The group Dantzig selector

Journal of Machine Learning Research

Volumn 9, Issue , 2010, Pages 461-468

  Liu, Han ^a   Zhang, Jian ^b   Jiang, Xiaoye ^c   Liu, Jun ^d  

^a Carnegie Mellon University   (United States)

^b PURDUE UNIVERSITY   (United States)

^c STANFORD UNIVERSITY   (United States)

^d Arizona State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BASIS PURSUITS; DANTZIG SELECTOR; GROUP STRUCTURE; HIGH-DIMENSIONAL; MACHINE LEARNING COMMUNITIES; NON-ASYMPTOTIC; NUMERICAL RESULTS; SPARSE REGRESSION;

ARTIFICIAL INTELLIGENCE;

GROUP THEORY;

EID: 84860608028     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (18)

1. F. Bach. Consistency of the group lasso and multiple kernel learning. Journal of Machine Learning Research, 8: 1179-1225, 2008.
2. T. Cai, L. Wang, and G. Xu. Shifting inequality and recovery of sparse signals. Technical report, University of Pennsylvania, 2009.
3. E. Candes and T. Tao. The dantzig selector: statistical estimation when p is much larger than n. The Annals of Statistics, 35:2313-2351, 2007.
4. E. J. Candes and T. Tao. Decoding by linear programming. Information Theory, IEEE Transactions on, 51 (12):4203-4215, 2005.
5. S. S. Chen, D. L. Donoho, and M. A. Saunders. Atomic decomposition by basis pursuit. SIAM Journal on Scientific and Statistical Computing, 20:33-61, 1998.
6. C. Chesneau and M. Hebiri. Some theoretical results on the grouped variables lasso. Mathematical Methods of Statistics, 27(4):317-326, 2008.
7. J. Huang and T. Zhang. The benefit of group sparsity,. Technical report, Rutgers University, 2009.
8. 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.
9. H. Liu and J. Zhang. On the estimation consistency of the group lasso and its applications. Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics, 2009.
10. K. Lounici, M. Pontil, A. B. Tsybakov, and S. van de Geer. Taking advantage of sparsity in multi-task learning. Proceedings of the Annual Conference on Learning Theory (COLT 2009), 2009.
11. L. Meier, S. van de Geer, and P. Bühlmann. The group lasso for logistic regression. Journal of the Royal Statistical Society, Series B, Methodological, 70:53-71, 2007.
12. N. Meinshausen, G. Rocha, and B. Yu. Discussion: A tale of three cousins: Lasso, l2boosting and dantzig. The Annals of Statistics, 35:2373-2384, 2007.
13. Y. Nardi and A. Rinaldo. On the asymptotic properties of the group lasso estimator for linear models. Electronic Journal of Statistics, 2:605-633, 2008.
14. G. Obozinski and M. Wainwright. Union support recovery in high-dimensional multivariate regression. In Advances in Neural Information Processing Systems 21, 2008.
15. P. Ravikumar, H. Liu, J. Lafferty, and L. Wasserman. Spam: Sparse additive models. In Advances in Neural Information Processing Systems 20, 2007.
16. R. Tibshirani. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society, Series B, Methodological, 58:267-288, 1996.
17. M. Yuan and Y. Lin. Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society, Series B, Methodological, 68:49-67, 2006.
18. P. Zhao and B. Yu. On model selection consistency of lasso. J. of Mach. Learn. Res., 7:2541-2567, 2007.