Decoding binary node labels from censored edge measurements: Phase transition and efficient recovery

IEEE Transactions on Network Science and Engineering

Volumn 1, Issue 1, 2014, Pages 10-22

  Abbe, Emmanuel ^a   Bandeira, Afonso S ^a   Bracher, Annina ^b   Singer, Amit ^a  

^a PRINCETON UNIVERSITY   (United States)

^b ETH ZURICH   (Switzerland)

Author keywords

Erdos Renyi graphs; graphbased codes; Information theoretic bounds; Semidefinite relaxations; Synchronization problem

Indexed keywords

INFORMATION THEORY; INVERSE PROBLEMS; RECOVERY; SIGNAL TO NOISE RATIO; STOCHASTIC MODELS; STOCHASTIC SYSTEMS;

ERDOS-RENYI GRAPHS; GRAPH-BASED; INFORMATION THEORETIC BOUNDS; SEMIDEFINITE RELAXATION; SYNCHRONIZATION PROBLEM;

GRAPH THEORY;

EID: 84937128834     PISSN: None     EISSN: 23274697     Source Type: Journal    
DOI: 10.1109/TNSE.2014.2368716     Document Type: Review

References (37)

1. E. Abbe, A. S. Bandeira, A. Bracher, and A. Singer, "Linear inverse problems on Erdos-Rényi graphs: Information-theoretic limits and efficient recovery," in Proc. IEEE Int. Symp. Inf. Theory, Jun. 2014, pp. 1251-1255.
2. P. Erdos and A. Rényi. (1959). On random graphs, I. Publicationes Math. (Debrecen) [Online]. 6, pp. 290-297. Available: http://www. renyi.hu/~pérdos/Erdos.html#1959-11
3. A. Goldenberg, A. X. Zheng, S. E. Fienberg, and E. M. Airoldi, "A survey of statistical network models," Found. Trends Mach. Learn., vol. 2, no. 2, pp. 129-233, 2010.
4. H. C. White, S. A. Boorman, and R. L. Breiger, "Social structure from multiple networks," Amer. J. Sociol., vol. 81, pp. 730-780, 1976.
5. P. W. Holland, K. Laskey, and S. Leinhardt. (1983). Stochastic blockmodels: First steps. Social Netw. [Online]. 5(2), pp. 109-137. Available: http://d.wanfangdata.com.cn/NSTLQK-10.1016-0378-8733(83)90021-7.aspx
6. M. Dyer and A. Frieze. (1989). The solution of some random NPhard problems in polynomial expected time. J. Algorithms. [Online]. 10(4) 451-489. Available http://www.sciencedirect. com/science/article/pii/0196677489900011
7. B. Karrer and M. E. J. Newman. (2011, Jan.) Stochastic blockmodels and community structure in networks. Phys. Rev. E. [Online]. 83, p. 016107. Available: http://link.aps.org/doi/10.1103/PhysRevE.83.016107
8. P. Doreian, V. Batagelj, and A. Ferligoj. (2004, Nov.) Generalized Blockmodeling (Structural Analysis in the Social Sciences). [Online]. Available: http://www.amazon.com/exec/obidos/redirect? tag=citeulike07-20&path=ASIN/0521840856
9. E. Abbe and A. Montanari, "Conditional random fields, planted constraint satisfaction and entropy concentration," in Proc. RANDOM, 2013, pp. 332-346.
10. A. Decelle, F. Krzakala, C. Moore, and L. Zdeborova, "Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications," Phys. Rev. E, vol. 84, pp. 066106, 2011.
11. E. Mossel, J. Neeman, and A. Sly, "Reconstruction and estimation in the planted partition model," Probability Theory and Related Fields, Springer Berlin Heidelberg, pp. 1-31, 2014
12. N. Bansal, A. Blum, and S. Chawla, "Correlation clustering," Mach. Learn., vol. 56, no. 1/3, pp. 89-113, Jun. 2004.
13. N. Cesa-bianchi, C. Gentile, F. Vitale, and G. Zappella, "A linear time active learning algorithm for link classification," in Proc. Adv. Neural Inf. Process. Syst., 2012, pp. 1619-1627.
