Getting feasible variable estimates from infeasible ones: MRF local polytope study

Proceedings of the IEEE International Conference on Computer Vision

Volumn , Issue , 2013, Pages 267-274

  Savchynskyy, Bogdan ^a   Schmidt, Stefan ^b  

^a UNIVERSITY OF HEIDELBERG   (Germany)

^b NONE

Author keywords

Duality gap; Feasible primal solution; Graphical models; LP relaxation; MAP inference; Markov random fields

Indexed keywords

MARKOV PROCESSES;

DUALITY GAP; GRAPHICAL MODEL; LP RELAXATION; MAP INFERENCES; MARKOV RANDOM FIELDS;

OPTIMIZATION;

EID: 84897490148     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ICCVW.2013.43     Document Type: Conference Paper

References (42)

1. B. Andres, T. Beier, and J. H. Kappes. OpenGM: A C++ library for discrete graphical models. Technical report, arXiv:1206.0111, 2012.
2. M. S. Bazaraa and J. J. Jarvis. Linear Programming and Network Flows. Wiley, 1977.
3. R. Bland. New finite pivoting rules. Discussion Paper 7612, Center for Operations Research and Econometrics (CORE), Université Catholique de Louvain, Heverlee, Belgium, 1976.
4. S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press, New York, USA, 2004.
5. Y. Boykov, O. Veksler, and R. Zabih. Fast approximate energy minimization via graph cuts. PAMI, vol. 23, no. 11, pp. 1222-1239, 23:1222-1239, 2001.
6. A. Chambolle and T. Pock. A first-order primal-dual algorithm for convex problems with applications to imaging. Journal of Mathematical Imaging and Vision, pages 1-26, 2010.
7. Q. Fu and H. W. A. Banerjee. Bethe-admm for tree decomposition based parallel map inference. In UAI 2013.
8. A. Globerson and T. Jaakkola. Fixing max-product: Convergent message passing algorithms for MAP LP-relaxations. In NIPS, 2007.
9. T. Hazan, J. Peng, and A. Shashua. Tightening fractional covering upper bounds on the partition function for highorder region graphs. In UAI, 2012.
10. T. Hazan and A. Shashua. Norm-product belief propagation: Primal-dual message-passing for approximate inference. IEEE Trans. on Inf. Theory, 56(12):6294-6316, Dec. 2010.
11. T. Heskes. On the uniqueness of loopy belief propagation fixed points. Neural Computation, 16(11):2379-2413, 2004.
12. J. Jancsary and G. Matz. Convergent decomposition solvers for tree-reweighted free energies. In AISTATS, 2011.
13. J. K. Johnson, D. Malioutov, and A. S. Willsky. Lagrangian relaxation for MAP estimation in graphical models. In 45th Ann. Allerton Conf. on Comm., Control and Comp., 2007.
14. V. Jojic, S. Gould, and D. Koller. Accelerated dual decomposition for MAP inference. In ICML, pages 503-510, 2010.
15. J. H. Kappes, B. Savchynskyy, and C. Schnörr. A bundle approach to efficient MAP-inference by lagrangian relaxation. In CVPR 2012, 2012. in press.
16. V. Kolmogorov. Convergent tree-reweighted message passing for energy minimization. IEEE Trans. on PAMI, 28(10):1568-1583, 2006.
17. N. Komodakis, N. Paragios, and G. Tziritas. MRF optimization via dual decomposition: Message-passing revisited. In ICCV, 2007.
18. N. Komodakis, N. Paragios, and G. Tziritas. MRF energy minimization and beyond via dual decomposition. IEEE Trans. PAMI, 33:531-552, March 2011.
19. T. Larsson, M. Patriksson, and A.-B. Strömberg. Ergodic, primal convergence in dual subgradient schemes for convex programming. Mathematical Programming, 86:283-312, 1999.
20. A. F. T. Martins, M. A. T. Figueiredo, P. M. Q. Aguiar, N. A. Smith, and E. P. Xing. An augmented lagrangian approach to constrained MAP inference. In ICML, 2011.
