A group VISA algorithm for variable selection

Statistical Methods and Applications

Volumn 24, Issue 1, 2015, Pages 41-60

  Mkhadri, Abdallah ^a   Ouhourane, Mohamed ^a  

^a CADI AYYAD UNIVERSITY   (Morocco)

Author keywords

Group variable selection; Grouped Lars; Linear regression; VISA

Indexed keywords

EID: 85027938740     PISSN: 16182510     EISSN: 1613981X     Source Type: Journal    
DOI: 10.1007/s10260-014-0281-8     Document Type: Article

References (32)

1. Bach P (2008) Consistency of the group Lasso and multiple kernel learning. J Mach Learn Res 9:1179–1225
2. Bakin S (1999) Adaptive regression and variable selection in data mining problems. Ph. D. thesis, Australian National University, Canberra
3. Bühlmann P, van De Geer S (2011) Statistics for high dimensional data: methods, theory and applications. Springer, Berlin
4. Breheny P, Huang J (2014) Group descent algorithms for nonconvex penalized linear and logistic regression models with grouped predictors. Stat Comput. doi:10.1007/s11222-013-9424-2
5. Candes E, Tao T (2007) The Dantzig selector: statistical estimation when p is much large than n. Ann Stat 35:2313–2351
6. Duarte M, Bajwa W, Calderbank R (2011) The performance of group Lasso linear regression of grouped variables. Technical Report TR-2010-10, Department of Computer Sciences, Duck University
7. Efron B, Hastie T, Johnstone I, Tibshirani R (2004) Least angle regression. Ann Stat 32:407–499
8. Fan J, Li R (2001) Variable selection via nonconcave penalized likelihood and its oracle properties. J Am Stat Assoc 96:1348–1360
9. Friedman J, Hastie T, Tibshirani (2010) A note on the group lasso and a sparse group lasso. Preprint
10. Forgel R, Drton M (2010) Exact block-wise optimization in group Lasso for linear regression. Arxiv preprint
11. Grandvalet Y, Canu S (1999) Outcomes of the equivalence of adaptive ridge with least absolute shrinkage. In: Advances in neural information processing systems 11 (NIPS 1998), pp 445–451
12. Jacob L, Obozinski G, Vert J (2009) Group Lasso with overlap and graph Lasso. In: Proceedings of the 26th annual international conference on machine learning, pp 433–440
13. Huang J, Ma S, Xie H, Zhang C-H (2009) A group bridge approach for variable selection. Biometrika 96:339–355
14. Lin Y, Zhang HH (2003) Component selection and smoothing in smoothing spline analysis of variance models. Technical Report 1072. Department of Statistics, University of Wisconsin, Madison
15. Liu H, Zhang J, Jiang X, Liu J (2010) The group Dantzig selector. J Mach Learn Res Proc Track 9:461–468
16. Lounici K, Pontil M, van de Geer S, Tsybakov A (2011) Oracle inequalities and optimal inference under group sparsity. Ann Stat 39:2164–2204
17. Meier L, van De Geer S (2008) The group for logistic regression. J R Stat Soc Ser B 70:53–71
18. Meinshausen N (2007) Relaxed lasso. Comput Stat Data Anal 52:374–393
19. Meinshausen P, Bühlmann P (2006) High-dimensional graphs and variable selection with the Lasso. Ann Stat 34:1049–1579
20. Mkhadri A, Ouhourane M (2013) An extended variable inclusion and shrinkage algorithm for correlated variables. Comput Stat Data Anal 57:631–644
21. Nardi Y, Rinaldo A (2008) On the asymptotic properties of the group Lasso estimator for linear models. Electron J Stat 2:605–633
22. Negahban S, Ravikumar P, Wainwrigt M, Yu B (2012) A unified framework for high-dimensional analysis of M-estimators with decomposable regularizers. Stat Sci 27:538–557
23. Park M, Hastie T (2007) An ℓ1 regularization path algorithm for generalized linear models. J R Stat Soc Ser B 69:659–677
24. Radchenko P, James GM (2008) Variable inclusion and shrinkage algorithms. J Am Stat Assoc 103(483):1304–1315
25. Ravikumar P, Liu H, Lafferty J, Wasserman L (2007) Spam: Sparse additive models. Adv Neural Inf Process Syst 20:1201–1208
26. Roth V, Fisher B (2008) The group-Lasso for generalized linear model: uniqueness of solutions and efficient algorithms. In: ICML08: proceedings of 25th international conference on machine learning
27. She Y (2012) An iterative algorithm for fitting nonconvex penalized generalized linear models with grouped predictors. Comput Stat Data Anal 56(10):2976–2990
28. Tibshirani R (1996) Regression shrinkage and selection via the Lasso. J R Stat Soc B 58:267–288
29. Wei F, Zhu H (2012) Group coordinate descent algorithms for nonconvex penalized regression. Comput Stat Data Anal 56:316–326
30. Yuan M, Lin Y (2006) Model selection and estimation in regression with grouped variables. J R Stat Soc Ser B 68:49–67
31. Zhang CH (2010) Nearly unbiased variable selection under minimax concave penalty. Annals Stat 38(2):894–942
32. Zou H, Hastie T (2005) Regularization and variable selection via the elastic-net. J R Stat Soc Ser B 67:301–320