A. Agarwal, S. Negahban, and M. J. Wainwright, Noisy matrix decomposition via convex relaxation: Optimal rates in high dimensions, The Annals of Statistics, vol.40, issue.2, 2011.
DOI : 10.1214/12-AOS1000SUPP

F. Bach, Consistency of the group lasso and multiple kernel learning, J. Mach. Learn. Res, vol.9, pp.1179-1225, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00164735

F. Bach, Exploring large feature spaces with hierarchical multiple kernel learning, Adv. Neural. Inform. Process Syst, pp.105-112, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00319660

F. Bach, Structured sparsity-inducing norms through submodular functions
URL : https://hal.archives-ouvertes.fr/hal-00511310

F. Bach, R. Jenatton, J. Mairal, and G. Obozinski, Optimization with sparsityinducing penalties
URL : https://hal.archives-ouvertes.fr/hal-00613125

F. R. Bach, Bolasso, Proceedings of the 25th international conference on Machine learning, ICML '08, pp.33-40, 2008.
DOI : 10.1145/1390156.1390161

URL : https://hal.archives-ouvertes.fr/hal-00271289

F. R. Bach, G. R. Lanckriet, and M. I. Jordan, Multiple kernel learning, conic duality, and the SMO algorithm, Twenty-first international conference on Machine learning , ICML '04, 2004.
DOI : 10.1145/1015330.1015424

R. G. Baraniuk, V. Cevher, M. F. Duarte, and C. Hegde, Model-based compressive sensing. Information Theory, IEEE Transactions on, vol.56, issue.4, pp.1982-2001, 2010.

C. Berge, Espaces topologiques et fonctions multivoques, 1959.

P. J. Bickel, Y. Ritov, and A. Tsybakov, Simultaneous analysis of Lasso and Dantzig selector, The Annals of Statistics, vol.37, issue.4, pp.1705-1732, 2009.
DOI : 10.1214/08-AOS620

URL : https://hal.archives-ouvertes.fr/hal-00401585

K. C. Border, Fixed point theorems with applications to economics and game theory, 1985.
DOI : 10.1017/CBO9780511625756

E. J. Candes, X. Li, Y. Ma, and J. Wright, Robust principal component analysis?, Journal of the ACM, vol.58, issue.3, pp.1-37, 2009.
DOI : 10.1145/1970392.1970395

V. Chandrasekaran, B. Recht, P. A. Parrilo, and A. S. Willsky, The Convex Geometry of Linear Inverse Problems, Foundations of Computational Mathematics, vol.1, issue.10, 2010.
DOI : 10.1007/s10208-012-9135-7

S. S. Chen, D. L. Donoho, and M. Saunders, Atomic Decomposition by Basis Pursuit, SIAM Journal on Scientific Computing, vol.20, issue.1, pp.33-61, 1998.
DOI : 10.1137/S1064827596304010

Y. Chen, H. Xu, C. Caramanis, and S. Sanghavi, Robust matrix completion with corrupted columns, 2011.

H. Chuang, E. Lee, Y. Liu, D. Lee, and T. Ideker, Network-based classification of breast cancer metastasis, Molecular Systems Biology, vol.5, p.140, 2007.
DOI : 10.1038/msb4100180

B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, Least angle regression, Ann. Stat, vol.32, issue.2, pp.407-499, 2004.

L. He and L. Carin, Exploiting structure in wavelet-based Bayesian compressive sensing, IEEE Transactions on Signal Processing, vol.57, pp.3488-3497, 2009.

J. B. Hiriart-urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms I.: Fundamentals, 1994.
DOI : 10.1007/978-3-662-02796-7

J. Huang and T. Zhang, The benefit of group sparsity, The Annals of Statistics, vol.38, issue.4, pp.9-778, 1978.
DOI : 10.1214/09-AOS778

J. Huang, T. Zhang, and D. Metaxas, Learning with structured sparsity, Proceedings of the 26th Annual International Conference on Machine Learning, ICML '09, 2009.
DOI : 10.1145/1553374.1553429

L. Jacob, G. Obozinski, and J. Vert, Group lasso with overlap and graph lasso, Proceedings of the 26th Annual International Conference on Machine Learning, ICML '09, pp.433-440, 2009.
DOI : 10.1145/1553374.1553431

A. Jalali, P. Ravikumar, S. Sanghavi, and C. Ruan, A dirty model for multitask learning, Adv. Neural. Inform. Process Syst, pp.964-972, 2010.

R. Jenatton, J. Audibert, and F. Bach, Structured variable selection with sparsityinducing norms, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00377732

R. Jenatton, J. Mairal, G. Obozinski, and F. Bach, Proximal methods for hierarchical sparse coding, J. Mach. Learn. Res, vol.12, pp.2297-2334, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00516723

K. Knight and W. Fu, Asymptotics for lasso-type estimators, Ann. Stat, vol.28, issue.5, pp.1356-1378, 2000.

M. Kolar, J. Lafferty, and L. Wasserman, Union support recovery in multi-task learning, J. Mach. Learn. Res, vol.12, pp.2415-2435, 2011.

