Fast global convergence of gradient methods for high-dimensional statistical recovery

Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010

Volumn , Issue , 2010, Pages

  Agarwal, Alekh ^a   Negahban, Sahand N ^a   Wainwright, Martin J ^a,b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTATION THEORY; COMPUTATIONAL METHODS; CONVEX OPTIMIZATION; STATISTICS;

CONDITION; CONVEX OPTIMIZATION PROBLEMS; GLOBAL CONVER-GENCE; GRADIENT'S METHODS; HIGH-DIMENSIONAL; HIGHER-DIMENSIONAL; M-ESTIMATORS; STATISTIC MODELING; STATISTICAL PRECISION; WEIGHTED SUM;

GRADIENT METHODS;

EID: 85162018878     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (19)

1. A. Beck and M. Teboulle. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences, 2(1):183-202, 2009.
2. S. Becker, J. Bobin, and E. J. Candes. Nesta: a fast and accurate first-order method for sparse recovery. Technical report, Stanford University, 2009.
3. K. Bredies and D. A. Lorenz. Linear convergence of iterative soft-thresholding. Journal of Fourier Analysis and Applications, 14:813-837, 2008.
4. R. Garg and R. Khandekar. Gradient descent with sparsification: an iterative algorithm for sparse recovery with restricted isometry property. In ICML, New York, NY, USA, 2009. ACM.
5. E. T. Hale, Y. Wotao, and Y. Zhang. Fixed-point continuation for ℓ1-minimization: Methodology and convergence. SIAM J. on Optimization, 19(3):1107-1130, 2008.
6. S. Ji and J. Ye. An accelerated gradient method for trace norm minimization. In International Conference on Machine Learning, New York, NY, USA, 2009. ACM.
7. Z. Lin, A. Ganesh, J. Wright, L. Wu, M. Chen, and Y. Ma. Fast convex optimization algorithms for exact recovery of a corrupted low-rank matrix. Technical Report UILU- ENG-09-2214, Univ. Illinois, Urbana-Champaign, July 2009.
8. S. Negahban, P. Ravikumar, M. J. Wainwright, and B. Yu. A unified framework for high-dimensional analysis of M-estimators with decomposable regularizers. In NIPS Conference, Vancouver, Canada, December 2009. Full length version arxiv:1010.2731v1.
9. S. Negahban and M. J. Wainwright. Restricted strong convexity and (weighted) matrix completion: Optimal bounds with noise. Technical report, UC Berkeley, August 2010. arxiv:1009.2118.
10. S. Negahban and M. J. Wainwright. Estimation of (near) low-rank matrices with noise and high-dimensional scaling. Annals of Statistics, To appear. Originally posted as arxiv:0912.5100.
11. Y. Nesterov. Introductory Lectures on Convex Optimization. Kluwer Academic Pub- lishers, New York, 2004.
12. Y. Nesterov. Gradient methods for minimizing composite objective function. Techni- cal Report 76, Center for Operations Research and Econometrics (CORE), Catholic University of Louvain (UCL), 2007.
13. q-balls. Technical Report arXiv:0910.2042, UC Berkeley, Department of Statistics, 2009.
14. G. Raskutti, M. J. Wainwright, and B. Yu. Restricted eigenvalue conditions for corre- lated Gaussian designs. Journal of Machine Learning Research, 11:2241-2259, August 2010.
15. B. Recht. A simpler approach to matrix completion. Journal of Machine Learning Research, 2010. Posted as arXiv:0910.0651v2.
16. B. Recht, M. Fazel, and P. Parrilo. Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. SIAM Review, Vol 52(3):471-501, 2010.
17. A. Rohde and A. Tsybakov. Estimation of high-dimensional low-rank matrices. Tech- nical Report arXiv:0912.5338v2, Universite de Paris, January 2010.
18. J. A. Tropp and A. C. Gilbert. Signal recovery from random measurements via orthog- onal matching pursuit. IEEE Transactions on Information Theory, 53(12):4655-4666, December 2007.
19. M. Yuan, A. Ekici, Z. Lu, and R. Monteiro. Dimension reduction and coefficient estimation in multivariate linear regression. Journal Of The Royal Statistical Society Series B, 69(3):329-346, 2007.