Theoretical analysis and practical insights on importance sampling in Bayesian networks

International Journal of Approximate Reasoning

Volumn 46, Issue 2, 2007, Pages 320-333

  Yuan, Changhe ^a   Druzdzel, Marek J ^b  

^a MISSISSIPPI STATE UNIVERSITY   (United States)

^b School of Information Sciences ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ARTIFICIAL INTELLIGENCE; HEURISTIC METHODS; MATHEMATICAL MODELS; PROBABILITY;

POSTERIOR PROBABILITY DISTRIBUTION; SAMPLING BASED ALGORITHM;

BAYESIAN NETWORKS;

EID: 34648834540     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijar.2006.09.006     Document Type: Article

References (25)

1. Andrieu C., de Freitas N., Doucet A., and Jordan M. An introduction to MCMC for machine learning. Machine Learning 350 (2003) 5-43
2. Cheng J., and Druzdzel M.J. BN-AIS: An adaptive importance sampling algorithm for evidential reasoning in large Bayesian networks. Journal of Artificial Intelligence Research 13 (2000) 155-188
3. Cooper G.F. The computational complexity of probabilistic inference using Bayesian belief networks. Artificial Intelligence 42 2-3 (1990) 393-405
4. Dagum P., and Luby M. Approximating probabilistic inference in Bayesian belief networks is NP-hard. Artificial Intelligence 60 1 (1993) 141-153
5. Druzdzel M.J. Some properties of joint probability distributions. Proceedings of the 10th Conference on Uncertainty in Artificial Intelligence (UAI-94) (1994), Morgan Kaufmann Publishers, San Francisco, California 187-194
6. Fung R., and Chang K.C. Weighing and integrating evidence for stochastic simulation in Bayesian networks. In: Henrion M., Shachter R., Kanal L., and Lemmer J. (Eds). Uncertainty in Artificial Intelligence 5 (1989), Elsevier Science Publishing Company, Inc., New York, NY 209-219
7. Fung R., and del Favero B. Backward simulation in Bayesian networks. Proceedings of the Tenth Annual Conference on Uncertainty in Artificial Intelligence (UAI-94) (1994), Morgan Kaufmann Publishers, Inc., San Mateo, CA 227-234
8. Geweke J. Bayesian inference in econometric models using Monte Carlo integration. Econometrica 57 6 (1989) 1317-1339
9. Grassberger P. Pruned-enriched Rosenbluth method: Simulations of θ polymers of chain length up to 1 000 000. Physical Review E 56 Sept. (1997) 3682-3693
10. Henrion M. Propagating uncertainty in Bayesian networks by probalistic logic sampling. Uncertainty in Artificial Intelligence vol. 2 (1988), Elsevier Science Publishing Company, Inc., New York, NY 149-163
11. Hernandez L.D., Moral S., and Salmeron A. A Monte Carlo algorithm for probabilistic propagation in belief networks based on importance sampling and stratified simulation techniques. International Journal of Approximate Reasoning 18 (1998) 53-91
12. Jordan M.I., Ghahramani Z., Jaakkola T., and Saul L. An Introduction to Variational Methods for Graphical Models (1998), The MIT Press, Cambridge, Massachusetts
13. Liang F. Dynamically weighted importance sampling in Monte Carlo computation. Journal of the American Statistical Association 97 (2002) 807-821
14. Liu J.S. Monte Carlo Strategies in Scientific Computing (2001), Springer Verlag, New York
15. MacKay D. Introduction to Monte Carlo Methods (1998), The MIT Press, Cambridge, Massachusetts
16. S. Moral, A. Salmeron, Dynamic importance sampling computation in Bayesian networks, in: Proceedings of Seventh European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU-03), 2003, pp. 137-148.
17. R.M. Neal, Annealed importance sampling. Technical report no. 9805, Dept. of Statistics, University of Toronto, 1998.
18. Ortiz L., and Kaelbling L. Adaptive importance sampling for estimation in structured domains. Proceedings of the 16th Annual Conference on Uncertainty in Artificial Intelligence (UAI-00) (2000), Morgan Kaufmann Publishers, San Francisco, California 446-454
19. Press W.H. Numerical Recipes in C (1992), Cambridge University Press
20. Rosenbluth M.N., and Rosenbluth A.W. Monte Carlo calculation of the average extension of molecular chains. Journal of Chemical Physics 23 256 (1955)
21. Rubinstein R.Y. Simulation and the Monte Carlo Method (1981), John Wiley & Sons
22. Shachter R.D., and Peot M.A. Simulation approaches to general probabilistic inference on belief networks. In: Henrion M., Shachter R., Kanal L., and Lemmer J. (Eds). Uncertainty in Artificial Intelligence vol. 5 (1989), Elsevier Science Publishing Company, Inc., New York, NY 221-231
23. Yuan C., and Druzdzel M. How heavy should the tails be. In: Russell I., and Markov Z. (Eds). Proceedings of the Eighteenth International FLAIRS Conference (FLAIRS-05) (2005), AAAI Press/The MIT Press, Menlo Park, CA 799-804
24. C. Yuan, M.J. Druzdzel, A comparison of the effectiveness of two heuristics for importance sampling, in: Proceedings of the Second European Workshop on Probabilistic Graphical Models (PGM'04), Leiden, The Netherlands, 2004, pp. 225-232.
25. Yuan C., and Druzdzel M.J. Importance sampling algorithms for Bayesian networks: principles and performance. Mathematical and Computer Modelling 43 (2006) 1189-1207