21. O. Meshi and A. Globerson. An alternating direction method for dual MAP LP relaxation. In ECML/PKDD (2), pages 470-483, 2011.
22. O. Meshi, A. Globerson, and T. S. Jaakkola. Convergence rate analysis of map coordinate minimization algorithms. In NIPS, pages 3023-3031, 2012.
23. C. Michelot. A finite algorithm for finding the projection of a point onto the canonical simplex of Rn. J. Optim. Theory Appl., 50:195-200, July 1986.
24. Y. Nesterov. Smooth minimization of non-smooth functions. Math. Program., Ser. A(103):127-152, 2004.
25. C. H. Papadimitriou and K. Steiglitz. Combinatorial optimization: algorithms and complexity. Mineola, N.Y. : Dover Publications, 2nd edition, 1998.
26. P. Ravikumar, A. Agarwal, and M. Wainwright. Messagepassing for graph-structured linear programs: Proximal methods and rounding schemes. JMLR, 11:1043-1080, 2010.
27. B. Savchynskyy, J. Kappes, S. Schmidt, and C. Schnörr. A study of Nesterov's scheme for Lagrangian decomposition and MAP labeling. In CVPR 2011, 2011.
28. B. Savchynskyy and S. Schmidt. Getting feasible variable estimates from infeasible ones: MRF local polytope study. Technical report, arXiv:1210.4081, 2012.
29. B. Savchynskyy, S. Schmidt, J. Kappes, and C. Schnörr. Efficient MRF energy minimization via adaptive diminishing smoothing. In UAI 2012, pages 746-755, 2012.
30. M. Schlesinger and V. Giginyak. Solution to structural recognition (max,+)-problems by their equivalent transformations. in 2 Parts. Control Systems and Computers, (1-2), 2007.
31. M. Schlesinger, E. Vodolazskiy, and N. Lopatka. Stop condition for subgradient minimization in dual relaxed (max,+) problem. In EMMCVPR, 2011.
32. M. I. Schlesinger. Syntactic analysis of two-dimensional visual signals in the presence of noise. Kibernetika, (4):113-130, July-August 1976.
33. S. Schmidt, B. Savchynskyy, J. Kappes, and C. Schnörr. Evaluation of a first-order primal-dual algorithm for MRF energy minimization. In EMMCVPR 2011, 2011.
34. D. Sontag, A. Globerson, and T. Jaakkola. Introduction to dual decomposition for inference. Optimization for Machine Learning, 1, 2011.
35. D. Sontag, T. Meltzer, A. Globerson, Y. Weiss, and T. Jaakkola. Tightening LP relaxations for MAP using message-passing. In UAI, pages 503-510, 2008.
36. M. Wainwright, T. Jaakkola, and A. Willsky. A new class of upper bounds on the log partition function. IEEE Trans. on Information Theory, 51:2313-2335, 2005.
37. M. J. Wainwright and M. I. Jordan. Graphical models, exponential families, and variational inference. Found. Trends Mach. Learn., 1(1-2):1-305, 2008.
38. Y. Weiss and W. T. Freeman. On the optimality of solutions of the max-product belief-propagation algorithm in arbitrary graphs. IEEE Transactions on Information Theory, 47(2):736-744, 2001.
39. Y.Weiss, C. Yanover, and T. Meltzer. Map estimation, linear programming and belief propagation with convex free energies. In Uncertainty in Artificial Intelligence (UAI), 2007.
40. T. Werner. A linear programming approach to max-sum problem: A review. IEEE Trans. on PAMI, 29(7), July 2007.
41. T. Werner. Revisiting the decomposition approach to inference in exponential families and graphical models. Technical report, CMP, Czech TU, 2009.
42. T.Werner. How to compute primal solution from dual one in MAP inference in MRF? Control Systems and Computers, (2), March-April 2011.