Cramér-rao-type bounds for sparse bayesian learning

IEEE Transactions on Signal Processing

Volumn 61, Issue 3, 2013, Pages 622-632

  Prasad, Ranjitha ^a   Murthy, Chandra R ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

Cram r Rao lower bounds; Expectation maximization; Mean square error; Sparse Bayesian learning

Indexed keywords

EXPECTATION - MAXIMIZATIONS; EXPECTATION-MAXIMIZATION ALGORITHMS; GENERALIZED PARETO DISTRIBUTIONS; LOWER BOUNDS; MULTIPLE MEASUREMENT VECTORS; PRIOR DISTRIBUTION; SPARSE BAYESIAN LEARNING; SPARSE BAYESIAN LEARNING (SBL);

ALGORITHMS; COMPRESSIBILITY; ESTIMATION; MAXIMUM PRINCIPLE; VECTORS;

MEAN SQUARE ERROR;

EID: 84897688433     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2012.2226165     Document Type: Article

References (26)

1. D. Needell and J. Tropp, "Cosamp: Iterative signal recovery from incomplete and inaccurate samples," Appl. Comput. Harmon. Anal., vol. 26, no. 3, pp. 301-321, 2009.
2. V. Cevher, "Learning with compressible priors," in Proc. Adv. NIPS, pp. 7-12.
3. R. Gribonval, V. Cevher, and M. Davies, "Compressible priors for high-dimensional statistics," IEEE Trans. Inf. Theory, vol. 58, no. 8, pp. 5016-5034, 2012.
4. M. E. Tipping, "Sparse Bayesian learning and the relevance vector machine," J. Mach. Learn. Res., vol. 1, pp. 211-214, 2001.
5. M. Tipping and A. Faul, "Fast marginal likelihood maximisation for sparse Bayesian models," in Proc. 9th Int. Workshop Artif. Intell. Statist., 2003, vol. 1, pp. 3-6.
6. D. Wipf and S. Nagarajan, "A new view of automatic relevance determination," Adv. NIPS, vol. 20, pp. 1625-1632, 2008.
7. D.Wipf and S. Nagarajan, "Iterative reweighted and methods for finding sparse solutions," Proc. Signal Process. Adapt. Sparse Structured Representations (SPARS), 2009.
8. O. Williams, A. Blake, and R. Cipolla, "Sparse Bayesian learning for efficient visual tracking," IEEE Trans. Pattern Anal. Mach. Intell., vol. 27, no. 8, pp. 1292-1304, 2005. (Pubitemid 41245058)
9. O.Williams, A. Blake, and R. Cipolla, "A sparse probabilistic learning algorithm for real-time tracking," in Proc. 9th Int. Conf. Comput. Vis., 2003, pp. 353-360.
10. D. Wipf, J. Owen, H. Attias, K. Sekihara, and S. Nagarajan, "Robust Bayesian estimation of the location, orientation, and time course of multiple correlated neural sources using MEG," NeuroImage, vol. 49, no. 1, pp. 641-655, 2010.
11. D. Wipf and S. Nagarajan, "Beamforming using the relevance vector machine," inProc. 24th Int. Conf.Mach. Learn., 2007, pp. 1023-1030.
12. R. Prasad and C. R. Murthy, "Bayesian learning for joint sparse OFDM channel estimation and data detection," in Proc. IEEE Global Telecommun. Conf. (GLOBECOM), Dec. 2010, pp. 1-6.
13. B. Babadi, N. Kalouptsidis, and V. Tarokh, "Asymptotic achievability of the Cramér-Rao bound for noisy compressive sampling," IEEE Trans. Signal Process., vol. 57, no. 3, pp. 1233-1236, 2009.
14. Z. Ben-Haim and Y. Eldar, "The Cramér-Rao bound for estimating a sparse parameter vector," IEEE Trans. Signal Process., vol. 58, no. 6, pp. 3384-3389, 2010.
15. R. Niazadeh,M. Babaie-Zadeh, and C. Jutten, "On the achievability of Cramér-Rao bound in noisy compressed sensing," IEEE Trans. Signal Process., vol. 60, no. 1, pp. 518-526, 2012.
16. J. Helferty and D. Mmiscudgett, "Optimal observer trajectories for bearings only tracking by minimizing the trace of the Cramér-Rao lower bound," in Proc. 32nd Conf. Decision Control, 1993, pp. 936-939.
17. D. P. Wipf and B. D. Rao, "Sparse Bayesian learning for basis selection," IEEE Trans. Signal Process., vol. 52, no. 8, pp. 2153-2164, 2004.
18. D. Wipf and B. Rao, "An empirical Bayesian strategy for solving the simultaneous sparse approximation problem," IEEE Trans. Signal Process., vol. 55, no. 7, pp. 3704-3716, 2007. (Pubitemid 47018850)
19. S. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Englewood Cliffs, NJ: Prentice-Hall, 1993.
20. H. V. Trees, Detection, Estimation, and Modulation Theory -Part I. New York: Wiley, 1968, vol. 2.
21. Y. Rockah and P. Schultheiss, "Array shape calibration using sources in unknown locations-Part I: Far-field sources," IEEE Trans. Acoust., Speech, Signal Process., vol. 35, no. 3, pp. 286-299, 1987. (Pubitemid 17549173)
22. J. Dauwels, "on graphical models for communications and machine learning: Algorithms, bounds, and analog implementation," Ph.D. dissertation, Swiss Federal Inst. Technol., Zürich, Switzerland, 2005.
23. D. Wipf, J. Palmer, and B. Rao, "Perspectives on sparse Bayesian learning," Adv. NIPS, vol. 16, p. 249, 2004.
24. A. Armagan, D. Dunson, and J. Lee, "Generalized double Pareto shrinkage," Arxiv preprint arXiv:1104.0861, Aug. 2011 [Online]. Available: http://arxiv.org/abs/1104.0861
25. S. Balakrishnan and D. Madigan, "Priors on the variance in sparse Bayesian learning; The Demi-Bayesian Lasso," 2009 [Online]. Available: http://www.stat.columbia.edu/~madigan/PAPERS/recent-Papers.html
26. K. Petersen and M. Pedersen, The Matrix Cookbook, 2008 [Online]. Available: http://matrixcookbook.com