Analysis of multi-stage convex relaxation for sparse regularization

Journal of Machine Learning Research

Volumn 11, Issue , 2010, Pages 1081-1107

  Zhang, Tong ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

Convex relaxation; Multi stage convex relaxation; Non convex optimization; Sparsity

Indexed keywords

CONVEX RELAXATION; GLOBAL SOLUTIONS; GRADIENT DESCENT; LEARNING FORMULATION; LOCAL MINIMUMS; LOCAL SOLUTION; MULTI-STAGE; NON-CONVEX OBJECTIVE FUNCTIONS; NONCONVEX OPTIMIZATION; REGULARIZARON; RELAXATION SCHEMES; SUBOPTIMAL SOLUTION; THEORY AND PRACTICE;

CONVEX OPTIMIZATION; HEURISTIC METHODS; OPTIMIZATION; PROBLEM SOLVING;

RELAXATION PROCESSES;

EID: 77951191949     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. Andreas Argyriou, Charles A. Micchelli, Massimiliano Pontil, and Yiming Ying. A spectral regularization framework for multi-task structure learning. In NIPS'07, 2008.
2. Peter L. Bartlett, Michael I. Jordan, and Jon D. McAuliffe. Convexity, classification, and risk bounds. Journal of the American Statistical Association, 101(473):138-156, 2006.
3. Peter Bickel, Yaacov Ritov, and Alexandre Tsybakov. Simultaneous analysis of Lasso and Dantzig selector. Annals of Statistics, 37(4): 1705-1732, 2009.
4. Florentina Bunea, Alexandre Tsybakov, and Marten H. Wegkamp. Sparsity oracle inequalities for the Lasso. Electronic Journal of Statistics, 1:169-194, 2007.
5. Emmanuel J. Candes and Terence Tao. Decoding by linear programming. IEEE Trans, on Information Theory, 51:4203-4215, 2005.
6. 1 minimization. Journal of Fourier Analysis and Applications, 14(5): 877-905, 2008.
7. Runze Li Jianqing Fan. Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association, 96:1348-1360, 2001.
8. Vladimir Koltchinskii. Sparsity in penalized empirical risk minimization. Annales de l'Institut Henri Poincaré, 2008.
9. Gilles Pisier. The Volume of Convex Bodies and Banach Space Geometry. Cambridge University Press, 1989.
10. R. Tyrrell Rockafellar. Convex Analysis. Princeton University Press, Princeton, NJ, 1970.
11. Alan L. Yuille and Anand Rangarajan. The concave-convex procedure. Neural Computation, 15: 915-936, 2003.
12. Cun-Hui Zhang. Nearly unbiased variable selection under minimax concave penalty. The Annals of Statistics, 2010. to appear.
13. Cun-Hui Zhang and Jian Huang. The sparsity and bias of the Lasso selection in high-dimensional linear regression. Annals of Statistics, 36(4): 1567-1594, 2008.
14. Tong Zhang. Statistical behavior and consistency of classification methods based on convex risk minimization. The Annals of Statistics, 32:56-85, 2004. with discussion.
15. 1 regularization. Ann. Statist., 31(5A):2109-2144, 2009a. ISSN 0090-5364. doi: 10.1214/08-AOS659.
16. Tong Zhang. Adaptive forward-backward greedy algorithm for sparse learning with linear models. In NIPS'08, 2009b.
17. Peng Zhao and Bin Yu. On model selection consistency of Lasso. Journal of Machine Learning Research, 7:2541-2567, 2006.
18. Hui Zou. The adaptive lasso and its oracle properties. Journal of the American Statistical Association, 101:1418-1429, 2006.
19. Hui Zou and Runze Li. One-step sparse estimates in nonconcave penalized likelihood models. Annals of Statistics, 36(4): 1509-1533, 2008.