14. I. Giotis and V. Guruswami, "Correlation clustering with a fixed number of clusters," in Proc. 37th Annu. ACM Symp.Theory Comput., 2006, pp. 1167-1176.
15. K. R. Kumar, P. Pakzad, A. Salavati, and A. Shokrollahi, "Phase transitions for mutual information," in Proc. 6th Int. Symp. Turbo Codes Iterative Inf. Process., 2010, pp. 137-141.
16. A. Shokrollahi, "Information theoretic security," in Lecture Notes in Computer Science, vol. 6673, S. Fehr, Ed., Berlin, Germany: Springer, 2011.
17. A. Singer, "Angular synchronization by eigenvectors and semidefinite programming," Appl. Comput. Harmonic Anal., vol. 30, no. 1, pp. 20-36, 2011.
18. A. S. Bandeira, A. Singer, and D. A. Spielman, "A Cheeger inequality for the graph connection Laplacian," SIAM J. Matrix Anal. Appl., vol. 34, no. 4, pp. 1611-1630, 2013.
19. L. Wang and A. Singer, "Exact and stable recovery of rotations for robust synchronization," Inf. Inference, vol. 2, no. 2, pp. 145-193, 2013.
20. B. Alexeev, A. S. Bandeira, M. Fickus, and D. G. Mixon, "Phase retrieval with polarization," SIAM J. Imaging Sci., vol. 7, no. 1, pp. 35-66, 2013.
21. N. Boumal, A. Singer, P.-A. Absil, and V. D. Blondel, "Cramér-Rao bounds for synchronization of rotations," Inf. Inference, vol. 3, pp. 1-39, 2014.
22. S. Heimlicher, M. Lelarge, and L. Massoulié, "Community detection in the labelled stochastic block model," arXiv:1209.2910 [cs. SI], 2012.
23. A. M.-C. So, "Probabilistic analysis of the semidefinite relaxation detector in digital communications," in Proc. 21st Annu. ACMSIAM Symp. Discr. Algorithms, 2010, pp. 698-711.
24. Q.-X. Huang and L. Guibas, "Consistent shape maps via semidefinite programming," Comput. Graph. Forum, vol. 32, no. 5, pp. 177-186, 2013.
25. Y. Chen, Q.-X. Huang, and L. Guibas, "Near-optimal joint object matching via convex relaxation," in Proc. 31st Int. Conf. Machine Learning, 2014, pp. 100-108.
26. Y. Chen and A. J. Goldsmith, "Information recovery from pairwise measurements," in Proc. IEEE Int. Symp. Inf. Theory, Jun. 2014, pp. 2012-2016.
27. E. V. Slud, "Distribution inequalities for the binomial law," Ann. Probability, vol. 5, no. 3, pp. 404-412, 1977.
28. T. Jiang, "Low eigenvalues of Laplacian matrices of large random graphs," Probability Theory Related Fields, vol. 153, no. 3-4, pp. 671-690, 2012.
29. N. Alon and A. Naor, "Approximating the cut-norm via Grothendieck's inequality," in Proc. 36th Annu. ACM Symp. Theory Comput., 2004, pp. 72-80.
30. A. S. Bandeira, C. Kennedy, and A. Singer, "Approximating the little Grothendieck problem over the orthogonal and unitary groups," arXiv:1308.5207 [cs.DS], 2013.
31. L. Vanderberghe and S. Boyd, "Semidefinite programming," SIAM Rev., vol. 38, pp. 49-95, 1996.
32. J. A. Tropp, "User-friendly tail bounds for sums of random matrices," Found. Comput. Math., vol. 12, no. 4, pp. 389-434, 2012.
33. D. Puder, "Expansion of random graphs: New proofs, new results," arXiv:1212.5216v2 [cs.CO], 2013.
34. J. Friedman, "A proof of Alon's second eigenvalue conjecture," in Proc. 35th Annu. ACM Symp. Theory Comput., 2003, pp. 720-724.
35. N. Alon, "Eigenvalues and expanders," Combinatorica, vol. 6, pp. 83-96, 1986.
36. N. Alon and V. Milman, "Isoperimetric inequalities for graphs, and superconcentrators," J. Combinatorial Theory, vol. 38, pp. 73-88, 1985.
37. E. Abbe, A. S. Bandeira, and G. Hall, "Exact recovery in the stochastic block model," arXiv:1405.3267 [cs.SI], 2014.