Probabilistic variational bounds for graphical models

Advances in Neural Information Processing Systems

Volumn 2015-January, Issue , 2015, Pages 1432-1440

  Liu, Qiang ^a   Fisher, John ^b   Ihler, Alexander ^c  

^a Dartmouth College   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; INFORMATION SCIENCE; MONTE CARLO METHODS;

BELIEF PROPAGATION; MONTE CARLO ESTIMATORS; PARTITION FUNCTIONS; PROBABILISTIC BOUNDS; PROPOSAL DISTRIBUTION; VARIATIONAL ALGORITHMS; VARIATIONAL METHODS; VARIATIONAL OPTIMIZATION;

IMPORTANCE SAMPLING;

EID: 84965139754     PISSN: 10495258     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (35)

1. T. Bengtsson, P. Bickel, and B. Li. Curse-of-dimensionality revisited: Collapse of the particle filter in very large scale systems. In Probability and statistics: Essays in honor of David A. Freedman, pages 316-334. Institute of Mathematical Statistics, 2008.
2. J. Cheng. Sampling algorithms for estimating the mean of bounded random variables. Computational Statistics, 16(1):1-23, 2001.
3. J. Cheng and M. Druzdzel. AIS-BN: An adaptive importance sampling algorithm for evidential reasoning in large Bayesian networks. Journal of Artificial Intelligence Research, 2000.
4. P. Dagum and M. Luby. An optimal approximation algorithm for Bayesian inference. Artificial Intelligence, 93(1):1-27, 1997.
5. P. Dagum, R. Karp, M. Luby, and S. Ross. An optimal algorithm for Monte Carlo estimation. SIAM Journal on Computing, 29:1484-1496, 2000.
6. N. De Freitas, P. Højen-Sørensen, M. Jordan, and S. Russell. Variational MCMC. In UAI, 2001.
7. R. Dechter and I. Rish. Mini-buckets: A general scheme for bounded inference. Journal of the ACM, 50(2):107-153, 2003.
8. R. Fung and K. Chang. Weighing and integrating evidence for stochastic simulation in Bayesian networks. In UAI, 1990.
9. A. Globerson and T. Jaakkola. Approximate inference using conditional entropy decompositions. In UAI, pages 130-138, 2007.
10. V. Gogate. Sampling Algorithms for Probabilistic Graphical Models with Determinism. PhD thesis, UC Irvine, 2009.
11. V. Gogate and R. Dechter. Sampling-based lower bounds for counting queries. Intelligenza Artificiale, 5(2):171-188, 2011.
12. T. Hazan and T. Jaakkola. On the partition function and random maximum a-posteriori perturbations. In ICML, 2012.
13. D. Koller and N. Friedman. Probabilistic graphical models: principles and techniques. MIT press, 2009.
14. S. Lauritzen. Graphical models. Oxford University Press, 1996.
15. J. Liu. Monte Carlo strategies in scientific computing. Springer Science & Business Media, 2008.
16. Q. Liu. Reasoning and Decisions in Probabilistic Graphical Models-A Unified Framework. PhD thesis, UC Irvine, 2014.
17. Q. Liu and A. Ihler. Bounding the partition function using Hölder's inequality. In ICML, 2011.
18. R. Mateescu, K. Kask, V. Gogate, and R. Dechter. Join-graph propagation algorithms. JAIR, 37(1):279-328, 2010.
19. A. Maurer and M. Pontil. Empirical Bernstein bounds and sample-variance penalization. In COLT, pages 115-124, 2009.
20. V. Mnih, C. Szepesvári, and J.-Y. Audibert. Empirical Bernstein stopping. In ICML, 2008.
21. M.-S. Oh and J. Berger. Adaptive importance sampling in Monte Carlo integration. J. Stat. Comput. Simul., 41(3-4):143-168, 1992.
22. F. Orabona, T. Hazan, A. Sarwate, and T. Jaakkola. On measure concentration of random maximum a-posteriori perturbations. In ICML, 2014.
23. G. Papandreou and A. Yuille. Perturb-and-map random fields: Using discrete optimization to learn and sample from energy models. In ICCV, 2011.
24. N. Ruozzi. The bethe partition function of log-supermodular graphical models. In NIPS, 2012.
25. T. Salimans, D. Kingma, and M. Welling. Markov chain Monte Carlo and variational inference: Bridging the gap. In ICML, 2015.
26. R. Shachter and M. Peot. Simulation approaches to general probabilistic inference on belief networks. In UAI, 1990.
27. E. Sudderth, M. Wainwright, and A. Willsky. Loop series and bethe variational bounds in attractive graphical models. In NIPS, pages 1425-1432, 2007.
28. M. Wainwright. Estimating the wrong graphical model: Benefits in the computation-limited setting. JMLR, 7:1829-1859, 2006.
29. M. Wainwright and M. Jordan. Graphical models, exponential families, and variational inference. Foundations and Trends in Machine Learning, 1(1-2):1-305, 2008.
30. M. Wainwright, T. Jaakkola, and A. Willsky. A new class of upper bounds on the log partition function. IEEE Trans. Information Theory, 51(7):2313-2335, 2005.
31. Y. Wexler and D. Geiger. Importance sampling via variational optimization. In UAI, 2007.
32. C. Yuan and M. Druzdzel. An importance sampling algorithm based on evidence pre-propagation. In UAI, pages 624-631, 2002.
33. C. Yuan and M. Druzdzel. Importance sampling algorithms for Bayesian networks: Principles and performance. Mathematical and Computer Modeling, 43(9):1189-1207, 2006.
34. C. Yuan and M. Druzdzel. Generalized evidence pre-propagated importance sampling for hybrid Bayesian networks. In AAAI, volume 7, pages 1296-1302, 2007.
35. C. Yuan and M. Druzdzel. Theoretical analysis and practical insights on importance sampling in Bayesian networks. International Journal of Approximate Reasoning, 46(2):320-333, 2007.