G. R. Lanckriet, N. Cristianini, P. Bartlett, L. Ghaoui, and M. I. Jordan, Learning the kernel matrix with semidefinite programming, J. Mach. Learn. Res, vol.5, pp.27-72, 2004.

C. Leng, Y. Lin, and G. Wahba, A note on the Lasso and related procedures in model selection, Statistica Sinica, vol.16, issue.4, pp.1273-1284, 2004.

K. Lounici, Sup-norm convergence rate and sign concentration property of lasso and dantzig estimators. Electron, J. Statist, vol.2, pp.90-10208, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00222251

K. Lounici, M. Pontil, A. B. Tsybakov, S. Van-de, and . Geer, Oracle inequalities and optimal inference under group sparsity, The Annals of Statistics, vol.39, issue.4
DOI : 10.1214/11-AOS896

URL : https://hal.archives-ouvertes.fr/hal-00652284

K. Lounici, M. Pontil, A. B. Tsybakov, and S. Van-de-geer, Taking advantage of sparsity in multi-task learning, Proceedings of COLT, 2009.

A. Maurer and M. Pontil, Structured sparsity and generalization

L. Meier, S. Van-de-geer, and P. Bühlmann, The group lasso for logistic regression, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.68, issue.1, pp.53-71, 2008.
DOI : 10.1111/j.1467-9868.2007.00627.x

C. A. Micchelli, J. M. Morales, and M. Pontil, Regularizers for structured sparsity, Advances in Computational Mathematics, vol.37, issue.6A, 2011.
DOI : 10.1007/s10444-011-9245-9

S. Mosci, S. Villa, A. Verri, and L. Rosasco, A primal-dual algorithm for group sparse regularization with overlapping groups, Adv. Neural. Inform. Process Syst, pp.2604-2612, 2010.

S. N. Negahban and M. J. Wainwright, Simultaneous support recovery in high dimensions: Benefits and perils of block ? 1 /? ? -regularization. Information Theory, IEEE Transactions on, vol.57, issue.6, pp.3841-3863, 2011.

J. Nocedal and S. Wright, Numerical optimization, 2006.
DOI : 10.1007/b98874

G. Obozinski and F. Bach, Convex relaxation of combinatorial penalties, 2011.

G. Obozinski, B. Taskar, and M. I. Jordan, Joint covariate selection and joint subspace selection for multiple classification problems, Statistics and Computing, vol.8, issue.68, pp.231-252, 2010.
DOI : 10.1007/s11222-008-9111-x

R. T. Rockafellar, Convex Analysis, 1997.
DOI : 10.1515/9781400873173

V. Roth and B. Fischer, The Group-Lasso for generalized linear models, Proceedings of the 25th international conference on Machine learning, ICML '08, pp.848-855, 2008.
DOI : 10.1145/1390156.1390263

A. Subramanian, P. Tamayo, V. K. Mootha, S. Mukherjee, B. L. Ebert et al., Gene set enrichment analysis: A knowledge-based approach for interpreting genome-wide expression profiles, Proc. Natl. Acad. Sci. USA, pp.15545-15550, 2005.
DOI : 10.1073/pnas.0506580102

R. Tibshirani, Regression shrinkage and selection via the lasso, J. R. Stat. Soc. Ser. B, vol.58, issue.1, pp.267-288, 1996.

S. Van-de-geer, -regularization in High-dimensional Statistical Models, Proceedings of the International Congress of Mathematicians 2010 (ICM 2010), pp.2251-2369, 2010.
DOI : 10.1142/9789814324359_0149

URL : https://hal.archives-ouvertes.fr/in2p3-00118805

M. J. Van-de-vijver, Y. D. He, L. J. Van-'t-veer, H. Dai, A. A. Hart et al., A Gene-Expression Signature as a Predictor of Survival in Breast Cancer, New England Journal of Medicine, vol.347, issue.25, pp.1999-2009, 2002.
DOI : 10.1056/NEJMoa021967

M. J. Wainwright, Sharp Thresholds for High-Dimensional and Noisy Sparsity Recovery Using <formula formulatype="inline"><tex Notation="TeX">$\ell _{1}$</tex> </formula>-Constrained Quadratic Programming (Lasso), IEEE Transactions on Information Theory, vol.55, issue.5, pp.2183-2202, 2009.
DOI : 10.1109/TIT.2009.2016018

M. Yuan and Y. Lin, Model selection and estimation in regression with grouped variables, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.58, issue.1, pp.49-67, 2006.
DOI : 10.1198/016214502753479356

P. Zhao and B. Yu, On model selection consistency of lasso, J. Mach. Learn. Res, vol.7, p.2541, 2006.

P. Zhao, G. Rocha, and B. Yu, The composite absolute penalties family for grouped and hierarchical variable selection, The Annals of Statistics, vol.37, issue.6A, pp.3468-3497, 2009.
DOI : 10.1214/07-AOS584