Approximate message passing with consistent parameter estimation and applications to sparse learning

Advances in Neural Information Processing Systems

Volumn 3, Issue , 2012, Pages 2438-2446

  Kamilov, Ulugbek S ^a   Rangan, Sundeep ^b   Fletcher, Alyson K ^c   Unser, Michael ^a  

^a EPFL   (Switzerland)

^b NEW YORK UNIVERSITY   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONALLY EFFICIENT; GAUSSIAN TRANSFORMS; LINEAR-NONLINEAR MODELS; MEASUREMENT CHANNELS; PARAMETER ESTIMATE; PARAMETER VALUES; RECONSTRUCTION QUALITY; STATE EVOLUTION EQUATIONS;

ALGORITHMS; DYNAMICAL SYSTEMS; PARAMETER ESTIMATION;

MATHEMATICAL TRANSFORMATIONS;

EID: 84877769740     PISSN: 10495258     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (26)

1. M. Tipping, "Sparse Bayesian learning and the relevance vector machine," J. Machine Learning Research, vol. 1, pp. 211-244, Sep. 2001.
2. M. West, "Bayesian factor regressionm models in the "large p, small n" paradigm," Bayesian Statistics, vol. 7, 2003.
3. D.Wipf and B. Rao, "Sparse Bayesian learning for basis selection," IEEE Trans. Signal Process., vol. 52, no. 8, pp. 2153-2164, Aug. 2004.
4. S. Ji, Y. Xue, and L. Carin, "Bayesian compressive sensing," IEEE Trans. Signal Process., vol. 56, pp. 2346-2356, Jun. 2008.
5. V. Cevher, "Learning with compressible priors," in Proc. NIPS, Vancouver, BC, Dec. 2009.
6. S. Billings and S. Fakhouri, "Identification of systems containing linear dynamic and static nonlinear elements," Automatica, vol. 18, no. 1, pp. 15-26, 1982.
7. I. W. Hunter and M. J. Korenberg, "The identification of nonlinear biological systems: Wiener and Hammerstein cascade models," Biological Cybernetics, vol. 55, no. 2-3, pp. 135-144, 1986.
8. O. Schwartz, J. W. Pillow, N. C. Rust, and E. P. Simoncelli, "Spike-triggered neural characterization," J. Vision, vol. 6, no. 4, pp. 484-507, Jul. 2006.
9. J. P. Vila and P. Schniter, "Expectation-maximization Bernoulli-Gaussian approximate message passing," in Conf. Rec. 45th Asilomar Conf. Signals, Syst. & Comput., Pacific Grove, CA, Nov. 2011, pp. 799-803.
10. - "Expectation-maximization Gaussian-mixture approximate message passing," in Proc. Conf. on Inform. Sci. & Sys., Princeton, NJ, Mar. 2012.
11. F. Krzakala, M. Mézard, F. Sausset, Y. Sun, and L. Zdeborová, "Statistical physics-based reconstruction in compressed sensing," arXiv:1109.4424, Sep. 2011.
12. - "Probabilistic reconstruction in compressed sensing: Algorithms, phase diagrams, and threshold achieving matrices," arXiv:1206.3953, Jun. 2012.
13. S. Rangan, A. K. Fletcher, V. K. Goyal, and P. Schniter, "Hybrid generalized approximation message passing with applications to structured sparsity," in Proc. IEEE Int. Symp. Inform. Theory, Cambridge, MA, Jul. 2012, pp. 1241-1245.
14. S. Rangan, "Generalized approximate message passing for estimation with random linear mixing," in Proc. IEEE Int. Symp. Inform. Theory, Saint Petersburg, Russia, Jul.-Aug. 2011, pp. 2174-2178.
15. D. Guo and C.-C. Wang, "Asymptotic mean-square optimality of belief propagation for sparse linear systems," in Proc. IEEE Inform. Theory Workshop, Chengdu, China, Oct. 2006, pp. 194-198.
16. - "Random sparse linear systems observed via arbitrary channels: A decoupling principle," in Proc. IEEE Int. Symp. Inform. Theory, Nice, France, Jun. 2007, pp. 946-950.
17. S. Rangan, "Estimation with random linear mixing, belief propagation and compressed sensing," in Proc. Conf. on Inform. Sci. & Sys., Princeton, NJ, Mar. 2010, pp. 1-6.
18. M. Bayati and A. Montanari, "The dynamics of message passing on dense graphs, with applications to compressed sensing," IEEE Trans. Inform. Theory, vol. 57, no. 2, pp. 764-785, Feb. 2011.
19. U. S. Kamilov, S. Rangan, A. K. Fletcher, and M. Unser, "Approximate message passing with consistent parameter estimation and applications to sparse learning," arXiv:1207.3859 [cs.IT], Jul. 2012.
20. J. Boutros and G. Caire, "Iterative multiuser joint decoding: Unified framework and asymptotic analysis,"IEEE Trans. Inform. Theory, vol. 48, no. 7, pp. 1772-1793, Jul. 2002.
21. T. Tanaka and M. Okada, "Approximate belief propagation, density evolution, and neurodynamics for CDMA multiuser detection," IEEE Trans. Inform. Theory, vol. 51, no. 2, pp. 700-706, Feb. 2005.
22. D. L. Donoho, A. Maleki, and A. Montanari, "Message-passing algorithms for compressed sensing," Proc. Nat. Acad. Sci., vol. 106, no. 45, pp. 18 914-18 919, Nov. 2009.
23. T. P. Minka, "A family of algorithms for approximate Bayesian inference," Ph.D. dissertation, Massachusetts Institute of Technology, Cambridge, MA, 2001.
24. M. Seeger, "Bayesian inference and optimal design for the sparse linear model," J. Machine Learning Research, vol. 9, pp. 759-813, Sep. 2008.
25. E. J. Candés and T. Tao, "Near-optimal signal recovery from random projections: Universal encoding strategies?" IEEE Trans. Inform. Theory, vol. 52, no. 12, pp. 5406-5425, Dec. 2006.
26. D. Donoho, I. Johnstone, A. Maleki, and A. Montanari, "Compressed sensing over ℓp-balls: Minimax mean square error," in Proc. ISIT, St. Petersburg, Russia, Jun. 2011.