A multi-stage framework for dantzig selector and LASSO

Journal of Machine Learning Research

Volumn 13, Issue , 2012, Pages 1189-1219

  Liu, Ji ^a   Wonka, Peter ^a   Ye, Jieping ^a  

^a ARIZONA STATE UNIVERSITY   (United States)

Author keywords

Dantzig selector; LASSO; Multi stage; Sparse signal recovery

Indexed keywords

DANTZIG SELECTOR; DESIGN MATRIX; ESTIMATION BOUNDS; HIGH PROBABILITY; LASSO; MULTI-STAGE; NOISE VECTORS; NOISY OBSERVATIONS; NONZERO ENTRIES; OBSERVATION VECTORS; PARAMETER VECTORS; SPARSE SIGNALS; TARGET SIGNALS;

ALGORITHMS; CESIUM; PROBABILITY; SIGNAL RECONSTRUCTION;

VECTORS;

EID: 84860682231     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Article

References (31)

1. P. J. Bickel, Y. Ritov, and A. B. Tsybakov. Simultaneous analysis of Lasso and Dantzig selector. Annals of Statistics, 37(4):1705-1732, 2009.
2. F. Bunea, A. Tsybakov, and M. Wegkamp. Sparsity oracle inequalities for the Lasso. Electronic Journal of Statistics, 1:169-194, 2007.
3. T. Cai and L.Wang. Orthogonal matching pursuit for sparse signal recovery. IEEE Transactions on Information Theory, 57(7):4680-4688, 2011.
4. T. Cai, G. Xu, and J. Zhang. On recovery of sparse signals via 1 minimization. IEEE Transactions on Information Theory, 55(7):3388-3397, 2009.
5. E. J. Candès and Y. Plan. Near-ideal model selection by 1 minimization. Annals of Statistics, 37 (5A):2145-2177, 2009.
6. E. J. Candès and T. Tao. Decoding by linear programming. IEEE Transactions on Information Theory, 51(12):4203-4215, 2005. (Pubitemid 41800353)
7. E. J. Candès and T. Tao. The Dantzig selector: Statistical estimation when p is much larger than n. Annals of Statistics, 35(6):2313-2351, 2007.
8. D. L. Donoho, M. Elad, and V. N. Temlyakov. Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Transactions on Information Theory, 52(1):6-18, 2006. (Pubitemid 43263116)
9. J. Fan and J. Lv. A selective overview of variable selection in high dimensional feature space. (invited review article) Statistica Sinica, 20:101-148, 2010.
10. J. Fan and J. Lv. Nonconcave penalized likelihood with np-dimensionality. IEEE Transactions on Information Theory, 57(8):5467-5484, 2011.
11. G. M. James, P. Radchenko, and J. Lv. DASSO: connections between the Dantzig selector and Lasso. Journal of The Royal Statistical Society Series B, 71(1):127-142, 2009.
12. V. Koltchinskii and M. Yuan. Sparse recovery in large ensembles of kernel machines on-line learning and bandits. In Proceedings of the Twenty-First Annual Conference on Learning Theory (COLT), pages 229-238, Helsinki, Finland, 2008.
13. K. Lounici. Sup-norm convergence rate and sign concentration property of Lasso and Dantzig estimators. Electronic Journal of Statistics, 2:90-102, 2008.
14. J. Lv and Y. Fan. A unified approach to model selection and sparse recovery using regularized least squares. Annals of Statistics, 37(6A):3498-3528, 2009.
15. N. Meinshausen, P. Bhlmann, and E. Zrich. High dimensional graphs and variable selection with the Lasso. Annals of Statistics, 34(3):1436-1462, 2006. (Pubitemid 44231168)
16. P. Ravikumar, G. Raskutti, M. J. Wainwright, and B. Yu. Model selection in gaussian graphical models: High-dimensional consistency of 1-regularized MLE. In Proceedings of the Twenty- Second Annual Conference on Neural Information Processing Systems (NIPS), pages 1329-1336, Vancouver, British Columbia, Canada, 2008.
17. J. Romberg. The Dantzig selector and generalized thresholding. In Proceedings of the Forty-Second Annual Conference on Information Sciences and Systems (CISS), pages 22-25, Princeton, New Jersey, USA, 2008.
18. R. Tibshirani. Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society: Series B, 58(1):267-288, 1996.
19. J. A. Tropp. Greed is good: Algorithmic results for sparse approximation. IEEE Transactions on Information Theory, 50(10):2231-2242, 2004.
20. M. J. Wainwright. Sharp thresholds for high-dimensional and noisy sparsity recovery using 1- constrained quadratic programming (Lasso). IEEE Transactions on Information Theory, 55(5): 2183-2202, 2009.
21. C.-H. Zhang. Nearly unbiased variable selection under minimax concave penalty. Annals of Statistics, 38(2):894-942, 2010a.
22. C.-H. Zhang and T. Zhang. A general theory of concave regularization for high dimensional sparse estimation problems. Technical report, Department of Statistics, Rutgers University, Piscataway, New Jersey, USA, 2012.
23. T. Zhang. Some sharp performance bounds for least squares regression with 1 regularization. Annals of Statistics, 37(5A):2109-2114, 2009a.
24. T. Zhang. On the consistency of feature selection using greedy least squares regression. Journal of Machine Learning Research, 10:555-568, 2009b.
25. T. Zhang. Analysis of multi-stage convex relaxation for sparse regularization. Journal of Machine Learning Research, 11:1081-1107, 2010b.
26. T. Zhang. Sparse recovery with orthogonal matching pursuit under RIP. IEEE Transactions on Information Theory, 57(9):5215-6221, 2011a.
27. T. Zhang. Adaptive forward-backward greedy algorithm for learning sparse representations. IEEE Transactions on Information Theory, 57(7):4689-4708, 2011b.
28. T. Zhang. Multi-stage convex relaxation for feature selection. Technical report, Department of Statistics, Rutgers University, Piscataway, New Jersey, USA, 2011c.
29. P. Zhao and B. Yu. On model selection consistency of Lasso. Journal of Machine Learning Research, 7:2541-2563, 2006. (Pubitemid 44866738)
30. S. Zhou. Thresholding procedures for high dimensional variable selection and statistical estimation. In Proceedings of the Twenty-Third Annual Conference on Neural Information Processing Systems (NIPS), pages 2304-2312, Vancouver, British Columbia, Canada, 2009.
31. H. Zou. The adaptive Lasso and its oracle properties. Journal of the American Statistical Association, 101(476):1418-1429, 2006.