Rank penalized estimators for high-dimensional matrices

Electronic Journal of Statistics

Volumn 5, Issue , 2011, Pages 1161-1183

  Klopp, Olga ^a  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

Author keywords

Low rank matrix estimation; Matrix completion; Recovery of the rank; Statistical learning

Indexed keywords

EID: 84859835859     PISSN: 19357524     EISSN: None     Source Type: Journal    
DOI: 10.1214/11-EJS637     Document Type: Article

References (17)

1. Argyriou, A., Evgeniou, T. and Pontil, M. (2008) Convex multi-task feature learning. Mach. Learn., 73, 243-272.
2. Argyriou, A., Micchelli, C.A. and Pontil, M. (2010) On spectral learning. J. Mach. Learn. Res., 11, 935-953. MR2600635.
3. Argyriou, A., Micchelli, C.A., Pontil, M. and Ying, Y. (2007) A spectral regularization framework for multi-task structure learning. In NIPS.
4. Bach, F.R. (2008) Consistency of trace norm minimization. J. Mach. Learn. Res., 9, 1019-1048. MR2417263.
5. Bunea, F., She, Y. and Wegkamp, M. (2011) Optimal selection of reduced rank estimators of high-dimensional matrices. Annals of Statistics, 39, 1282-1309.
6. Candés, E.J. and Plan, Y. (2009). Matrix completion with noise. Proceedings of IEEE.
7. Candés, E.J. and Plan, Y. (2010) Tight oracle bounds for lowrank matrix recovery from a minimal number of random measurements. ArXiv:1001.0339.
8. Candés, E.J. and Recht, B. (2009) Exact matrix completion via convex optimization. Fondations of Computational Mathematics, 9(6), 717-772. MR2565240.
9. Gaïffas, S. and Lecué, G. (2010) Sharp oracle inequalities for the prediction of a high-dimensional matrix. IEEE Transactions on Information Theory, to appear.
10. Giraud, C. (2011) Low rank Multivariate regression. Electronic Journal of Statistics, 5, 775-799.
11. Gross, D. Recovering low-rank matrices from few coefficients in any basis.(2011). IEEE Transactions, 57(3), 1548-1566. MR2815834.
12. Keshavan, R.H., Montanari, A. and Oh, S. (2010) Matrix completion from noisy entries. Journal of Machine Learning Research, 11, 2057-2078. MR2678022.
13. Koltchinskii, V., Lounici, K. and Tsybakov, A. Nuclear norm penalization and optimal rates for noisy low rank matrix completion. Annals of Statistics, to appear.
14. Negahban, S. and Wainwright, M.J. (2011). Estimation of (near) lowrank matrices with noise and high-dimensional scaling. Annals of Statistics, 39, 1069-1097.
15. Recht, B. (2009) A simpler approach to matrix completion. Journal of Machine Learning Research, to appear.
16. Reinsel, G.C. and Velu, R.P. Multivariate Reduced-Rank Regression: Theory and Applications. Springer, 1998. MR1719704.
17. Rohde, A. and Tsybakov, A. (2011) Estimation of High-Dimensional Low-Rank Matrices. Annals of Statistics, 39, 887-930.