D. Agarwal, L. Zhang, and R. Mazumder, Modeling item--item similarities for personalized recommendations on yahoo! front page, Ann. Appl. Stat, vol.5, issue.3, pp.1839-1875, 2011.

A. Agresti, Categorical Data Analysis, 2013.

J. Aubin and I. Ekeland, Applied nonlinear analysis. Pure and applied mathematics, 1984.

A. S. Bandeira and R. Van-handel, Sharp nonasymptotic bounds on the norm of random matrices with independent entries, Ann. Probab, vol.44, issue.4, pp.2479-2506, 2016.

P. Bühlmann and S. Van-de-geer, Statistics for High-Dimensional Data: Methods, Theory and Applications, 2011.

T. Cai and W. Zhou, A max-norm constrained minimization approach to 1-bit matrix completion, J. Mach. Learn. Res, vol.14, issue.1, pp.3619-3647, 2013.

E. J. Candès, X. Li, Y. Ma, and J. Wright, Robust principal component analysis?, J. ACM, vol.58, issue.3, p.37, 2011.

Y. Cao and Y. Xie, Poisson matrix recovery and completion, IEEE Transactions on Signal Processing, vol.64, issue.6, 2016.

V. Chandrasekaran, S. Sanghavi, P. A. Parrilo, and A. S. Willsky, Rank-sparsity incoherence for matrix decomposition, SIAM Journal on Optimization, vol.21, issue.2, pp.572-596, 2011.

S. Chatterjee, Matrix estimation by universal singular value thresholding, Ann. Statist, vol.43, issue.1, pp.177-214, 2015.

M. A. Davenport, Y. Plan, E. Van-den, M. Berg, and . Wootters, 1-bit matrix completion, 2012.

W. Fithian and R. Mazumder, Flexible low-rank statistical modeling with missing data and side information, Statist. Sci, vol.33, issue.2, pp.238-260, 2018.

J. Friedman, T. Hastie, and R. Tibshirani, Regularization paths for generalized linear models via coordinate descent, Journal of Statistical Software, vol.33, issue.1, p.1, 2010.

A. Gelman and J. Hill, Data Analysis Using Regression and Multilevel/Hierarchical Models, 2007.

S. Gunasekar, P. Ravikumar, and J. Ghosh, Exponential family matrix completion under structural constraints, Proceedings of the 31st International Conference on International Conference on Machine Learning, vol.32, 2014.

T. Hastie, R. Mazumder, J. Lee, and R. Zadeh, Matrix Completion and Low-Rank SVD via Fast Alternating Least Squares, The Journal of Machine Learning Research, vol.16, pp.3367-3402, 2015.

S. Heeringa, B. West, and P. Berlung, Applied Survey Data Analysis, 2010.

D. Hsu, S. M. Kakade, and T. Zhang, Robust matrix decomposition with sparse corruptions, EEE Transactions on Information Theory, vol.57, issue.11, pp.7221-7234, 2011.

F. Husson, J. Josse, B. Narasimhan, and G. Robin, Imputation of mixed data with multilevel singular value decomposition, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01781291

J. Josse and F. Husson, missMDA: A package for handling missing values in multivariate data analysis, Journal of Statistical Software, vol.70, issue.1, pp.1-31, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01314945

H. A. Kiers, Simple structure in component analysis techniques for mixtures of qualitative and quantitative variables, Psychometrika, vol.56, issue.2, pp.197-212, 1991.

O. Klopp, Noisy low-rank matrix completion with general sampling distribution, Bernoulli, vol.20, issue.1, pp.282-303, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00675413

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