter, Local computations with probabilities on graphical structures and their application to expert systems, J. Royal Statist. Soc. Ser. B 50 (1988).
22. M. Luby, B. Velickovic and A. Wigderson, Deterministic approximate counting of depth-2 circuits, in: Proceedings 2nd Israeli Symposium on Theory of Computing and Systems (1993).
23. R.M. Neal, Probabilistic inference using Markov chain Monte Carlo methods, Tech. Rept. CRG-TR-93-1, Department of Computer Science, University of Toronto, 1993.
24. N. Nisan, Pseudorandom bits for constant depth circuits, Combinatorica 11 (1991) 63-70.
25. J. Pearl, Evidential reasoning using stochastic simulation of causal models, Artificial Intelligence 32 (1987) 245-257.
26. J. Pearl, Evidential reasoning using stochastic simulation of causal models (Addendum), Artificial Intelligence 33 (1987) 131.
27. J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference (Morgan Kaufmann, San Mateo, CA, 1988).
28. Y. Peng and J.A. Reggia, A probabilistic causal model for diagnostic problem solving - Part 1: Integrating symbolic causal inference with numeric probabilistic inference, IEEE Trans. Systems, Man and Cybernetics 17 (1987) 146-162.
29. Y. Peng and J.A. Reggia, A probabilistic causal model for diagnostic problem solving - Part 2: Diagnostic strategy, IEEE Trans. Systems, Man and Cybernetics, Special Issue on Diagnosis 17 (1987) 395-406.
30. D. Poole, Average-case analysis of a search algorithm for estimating prior and posterior probabilities in Bayesian networks with extreme probabilities, in: Proceedings IJCAI-93, Chambery (1993) 606-612.
31. M. Pradhan and P. Dagum, Optimal Monte Carlo estimation of belief network inference, in: Proceedings 12th Conference on Uncertainty in Artificial Intelligence, Portland, OR (American Association for Artificial Intelligence, 1996) 446-453.
32. E. Santos and S. Shimony, Belief updating by enumerating high-probability independence-based assignments, in: Proceedings 10th Conference on Uncertainty in Artificial Intelligence, Seattle, WA (1994) 506-513.
33. R.D. Shachter and M. Peot, Simulation approaches to general probabilistic inference on belief networks, in: M. Henrion, R.D. Shachter, L.N. Kanal and J.F. Lemmer, eds., Uncertainty in Artificial Intelligence, Vol. 5 (Elsevier, Amsterdam, 1990) 221-231.
34. S.E. Shimony and E. Charniak, A new algorithm for finding MAP assignments to belief networks, in: Proceedings 6th Conference on Uncertainty in Artificial Intelligence, Cambridge, MA (1990) 98-103.
35. A. Yao, Separating the polynomial-time hierarchy by oracles, in: Proceedings 26th IEEE Annual Symposium on the Foundations of Computer Science, Portland, OR (1985) 1-10.