On convergence conditions of Gaussian belief propagation

IEEE Transactions on Signal Processing

Volumn 63, Issue 5, 2015, Pages 1144-1155

  Su, Qinliang ^a   Wu, Yik Chung ^a  

^a UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Convergence; factor graph; Gaussian belief propagation; graphical model; loopy belief propagation; message passing; sum product algorithm

Indexed keywords

DAMPING; GAUSSIAN DISTRIBUTION; MESSAGE PASSING; PROBABILITY DENSITY FUNCTION; SCHEDULING;

BELIEF PROPAGATION; CONVERGENCE; FACTOR GRAPHS; GRAPHICAL MODEL; LOOPY BELIEF PROPAGATION; SUM-PRODUCT ALGORITHM;

BACKPROPAGATION;

EID: 84922816567     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2015.2389755     Document Type: Article

References (34)

1. F. R. Kschischang, B. J. Frey, and H. A. Loeliger, "Factor graphs and the sum-product algorithm," IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 498-519, 2001.
2. H. A. Loeliger, "An introduction to factor graphs," IEEE Signal Process. Mag., vol. 21, pp. 28-41, 2004.
3. H. A. Loeliger, J. Dauwels, H. Junli, S. Korl, P. Li, and F. R. Kschischang, "The factor graph approach to model-based signal processing,"Proc. IEEE, vol. 95, no. 6, pp. 1295-1322, Jun. 2007.
4. C. M. Bishop, Pattern Recognition and Machine Learning. New York, NY, USA: Springer, 2006.
5. K. P. Murphy, Machine Learning: A Probabilistic Perspective. Cambridge, MA, USA: MIT Press, 2012.
6. Y. Weiss and W. T. Freeman, "Correctness of belief propagation in Gaussian graphical models of arbitrary topology," Neural Comput., vol. 13, pp. 2173-2200, 2001.
7. A. Montanari, B. Prabhakar, and D. Tse, "Belief propagation based multi-user detection," presented at the IEEE Inf. Theory Workshop, Punta del Este, Uruguay, Mar. 2006.
8. Q. Guo and D. Huang, "EM-based joint channel estimation and detection for frequency selective channels using Gaussian message passing,"IEEE Trans. Signal Process., vol. 59, pp. 4030-4035, 2011.
9. Q. Guo and P. Li, "LMMSE turbo equalization based on factor graphs,"IEEE J. Sel. Areas Commun., vol. 26, pp. 311-319, 2008.
10. Y. El-Kurdi, W. J. Gross, and D. Giannacopoulos, "Efficient implementation of Gaussian belief propagation solver for large sparse diagonally dominant linear systems," IEEE Trans. Magn., vol. 48, no. 2, pp. 471-474, Feb. 2012.
11. O. Shental, P. H. Siegel, J. K. Wolf, D. Bickson, and D. Dolev, "Gaussian belief propagation solver for systems of linear equations,"in Proc. IEEE Int. Symp. Inf. Theory (ISIT), 2008, pp. 1863-1867.
12. M. W. Seeger and D. P. Wipf, "Variational Bayesian inference techniques,"IEEE Signal Process. Mag., vol. 27, no. 6, pp. 81-91, Nov. 2010.
13. V. Chandrasekaran, J. K. Johnson, and A. S. Willsky, "Estimation in Gaussian graphicalmodels using tractable subgraphs: a walk-sumanalysis,"IEEE Trans. Signal Process., vol. 56, pp. 1916-1930, 2008.
14. Y. Liu, V. Chandrasekaran, A. Anandkumar, and A. S. Willsky, "Feedback message passing for inference in Gaussian graphical models,"IEEE Trans. Signal Process., vol. 60, no. 8, pp. 4135-4150, 2012.
15. N. B. Loong, J. S. Evans, S. V. Hanly, and D. Aktas, "Distributed downlink beamforming with cooperative base stations," IEEE Trans. Inf. Theory, vol. 54, pp. 5491-5499, 2008.
