A. A. Amini and M. J. Wainwright, High-dimensional analysis of semidefinite relaxations for sparse principal components, IEEE Int. Symp. on Inf. Theory, p.2454, 2008.

J. Baik, G. B. Arous, and S. Péché, Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices, The Annals of Probability, vol.33, issue.5, p.1643, 2005.
DOI : 10.1214/009117905000000233

J. Barbier, M. Dia, and N. Macris, Threshold saturation of spatially coupled sparse superposition codes for all memoryless channels, 2016 IEEE Information Theory Workshop (ITW)
DOI : 10.1109/ITW.2016.7606799

M. Bayati and A. Montanari, The Dynamics of Message Passing on Dense Graphs, with Applications to Compressed Sensing, IEEE Transactions on Information Theory, vol.57, issue.2, pp.764-785, 2011.
DOI : 10.1109/TIT.2010.2094817

Q. Berthet and P. Rigollet, Computational lower bounds for sparse pca, 2013.

E. J. Candès and B. Recht, Exact Matrix Completion via Convex Optimization, Foundations of Computational Mathematics, vol.170, issue.1, pp.717-772, 2009.
DOI : 10.1017/CBO9780511814068

A. Aspremont, L. Ghaoui, M. I. Jordan, and G. R. Lanckriet, A Direct Formulation for Sparse PCA Using Semidefinite Programming, SIAM Review, vol.49, issue.3, p.434, 2007.
DOI : 10.1137/050645506

Y. Deshpande and A. Montanari, Information-theoretically optimal sparse PCA, 2014 IEEE International Symposium on Information Theory, pp.2197-2201, 2014.
DOI : 10.1109/ISIT.2014.6875223
URL : http://arxiv.org/abs/1402.2238

Y. Deshpande and A. Montanari, Finding Hidden Cliques of Size $$\sqrt{N/e}$$ N / e in Nearly Linear Time, Foundations of Computational Mathematics, vol.15, issue.4, pp.1069-1128, 2015.
DOI : 10.1198/106186006X113430

Y. Deshpande, E. Abbe, and A. Montanari, Asymptotic mutual information for the two-groups stochastic block model, 2015.
DOI : 10.1109/isit.2016.7541286

F. Guerra, An introduction to mean field spin glass theory: methods and results, Mathematical Statistical Physics, pp.243-271, 2005.
DOI : 10.1016/s0924-8099(06)80042-9

D. Guo, S. Shamai, and S. Verdú, Mutual Information and Minimum Mean-Square Error in Gaussian Channels, IEEE Transactions on Information Theory, vol.51, issue.4, p.51, 2005.
DOI : 10.1109/TIT.2005.844072
URL : http://arxiv.org/abs/cs/0412108

S. H. Hassani, N. Macris, and R. Urbanke, Coupled graphical models and their thresholds, 2010 IEEE Information Theory Workshop, 2010.
DOI : 10.1109/CIG.2010.5592881
URL : http://arxiv.org/abs/1105.0785

A. Javanmard and A. Montanari, State evolution for general approximate message passing algorithms, with applications to spatial coupling, Information and Inference, vol.2, issue.2, p.115, 2013.
DOI : 10.1093/imaiai/iat004
URL : http://arxiv.org/abs/1211.5164

I. M. Johnstone and A. Y. Lu, On Consistency and Sparsity for Principal Components Analysis in High Dimensions, Journal of the American Statistical Association, vol.104, issue.486, 2012.
DOI : 10.1198/jasa.2009.0121

S. B. Korada and N. Macris, Exact Solution of the Gauge Symmetric p-Spin Glass Model on a Complete Graph, Journal of Statistical Physics, vol.163, issue.29, pp.205-230, 2009.
DOI : 10.1017/CBO9780511791338

F. Krzakala, J. Xu, and L. Zdeborová, Mutual information in rank-one matrix estimation, 2016 IEEE Information Theory Workshop (ITW), 2016.
DOI : 10.1109/ITW.2016.7606798
URL : http://arxiv.org/abs/1603.08447

S. Kudekar, T. J. Richardson, and R. Urbanke, Threshold saturation via spatial coupling: Why convolutional ldpc ensembles perform so well over the bec, IEEE Trans. on Inf. Theory, vol.57, 2011.
DOI : 10.1109/isit.2010.5513587
URL : http://arxiv.org/abs/1001.1826

T. Lesieur, F. Krzakala, and L. Zdeborová, MMSE of probabilistic low-rank matrix estimation: Universality with respect to the output channel, 2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2015.
DOI : 10.1109/ALLERTON.2015.7447070
URL : https://hal.archives-ouvertes.fr/cea-01222294

T. Lesieur, F. Krzakala, and L. Zdeborová, Phase transitions in sparse PCA, 2015 IEEE International Symposium on Information Theory (ISIT), p.1635, 2015.
DOI : 10.1109/ISIT.2015.7282733
URL : https://hal.archives-ouvertes.fr/cea-01140712

S. Rangan and A. K. Fletcher, Iterative estimation of constrained rank-one matrices in noise, 2012 IEEE International Symposium on Information Theory Proceedings, pp.1246-1250, 2012.
DOI : 10.1109/ISIT.2012.6283056

A. Yedla, Y. Y. Jian, P. S. Nguyen, and H. D. Pfister, A Simple Proof of Maxwell Saturation for Coupled Scalar Recursions, IEEE Transactions on Information Theory, vol.60, issue.11, pp.606943-6965, 2014.
DOI : 10.1109/TIT.2014.2352296

H. Zou, T. Hastie, and R. Tibshirani, Sparse Principal Component Analysis, Journal of Computational and Graphical Statistics, vol.15, issue.2, pp.265-286, 2006.
DOI : 10.1198/106186006X113430