MAP estimation, message passing, and perfect graphs

Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, UAI 2009

Volumn , Issue , 2009, Pages 258-267

  Jebara, Tony ^a  

^a Och Spine at New York Presbyterian Hospitals   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; GRAPH ALGORITHMS; GRAPHIC METHODS; LINEAR PROGRAMMING; MARKOV PROCESSES; MESSAGE PASSING; POLYNOMIAL APPROXIMATION;

GRAPHICAL MODEL; INTEGRAL LINEAR PROGRAMMING; LINEAR PROGRAMMING RELAXATION; MARKOV RANDOM FIELDS; MAXIMUM A POSTERIORI; MESSAGE PASSING ALGORITHM; POLYNOMIAL-TIME ALGORITHMS; RECENT PROGRESS;

GRAPH THEORY;

EID: 80053137346     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (28)

1. Bayati, M., Borgs, C., Chayes, J., & Zecchina, R. (2008). On the exactness of the cavity method for weighted bmatchings on arbitrary graphs and its relation to linear programs. Journal of Statistical Mechanics: Theory and Experiment, 2008, L06001 (10pp).
2. Bayati, M., Shah, D., & Sharma, M. (2005). Maximum weight matching via max-product belief propagation. IEEE International Symposium on Information Theory.
3. Berge, C. (1963). Six papers on graph theory, chapter Perfect graphs, 1-21. Calcutta: Indian Statistical Institute.
4. Berge, C., & Chvátal, V. (Eds.). (1984). Topics on perfect graphs. North-Holland, Amsterdam.
5. Berge, C., & Ramírez-Alfonsín, J. (2001). Perfect graphs, chapter Origins and genesis, 1-12. Wiley.
6. Chudnovsky, M., Cornuéjols, G., Liu, X., Seymour, P., & Vusković, K. (2005). Recognizing Berge graphs. Combinatorica, 25, 143-186. (Pubitemid 40630741)
7. Chudnovsky, M., Robertson, N., Seymour, P., & Thomas, R. (2006). The strong perfect graph theorem. Ann. Math, 164, 51-229. (Pubitemid 44372091)
8. Chvátal, V. (1975). On certain polytopes associated with graphs. Journal of Combinatorial Theory, Series B, 13, 138-154.
9. Cornuéjols, M., & Cunningham, W. (2001). Composition for perfect graphs. Discrete Mathematics, 55, 245-254.
10. Edmonds, J. (1965). Paths, trees and flowers. Canadian Journal of Mathematics, 17.
11. Globerson, A., & Jaakkola, T. (2007). Fixing max-product: Convergent message passing algorithms for MAP LPrelaxations. Neural Information Processing Systems.
12. Grötschel, M., Lovász, L., & Schrijver, A. (1988). Geometric algorithms and combinatorial optimization, chapter Stable sets in graphs. Springer-Verlag.
13. Huang, B., & Jebara, T. (2007). Loopy belief propagation for bipartite maximum weight b-matching. Artificial Intelligence and Statistics.
14. Lovász, L. (1972). Normal hypergraphs and the weak perfect graph conjecture. Discrete Math., 2, 253-267.
15. Lovász, L. (1983). Selected topics in graph theory, volume 2, chapter Perfect graphs, 55-87. Academic Press.
16. Nikolopoulos, S., & Palios, L. (2004). Hole and antihole detection in graphs. Symposium on Discrete Algorithms.
17. Pearl, J. (1988). Probabilistic reasoning in intelligent systems: Networks of plausible inference. Morgan Kaufmann.
18. Ravikumar, P., & Lafferty, J. (2006). Quadratic programming relaxations for metric labeling and Markov random field MAP estimation. International Conference on Machine Learning.
19. Salez, J., & Shah, D. (2009). Optimality of belief propagation for random assignment problem. Symposium on Discrete Algorithms.
20. Sanghavi, S., Malioutov, D., & Willsky, A. (2008). Linear programming analysis of loopy belief propagation for weighted matching. Neural Information Processing Systems.
21. Santos, E. (1991). On the generation of alternative explanations with implications for belief revision. Uncertainty in Artificial Intelligence.
22. Shimony, Y. (1994). Finding the MAPs for belief networks is NP-hard. Aritifical Intelligence, 68, 399-410.
23. Wainwright, M., Jaakkola, T., & Willsky, A. (2005). MAP estimation via agreement on trees: message-passing and linear programming. IEEE Transactions on Information Theory, 51, 3697-3717. (Pubitemid 41622574)
24. Wainwright, M., & Jordan, M. (2008). Graphical models, exponential families and variational inference. Foundations and Trends in Machine Learning, 1, 1-305.
25. Weiss, Y. (2000). Correctness of local probability propagation in graphical models with loops. Neural Computation, 12, 1-41.
26. Weiss, Y., & Freeman, W. (2001). On the optimality of solutions of the max-productbelief-propagation algorithm in arbitrary graphs. IEEE Transactions on Information Theory, 47, 736-744. (Pubitemid 32318100)
27. Weiss, Y., Yanover, C., & Meltzer, T. (2007). MAP estimation, linear programming and belief propagation with convex free energies. Uncertainty in Artificial Intelligence.
28. Yedidia, J., Freeman, W., & Weiss, Y. (2001). Understanding belief propagation and its generalizations. International Joint Conference on Artificial Intelligence, Distinguished Lecture Track.