Robust Lasso with missing and grossly corrupted observations

Advances in Neural Information Processing Systems 24: 25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011

Volumn , Issue , 2011, Pages

  Nguyen, Nam H ^a   Nasrabadi, Nasser M ^b   Tran, Trac D ^a  

^a JOHNS HOPKINS UNIVERSITY   (United States)

^b U S ARMY RESEARCH LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CRIME; RECOVERY;

BOUNDED NOISE; DESIGN MATRIX; ERROR VECTOR; LINEAR MEASUREMENTS; NONZERO ENTRIES; OPTIMISATIONS; PRIOR INFORMATION; SPARSE ERRORS; SPARSE PRIOR; SPARSE VECTORS;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 85162357937     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (23)

1. A. Agarwal, S. Negahban, and M. Wainwright. Noisy matrix decomposition via convex relaxation: Optimal rates in high dimensions. Proc. 28th Inter. Conf. Mach. Learn. (ICML-11), pages 1129-1136, 2011.
2. P. Bickel, Y. Ritov, and A. Tsybakov. Simultaneous analysis of Lasso and Dantzig selector. Annals of statistics, 37(4):1705-1732, 2009.
3. E. J. Candès, X. Li, Y. Ma, and J. Wright. Robust principal component analysis? Submitted for publication, 2009.
4. E. J. Candès and Y. Plan. Near-ideal model selection by l1 minimization. Annals of Statistics, 37:2145-2177, 2009.
5. 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.
6. E. Elhamifar and R. Vidal. Sparse subspace clustering. IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 2790-2797, 2009.
7. J. N. Laska, M. A. Davenport, and R. G. Baraniuk. Exact signal recovery from sparsely corrupted measurements through the pursuit of justice. In Asilomar conference on Signals, Systems and Computers, pages 1556-1560, 2009.
8. X. Li. Compressed sensing and matrix completion with constant proportion of corruptions. Preprint, 2011.
9. Z. Li, F.Wu, and J. Wright. On the systematic measurement matrix for compressed sensing in the presence of gross error. In Data compression conference (DCC), pages 356-365, 2010.
10. N. Meinshausen and P. Buehlmann. High dimensional graphs and variable selection with the lasso. Annals of statistics, 34(3):1436-1462, 2008.
11. N. Meinshausen and B. Yu. Lasso-type recovery of sparse representations for high-dimensional data. Annals of statistics, 37(1):2246-2270, 2009.
12. S. Negahban, P. Ravikumar, M. J. Wainwright, and B. Yu. A unified framework for high-dimensional analysis of m-estimators with decomposable regularizers. Preprint, 2010.
13. N. H. Nguyen and Trac. D. Tran. Exact recoverability from dense corrupted observations via l1 minimization. preprint, 2010.
14. G. Raskutti, M. J.Wainwright, and B. Yu. Restricted eigenvalue properties for correlated gaussian designs. Journal of Machine Learning Research, 11:2241-2259, 2010.
15. R. Tibshirani. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B, 58(1):267-288, 1996.
16. S. A. van de Geer and P. Buehlmann. On the conditions used to prove oracle results for the lasso. Electronic Journal of Statistics, 3(1360-1392), 2009.
17. M. J.Wainwright. Sharp thresholds for high-dimensional and noisy sparsity recovery using l1 -constrained quadratic programming ( lasso ). IEEE Trans. Information Theory, 55(5):2183-2202, 2009.
18. J. Wright and Y. Ma. Dense error correction via l1 minimization. IEEE Transaction on Information Theory, 56(7):3540-3560, 2010.
19. J. Wright, A. Y. Yang, A. Ganesh, S. S. Sastry, and Y. Ma. Robust face recognition via sparse representation. IEEE Transaction on Pattern Analysis and Machine Intelligence, 31(2):210-227, 2009.
20. H. Xu, C. Caramanis, and S. Sanghavi. Robust pca via outlier pursuit. Ad. Neural Infor. Proc. Sys. (NIPS), pages 2496-2504, 2010.
21. M. Yuan and Y. Lin. Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society: Series B, 68(1):49-67, 2006.
22. T. Zhang. Some sharp performance bounds for least squares regression with l1 regularization. Annals of statistics, 37(5):2109-2144, 2009.
23. P. Zhao and B. Yu. On model selection consistency of Lasso. The Journal of Machine Learning Research, 7:2541-2563, 2006.