Intersecting singularities for multi-structured estimation

30th International Conference on Machine Learning, ICML 2013

Volumn , Issue PART 3, 2013, Pages 2194-2202

  Richard, Emile ^a   Bach, Francis ^b   Vert, Jean Philippe ^a  

^a INSERM U900   (France)

^b Centre National de la Recherche Scientifique   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; SOFTWARE ENGINEERING;

LINEAR FUNCTIONS; LOW-RANK MATRICES; NUMERICAL EXPERIMENTS; ORACLE INEQUALITIES; PENALTY TERM; REGULARIZER; STRUCTURAL EFFECT; TRACE-NORMS;

LEARNING SYSTEMS;

EID: 84897520091     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (21)

1. Alon, N., Krivelevich, M., and Sudakov, B. Finding a large hidden clique in a random graph. Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms, 1998.
2. Bach, F., Jenatton, R., Mairal, J., and Obozinski, G. Convex optimization with sparsity-inducing norms. S. Sra, S. Nowozin, S. J. Wright, editors, Optimization for Machine Learning, 2011.
3. Boyd, S., Parikh, N., Chu, E. Peleato, B., and Eckstein, J. Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends in Machine Learning, 3, 2011.
4. Candès, E. J., Li, X., Ma, Y., and W., John. Robust principal component analysis? Journal of ACM, 8:1-37, 2009.
5. Chambolle, A. and Pock, T. A first-order primal-dual algorithm for convex problems with applications to imaging. Journal of Mathematical Imaging and Vision, 2011.
6. Chandrasekaran, V. and Jordan, M. I. Computational and statistical tradeoffs via convex relaxation. Preprint, 2012.
7. Chandrasekaran, V., Sanghavi, S., Parrilo, P.A., and Willsky, A.S. Rank-sparsity incoherence for matrix decomposition. SIAM J. Opt., 21:572-596, 2011.
8. Chandrasekaran, V., Recht, B., Parrilo, P.A., and Willsky, A.S. The convex geometry of linear inverse problems. Foundations of Computational Mathematics, 12, 2012.
9. Dalalyan, A. S. and Chen, Y. Fused sparsity and robust estimation for linear models with unknown variance. In NIPS 2012, 2012.
10. d'Aspremont, A., El Ghaoui, L., Jordan, M.I., and Lanckriet, G.R.G. A direct formulation for sparse pca using semidefinite programming. SIAM review, 49(3):434-448, 2007. (Pubitemid 47377693)
11. Doan, X.V. and Vavasis, S.A. Finding approximately rank-one submatrices with the nuclear norm and 11 norm. arXiv preprint arXiv:1011.1839, 2010.
12. Golbabaee, M. and Vandergheynst, P. Compressed sensing of simultaneous low-rank and joint-sparse matrices. submitted to IEEE transaction in Information Theory, 2012.
13. Grave, E., Obozinski, G., and Bach, F. Trace lasso: a trace norm regularization for correlated designs. In Advances in Neural Information Processing Systems 24, pp. 2187-2195, 2011.
14. Hosseini Kamal, M. and Vandergheynst, P. Joint low-rank and sparse light field modeling for dense multiview data compression. ICASSP, 2013.
15. Jaggi, M. Revisiting frank-wolfe: Projection-free sparse convex optimization. Proceedings of the 30th Annual International Conference on Machine Learning, 2013.
16. Koltchinskii, V., Lounici, K., and Tsybakov, A. Nuclear norm penalization and optimal rates for noisy matrix completion. Annals of Statistics, 2011.
17. Oymak, S., Jalali, A., Fazel, M., Eldar, Y., and Hassibi, B. Simultaneously structured models with application to sparse and low-rank matrices, submitted, 2012. URL http://arxiv.org/pdf/1212.3753v1.pdf.
18. Richard, E., Savalle, P.-A., and Vayatis, N. Estimation of simultaneously sparse and low-rank matrices. In Proceeding of 29th Annual International Conference on Machine Learning, 2012.
19. Tropp, J. A. User-friendly tail bounds for sums of random matrices. ArXiv e-prints, April 2010.
20. Vaiter, S., Peyré, G., Dossal, C., and Fadili, J. Robust sparse analysis regularization, to appear in IEEE Transactions on Information Theory, 2012.
21. Vert, J.-P and Bleakley, K. Fast detection of multiple change-points shared by many signals using group lars. Advances in Neural Information Processing Systems 23 (NIPS), pp. 2343-2351, 2010.