16. D. Dolev, A. Zymnis, S. P. Boyd, D. Bickson, and Y. Tock, "Distributed large scale network utility maximization," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), 2009, pp. 829-833.
17. M. Leng and Y. C. Wu, "Distributed clock synchronization for wireless sensor networks using belief propagation," IEEE Trans. Signal Process., vol. 59, no. 11, pp. 5404-5414, Nov. 2011.
18. A. Ahmad, D. Zennaro, E. Serpedin, and L. Vangelista, "A factor graph approach to clock offset estimation in wireless sensor networks," IEEE Trans. Inf. Theory, vol. 58, no. 7, pp. 4244-4260, Jul. 2012.
19. M. Leng, T. Wee-Peng, and T. Q. S. Quek, "Cooperative and distributed localization for wireless sensor networks in multipath environments,"in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP), 2012, pp. 3125-3128.
20. Y. Song, B. Wang, Z. Shi, K. Pattipati, and S. Gupta, "Distributed algorithms for energy-efficient even self-deployment in mobile sensor networks," in IEEE Trans. Mobile Comput., 2013, pp. 1-14.
21. G. Zhang, W. Xu, and Y. Wang, "Fast distributed rate control algorithm with QoS support in Ad Hoc networks," in Proc. IEEE Global Telecommun. Conf. (GLOBECOM), 2010.
22. F. Lehmann, "Iterative mitigation of intercell interference in cellular networks based on Gaussian belief propagation," IEEE Trans. Veh. Technol., vol. 61, pp. 2544-2558, 2012.
23. C. C. Moallemi and B. V. Roy, "Convergence of min-sum message passing for quadratic optimization," IEEE Trans. Inf. Theory, vol. 55, pp. 2413-2423, 2009.
24. D. M. Malioutov, J. Johnson, and A. Willsky, "Walk-sums and belief propagation in Gaussian graphical models," J. Mach. Learn. Res., vol. 7, no. 1, pp. 2031-2064, 2006.
25. th Conf. Uncertainty Artif. Intell. (UAI), Stockholm, Sweden, Jul. 1999, pp. 467-475.
26. Y. El-Kurdi, D. Giannacopoulos, and W. J. Gross, "Relaxed Gaussian belief propagation," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), 2012, pp. 2002-2006.
27. M. Pretti, "A message-passing algorithm with damping," J. Statist. Mech., vol. 2005, no. 11, pp. 11008-11022, 2005.
28. P. Som, T. Datta, N. Srinidhi, A. Chockalingam, and B. S. Rajan, "Low-complexity detection in large-dimension MIMO-ISI channels using graphical models," IEEE J. Sel. Topics Signal Process., vol. 5, no. 8, pp. 1497-1511, Dec. 2011.
29. Q. Su and Y. C. Wu, "Convergence analysis of the variance in Gaussian belief propagation," IEEE Trans. Signal Process., vol. 62, no. 19, pp. 5119-5131, Oct. 2014.
30. D. P. Bertsekas and J. N. Tsitsiklis, Parallel and distributed computation: Numericalmethods. Englewood Cliffs, NJ, USA: Prentice-Hall, 1989.
31. L. Vandenberghe and S. Boyd, "Semidefinite programming," SIAM Rev., vol. 38, no. 1, pp. 49-95, Mar. 1996.
32. M. Grant, S. Boyd, and Y. Ye, CVX: Matalab software for disciplined convex programming. [Online]. Available: http://www.stanford.edu/~boyd/cvx/
33. J. F. Sturm, "Using SeDumi 1.02, a MATLAB toolbox for optimization over symmetric cones," Optim. Methods Softw., no. 11-22, pp. 625-653, 1999.
34. R. Horn and C. R. Johnson, Matrix analysis. NewYork, NY, USA: Cambridge Univ. Press, 1985.