Linear Response Algorithms for Approximate Inference in Graphical Models

Neural Computation

Volumn 16, Issue 1, 2004, Pages 197-221

  Welling, Max ^a   Teh, Yee Whye ^b  

^a UNIVERSITY OF TORONTO   (Canada)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; ARTIFICIAL NEURAL NETWORK; NORMAL DISTRIBUTION; REPRODUCIBILITY; STATISTICAL MODEL; THERMODYNAMICS;

ALGORITHMS; LINEAR MODELS; NEURAL NETWORKS (COMPUTER); NORMAL DISTRIBUTION; REPRODUCIBILITY OF RESULTS; SUPPORT, NON-U.S. GOV'T; THERMODYNAMICS;

EID: 0347526306     PISSN: 08997667     EISSN: None     Source Type: Journal    
DOI: 10.1162/08997660460734056     Document Type: Article

References (19)

1. Frey, B., & MacKay, D. (1997). A revolution: Belief propagation in graphs with cycles. In M. Jordan, M. Kearns, & S. Solla (Eds.), Advances in neural information processing systems, 10 (pp. 479-485). Cambridge, MA: MIT Press.
2. Georges, A., & Yedidia, J. (1991). How to expand around mean-field theory using high-temperature expansions. J. Phys A: Math. Gen., 24, 2173-2192.
3. Heskes, T. (in press). Stable fixed points of loopy belief propagation are minima of the bethe free energy. In S. Becker, S. Thrun, & K. Obermayer (Eds.), Advances in neural information processing systems, 15. Cambridge, MA: MIT Press.
4. Kappen, H., & Rodriguez, F. (1998). Efficient learning in Boltzmann machines using linear response theory. Neural Computation, 10, 1137-1156.
5. Kschischang, F., Frey, B., & Loeliger, H. (2001). Factor graphs and the sum-product algorithm. IEEE Transactions on Information Theory, 47(2), 498-519.
6. Minka, T. (2001). Expectation propagation for approximate Bayesian inference. In Proceedings of the Conference on Uncertainty in Artificial Intelligence (pp. 362-369). San Francisco: Morgan Kaufmann.
7. Murphy, K., Weiss, Y., & Jordan, M. (1999). Loopy belief propagation for approximate inference: An empirical study. In Proceedings of the Conference on Uncertainty in Artificial Intelligence (pp. 467-475). San Francisco: Morgan Kaufmann.
8. Tanaka, K. (2003). Probabilistic inference by means of cluster variation method and linear response theory. IEICE Transactions in Information and Systems, E 6-D (7), 1-15.
9. Teh, Y., & Welling, M. (2001). The unified propagation and scaling algorithm. In T. G. Dietterich, S. Becker, & Z. Ghahramani (Eds.), Advances in neural information processing systems, 14 (pp. 953-960). Cambridge, MA: MIT Press.
10. Wainwright, M., Jaakkola, T., & Willsky, A. (2002). A new class of upper bounds on the log partition function. In Proceedings of the Conference on Uncertainty in Artificial Intelligence (pp. 536-543). San Francisco: Morgan Kaufmann.
11. Wainwright, M., & Jordan, M. (2003). Semidefinite relaxations for approximate inference on graphs with cycles (Tech. Rep. No. UCB/CSD-3-1226). Berkeley: CS Division, University of California, Berkeley.
12. Wainwright, M., Sudderth, E., & Willsky, A. (2000). Tree-based modeling and estimation of gaussian processes on graphs with cycles. In T. Leen, T. Dietterich, & V. Tresp (Eds.), Advances in neural information processing systems, 13 (661-667). Cambridge, MA: MIT Press.
13. Weiss, Y. (2000). Correctness of local probability propagation in graphical models with loops. Neural Computation, 12, 1-41.
14. Weiss, Y, & Freeman, W. (1999). Correctness of belief propagation in gaussian graphical models of arbitrary topology. In S. A. Solla, T. K. Leen, & K. R. Muller (Eds.), Advances in neural information processing systems, 12 (pp. 673-679). Cambridge, MA: MIT Press.
15. Weiss, Y, & Freeman, W. (2001). On the optimality of solutions of the max-product belief-propagation algorithm in arbitrary graphs. IEEE Transactions on Information Theory, 47, 723-735.
16. Welling, M, & Teh, Y. (2003). Approximate inference in Boltzmann machines. Artificial Intelligence, 143, 19-50.
17. Yedidia, J., Freeman, W., & Weiss, Y. (2000). Generalized belief propagation. In T. Leen, T. Dietterich, & V. Tresp (Eds.), Advances in neural information processing systems, 13 (pp. 689-695). Cambridge, MA: MIT Press.
18. Yedidia, J., Freeman, W., & Weiss, Y. (2002). Constructing free energy approximations and generalized belief propagation algorithms (Tech. Rep. TR-2002-35). Cambridge, MA: Mitsubishi Electric Research Laboratories.
19. Yuille, A. (2002). CCCP algorithms to minimize the Bethe and Kikuchi free energies: Convergent alternatives to belief propagation. Neural Computation, 14 (7), 1691-1722.