Noisy matrix decomposition via convex relaxation: Optimal rates in high dimensions, The Annals of Statistics, vol.40, issue.2, pp.1171-1197, 2012. ,
DOI : 10.1214/12-AOS1000SUPP
Applied nonlinear analysis. Pure and applied mathematics, 1984. ,
Absolute and monotonic norms, Numerische Mathematik, vol.63, issue.1, pp.257-264, 1961. ,
DOI : 10.1007/BF01386026
Statistics for High-Dimensional Data: Methods, Theory and Applications, 2011. ,
DOI : 10.1007/978-3-642-20192-9
Matrix completion via max-norm constrained optimization, Electronic Journal of Statistics, vol.10, issue.1 ,
DOI : 10.1214/16-EJS1147
Robust principal component analysis?, Journal of the ACM, vol.58, issue.3, pp.1-37, 2009. ,
DOI : 10.1145/1970392.1970395
The power of convex relaxation: near-optimal matrix completion, IEEE Trans. Inform. Theory, vol.56, issue.5, pp.2053-2080, 2010. ,
Rank-Sparsity Incoherence for Matrix Decomposition, SIAM Journal on Optimization, vol.21, issue.2, pp.572-596, 2011. ,
DOI : 10.1137/090761793
Robust matrix completion with corrupted columns, ICML, pp.873-880, 2011. ,
Low-Rank Matrix Recovery From Errors and Erasures, IEEE Transactions on Information Theory, vol.59, issue.7, pp.4324-4337, 2013. ,
DOI : 10.1109/TIT.2013.2249572
Probability and its Applications From dependence to independence, Randomly stopped processes. U -statistics and processes, 1999. ,
Concentration-based guarantees for low-rank matrix reconstruction, Journal 24nd Annual Conference on Learning Theory (COLT), 2011. ,
Exponential and Moment Inequalities for U-Statistics, High dimensional probability, II, pp.13-38, 1999. ,
DOI : 10.1007/978-1-4612-1358-1_2
Recovering Low-Rank Matrices From Few Coefficients in Any Basis, IEEE Transactions on Information Theory, vol.57, issue.3, pp.1548-1566, 2011. ,
DOI : 10.1109/TIT.2011.2104999
Robust Matrix Decomposition With Sparse Corruptions, IEEE Transactions on Information Theory, vol.57, issue.11, pp.7221-7234, 2011. ,
DOI : 10.1109/TIT.2011.2158250
Matrix completion from noisy entries, J. Mach. Learn. Res, vol.11, pp.2057-2078, 2010. ,
Noisy low-rank matrix completion with general sampling distribution, Bernoulli, vol.20, issue.1, pp.282-303, 2014. ,
DOI : 10.3150/12-BEJ486
URL : https://hal.archives-ouvertes.fr/hal-00675413
Oracle inequalities in empirical risk minimization and sparse recovery problems, volume 2033 of Lecture Notes in Mathematics Lectures from the 38th Probability Summer School held in Saint-Flour, 2008. ,
Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion, The Annals of Statistics, vol.39, issue.5, pp.2302-2329, 2011. ,
DOI : 10.1214/11-AOS894
URL : https://hal.archives-ouvertes.fr/hal-00676868
Compressed Sensing and Matrix Completion with Constant Proportion of Corruptions, Constructive Approximation, vol.31, issue.2, p.2013 ,
DOI : 10.1007/s00365-012-9176-9
Restricted strong convexity and weighted matrix completion: Optimal bounds with noise, Journal of Machine Learning Research, vol.13, pp.1665-1697, 2012. ,
A simpler approach to matrix completion, Journal of Machine Learning Research, vol.12, pp.3413-3430, 2011. ,
Estimation of high-dimensional low-rank matrices, The Annals of Statistics, vol.39, issue.2, pp.887-930, 2011. ,
DOI : 10.1214/10-AOS860
URL : https://hal.archives-ouvertes.fr/hal-00606063
Hanson-Wright inequality and sub-gaussian concentration, Electronic Communications in Probability, vol.18, issue.0, 2013. ,
DOI : 10.1214/ECP.v18-2865
URL : http://arxiv.org/abs/1306.2872
Introduction to nonparametric estimation ,
DOI : 10.1007/b13794
Revised and extended from the 2004 French original, 2009. ,
Introduction to the non-asymptotic analysis of random matrices, ArXiv, vol.1011, p.3027, 2010. ,
DOI : 10.1017/CBO9780511794308.006
Robust PCA via Outlier Pursuit, IEEE Transactions on Information Theory, vol.58, issue.5, pp.3047-3064, 2012. ,
DOI : 10.1109/TIT.2011.2173156