Exactness of belief propagation for some graphical models with loops

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2008, Issue 10, 2008, Pages

  Chertkov, Michael ^a  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

Analysis of algorithms; Exact results; Messagepassing algorithms; Spin glasses (theory)

Indexed keywords

EID: 56349083313     PISSN: 17425468     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2008/10/P10016     Document Type: Article

References (27)

1. Bayati M, Borgs C, Chayes J and Zecchina R 2007 Belief-propagation for weighted b-matchings on arbitrary graphs and its relation to linear programs with integer solutions arXiv:0709.1190
2. Bayati M, Shah D and Sharma M 2008 Max-product for maximum weight matching: Convergence, correctness, and LP duality IEEE Trans. Inform. Theory 54 1241
3. Bayati M, Shah D and Sharma M 2006 A simpler max-product weight matching algorithm and the auction algorithm IEEE Symp. on Information Theory (Seattle, WA, 9-14 July 2006)
4. Bethe H A 1935 Statistical theory of superlattices Proc. R. Soc. A 150 552
5. Boros E and Hammer PL 2002 Pseudo-boolean optimization Discrete Appl. Math. 123 155
6. Chertkov M and Chernyak V 2006 Loop calculus in statistical physics and information science Phys. Rev. E 73 065102(R)
7. Chertkov M and Chernyak V 2006 Loop series for discrete statistical models on graphs J. Stat. Mech. P06009
8. Feldman J, Wainwright M and Karger D R 2005 Using linear programming to decode binary linear codes IEEE Trans. Inform. Theory 51 954
9. Gallager R G 1963 Low Density Parity Check Codes (Cambridge, MA: MIT Press)
10. Globerson A and Jaakola T 2007 Fixing max-product: convergent message-passing algorithms for map lp-relaxations Proc. NIPS
11. Hartmann A and Rieger H 2002 Optimization Algorithms in Physics (Berlin: Wiley VCH)
12. Huang B and Jebara T 2007 Loopy belief propagation for bipartite maximum weight b-matching AISTATS: Proc. of Artificial Intelligence and Statistics
13. Kolmogorov V and Wainwright M J 2005 On the optimality of tree-reweighted max-product message-passing Proc. 21st Ann. Conf. on Uncertainty in Artificial Intelligence (UA1-05) (Arlington, VA: AUAI Press) pp316-32
14. Malioutov DM, Johnson JK and Willsky AS 2006 Walk-sums and belief propagation in gaussian graphical models J. Mach. Learn. Res. 7 2031
15. Moallemi CC and Van Roy B 2006 Convergence of the min-sum message passing algorithm for quadratic optimization arXiv:cs/0603058
16. Papadimitriou H and Steiglitz I 1998 Combinatorial Optimization: Algorithms and Complexity (New York: Dover)
17. Pearl J 1988 Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference (San Francisco: Morgan Kaufmann Publishers)
18. Peierls H A 1936 Ising's model of ferromagnetism Proc. Cambridge Phil. Soc. 32 477
19. Sanghavi S, Malioutov D M and Willsky A 2007 Linear programming analysis of loopy belief propagation for weighted matching Proc. NIPS
20. Wainwright MJ and Jordan MI 2003 Graphical models, exponential families, and variational inference Technical Report 649 (UC Berkeley, Department of Statistics)
21. Wainwright M J, Jaakkola T S and Willsky A S 2003 Tree-based reparametrization framework for approximate estimation on graphs with cycles IEEE Trans. Inform. Theory 49 1120
22. Weiss Y and Freeman W T 2001 Correctness of belief propagation in Gaussian graphical models of arbitrary topology Neural Comput. 13 2173
23. Weiss Y, Yanover C and Melzer T 2007 Map estimation, linear programming and belief propagation with convex free energies Proc. UAI
24. Yedidia JS, Freeman WT and Weiss Y 2005 Constructing free-energy approximations and generalized belief propagation algorithms IEEE Trans. Inform. Theory 51 2282
25. Yedidia J S, Freeman W T and Weiss Y 2001 Generalized Belief Propagation vol 13 (Cambridge, MA: MIT Press) pp689-95
26. Yuille AL 2002 Cccp algorithms to minimize the Bethe and Kikuchi free energies: convergent alternatives to belief propagation Neural Comput. 14 1691
27. Yuille AL and Rangarajan A 2003 The concave-convex procedure Neural Comput. 15 915