Spectral detection in the censored block model

IEEE International Symposium on Information Theory - Proceedings

Volumn 2015-June, Issue , 2015, Pages 1184-1188

  Saade, Alaa ^a   Lelarge, Marc ^b   Krzakala, Florent ^c   Zdeborova, Lenka ^d  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b INRIA   (France)

^c SORBONNE UNIVERSITÉ   (France)

^d Centre National de la Recherche Scientifique   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTICALLY OPTIMAL; BINARY VARIABLES; COMMUNITY DETECTION; CORRELATION CLUSTERING; HESSIAN OPERATOR; PARTIAL RECOVERY; SPECTRAL ALGORITHM; SPECTRAL DETECTION;

INFORMATION THEORY;

EID: 84969812388     PISSN: 21578095     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ISIT.2015.7282642     Document Type: Conference Paper

References (26)

1. E. Abbe, A. S. Bandeira, A. Bracher, and A. Singer, "Decoding binary node labels from censored edge measurements: Phase transition and efficient recovery, " arXiv: 1404. 4749, 2014.
2. E. Abbe and A. Montanari, "Conditional random fields, planted constraint satisfaction and entropy concentration, " in Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. Springer, 2013, pp. 332-346.
3. S. Heimlicher, M. Lelarge, and L. Massoulíe, "Community detection in the labelled stochastic block model, " 09 2012. [Online]. Available: http: //arxiv. org/abs/1209. 2910
4. M. Lelarge, L. Massoulie, and J. Xu, "Reconstruction in the labeled stochastic block model, " in Information Theory Workshop (ITW), 2013 IEEE, Sept 2013, pp. 1-5.
5. N. Bansal, A. Blum, and S. Chawla, "Correlation clustering, " Machine Learning, vol. 56, no. 1-3, pp. 89-113, 2004.
6. A. Decelle, F. Krzakala, C. Moore, and L. Zdeborová, "Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications, " Phys. Rev. E, vol. 84, no. 6, p. 066106, 2011.
7. E. Mossel, J. Neeman, and A. Sly, "Stochastic block models and reconstruction, " arXiv preprint arXiv: 1202. 1499, 2012.
8. L. Massoulie, "Community detection thresholds and the weak ramanujan property, " arXiv preprint arXiv: 1311. 3085, 2013.
9. E. Mossel, J. Neeman, and A. Sly, "A proof of the block model threshold conjecture, " arXiv preprint arXiv: 1311. 4115, 2013.
10. F. Krzakala, C. Moore, E. Mossel, J. Neeman, A. Sly, L. Zdeborová, and P. Zhang, "Spectral redemption in clustering sparse networks, " Proceedings of the National Academy of Sciences, vol. 110, no. 52, pp. 20 935-20 940, 2013.
11. A. Saade, F. Krzakala, and L. Zdeborová, "Spectral clustering of graphs with the bethe hessian, " in Advances in Neural Information Processing Systems, 2014, pp. 406-414.
12. M. Mézard, M. A. Virasoro, and G. Parisi, Spin glass theory and beyond. World scientific, 1987.
13. F. Krzakala and L. Zdeborová, "Hiding quiet solutions in random constraint satisfaction problems, " Phys. Rev. Lett., vol. 102, p. 238701, 2009.
14. F. Krzakala, M.-C. Angelini, and F. Caltagirone, "Statistical physics of inference problems, " Lecture notes, http: //ipht. cea. fr/Docspht/articles/t14/045/public/notes. pdf, 2014.
15. H. Nishimori, "Internal energy, specific heat and correlation function of the bond-random ising model, " Progress of Theoretical Physics, vol. 66, no. 4, pp. 1169-1181, 1981.
16. L. Viana and A. J. Bray, "Phase diagrams for dilute spin glasses, " J. Phys. C: Solid State Physics, vol. 18, no. 15, p. 3037, 1985.
17. F. Guerra and F. L. Toninelli, "The high temperature region of the viana-bray diluted spin glass model, " Journal of statistical physics, vol. 115, no. 1-2, pp. 531-555, 2004.
18. P. Zhang, "Non-backtracking operator for ising model and its application in attractor neural networks, " arXiv: 1409. 3264, 2014.
19. J. Pearl, "Reverend bayes on inference engines: A distributed hierarchical approach, " in AAAI, 1982, pp. 133-136.
20. M. Mezard and A. Montanari, Information, physics, and computation. Oxford University Press, 2009.
21. A. Saade, F. Krzakala, and L. Zdeborová, "Spectral density of the non-backtracking operator on random graphs, " EPL, vol. 107, no. 5, p. 50005, 2014.
22. P. W. Holland, K. B. Laskey, and S. Leinhardt, "Stochastic blockmodels: First steps, " Social Networks, vol. 5, no. 2, p. 109, 1983.
23. C. Bordenave, M. Lelarge, and L. Massoulíe, "Non-backtracking spectrum of random graphs: community detection and non-regular ramanujan graphs, " arXiv, 2015.
24. H. Bass, "The ihara-selberg zeta function of a tree lattice, " International Journal of Mathematics, vol. 3, no. 06, pp. 717-797, 1992.
25. J. S. Yedidia, W. T. Freeman, and Y. Weiss, "Bethe free energy, kikuchi approximations, and belief propagation algorithms, " Advances in neural information processing systems, vol. 13, 2001.
26. M. Welling and Y. W. Teh, "Belief optimization for binary networks: A stable alternative to loopy belief propagation, " in Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence. Morgan Kaufmann Publishers Inc., 2001, pp. 554-561.