Studies in lower bounding probability of evidence using the Markov inequality

Proceedings of the 23rd Conference on Uncertainty in Artificial Intelligence, UAI 2007

Volumn , Issue , 2007, Pages 141-148

  Gogate, Vibhav ^a   Bidyuk, Bozhena ^b   Dechter, Rina ^a  

^a Ringgold Standard Institution Informatics   (United States)

^b GOOGLE INC   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ABSOLUTE ERROR; EMPIRICAL EVALUATIONS; ERROR BOUND; HARD PROBLEMS; HIGH CONFIDENCE; IMPORTANCE SAMPLING; LOWER BOUNDS; MARKOV INEQUALITY; NP-HARD;

ARTIFICIAL INTELLIGENCE; ERROR ANALYSIS;

PROBABILITY;

EID: 70049107583     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (21)

1. Bidyuk, B. and Dechter, R. (2006a). An anytime scheme for bounding posterior beliefs. In AAAI.
2. Bidyuk, B. and Dechter, R. (2006b). Improving bound propagation. In ECAI.
3. Breiman, L. (1968). Probability. Addison-Wesley.
4. Cheng, J. (2001). Sampling algorithms for estimating the mean of bounded random variables. In Computational Statistics. Volume 16(1).
5. Cheng, J. and Druzdzel, M. J. (2000). Ais-bn: An adaptive importance sampling algorithm for evidential reasoning in large bayesian networks. J. Artif. Intell. Res. (JAIR), 13:155-188. (Pubitemid 33682085)
6. Dagum, P. and Luby, M. (1993). Approximating probabilistic inference in bayesian belief networks is np-hard. In AAAI-1993.
7. Dagum, P. and Luby, M. (1997). An optimal approximation algorithm for bayesian inference. Artificial Intelligence, 93:1-27. (Pubitemid 127401111)
8. Dechter, R. and Mateescu, R. (2004). Mixtures of deterministic- probabilistic networks and their and/or search space. In UAL
9. Dechter, R. and Rish, I. (2003). Mini-buckets: A general scheme for bounded inference. J. ACM, 50(2): 107-153.
10. Fishelson, M. and Geiger, D. (2003). Optimizing exact genetic linkage computations. In RECOMB 2003.
11. Gogate, V. and Dechter, R. (2005). Approximate inference algorithms for hybrid bayesian networks with discrete constraints. UAL
12. Gogate, V. and Dechter, R. (2007). Samplesearch: A scheme that searches for consistent samples. AISTATS-2007.
13. Gomes, C., Hoffmann, J., Sabharwal, A., and Selman, B. (2007). From sampling to model counting. IJCAI.
14. Hernández, L., Moral, S., and Salmerön, A. (1998). A monte carlo algorithm for probabilistic propagation in belief networks based on importance sampling and stratified simulation techniques. International Journal of Approximate Reasoning, 18:53-91. (Pubitemid 128393704)
15. Hoeffding, W. (1963). Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association, 58(301):13-30.
16. Kaplan, H. M. (1987). A method of one-sided nonparametric inference for the mean of a nonnegative population. The American Statistician, 41(2):157-158.
17. Leisink, M. and Kappen, B. (2003). Bound propagation. Journal of Artificial Intelligence Research, 19:139-154. (Pubitemid 41525918)
18. Pradhan, M., Provan, G., Middleton, B., and Henrion, M. (1994). Knowledge engineering for large belief networks. In UAI-94.
19. Rubinstein, R. Y. (1981). Simulation and the Monte Carlo Method. John Wiley & Sons, Inc., New York, NY, USA.
20. Sorensson, N. and Een, N. (2005). Minisat v1.13 - a sat solver with conflict-clause minimization. In SAT 2005.
21. Yuan, C. and Druzdzel, M. J. (2006). Importance sampling algorithms for Bayesian networks: Principles and performance. Mathematical and Computer Modelling.