High-dimensional analysis of semidefinite relaxations for sparse principal components, IEEE International Symposium on Information Theory, pp.2454-2458, 2008. ,
Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices, The Annals of Probability, vol.33, issue.5, pp.1643-1697, 2005. ,
DOI : 10.1214/009117905000000233
Information-theoretic bounds and phase transitions in clustering, sparse PCA, and submatrix localization, 2016. ,
Thibault Lesieur, and Lenka Zdeborov'a. Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula, Advances In Neural Information Processing Systems, pp.424-432, 2016. ,
Statistical mechanics of the maximum-likelihood density estimation, Physical Review E, vol.50, issue.3, p.1766, 1994. ,
DOI : 10.1103/PhysRevE.50.1766
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
Computational lower bounds for sparse PCA. arXiv preprint, 2013. ,
Statistical mechanics of unsupervised structure recognition, Journal of Physics A: Mathematical and General, vol.27, issue.6, p.1885, 1994. ,
DOI : 10.1088/0305-4470/27/6/015
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.30.5984
On convergence of approximate message passing, 2014 IEEE International Symposium on Information Theory, pp.1812-1816, 2014. ,
DOI : 10.1109/ISIT.2014.6875146
URL : https://hal.archives-ouvertes.fr/cea-01223403
Biclustering of expression data, Ismb, pp.93-103, 2000. ,
Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications, Physical Review E, vol.84, issue.6, p.66106, 2011. ,
DOI : 10.1103/PhysRevE.84.066106
URL : https://hal.archives-ouvertes.fr/hal-00661643
Inference and Phase Transitions in the Detection of Modules in Sparse Networks, Physical Review Letters, vol.107, issue.6, p.65701, 2011. ,
DOI : 10.1103/PhysRevLett.107.065701
Asymptotic mutual information for the binary stochastic block model, 2016 IEEE International Symposium on Information Theory (ISIT), pp.185-189, 2016. ,
DOI : 10.1109/ISIT.2016.7541286
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
Sparse PCA via covariance thresholding, Advances in Neural Information Processing Systems, pp.334-342, 2014. ,
Finding Hidden Cliques of Size $$\sqrt{N/e}$$ N / e in Nearly Linear Time, Foundations of Computational Mathematics, vol.15, issue.4, pp.1-60, 2015. ,
DOI : 10.1007/s10208-014-9215-y
Message-passing algorithms for compressed sensing, Proc. Natl. Acad. Sci, pp.18914-18919, 2009. ,
The approximation of one matrix by another of lower rank, Psychometrika, vol.1, issue.3, pp.211-218, 1936. ,
DOI : 10.1007/BF02288367
Community detection in graphs, Physics Reports, vol.486, issue.3-5, pp.75-174, 2010. ,
DOI : 10.1016/j.physrep.2009.11.002
URL : http://arxiv.org/abs/0906.0612
Training restricted Boltzmann machine via the Thouless-Anderson- Palmer free energy, Advances in Neural Information Processing Systems, pp.640-648, 2015. ,
How to expand around mean-field theory using high-temperature expansions, Journal of Physics A: Mathematical and General, vol.24, issue.9, p.2173, 1991. ,
DOI : 10.1088/0305-4470/24/9/024
Mean-field theory of the Potts glass, Physical Review Letters, vol.55, issue.3, pp.304-307, 1985. ,
DOI : 10.1103/PhysRevLett.55.304
The elements of statistical learning: data mining, inference and prediction. The Mathematical Intelligencer, pp.83-85, 2005. ,
A Practical Guide to Training Restricted Boltzmann Machines, Momentum, vol.79, issue.7, p.926, 2010. ,
DOI : 10.1073/pnas.79.8.2554
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.170.9573
A fast learning algorithm for deep belief nets, Neural computation, vol.18, issue.7, pp.1527-1554, 2006. ,
Neural networks and physical systems with emergent collective computational abilities, Proceedings of the national academy of sciences, pp.2554-2558, 1982. ,
Principal-component-analysis eigenvalue spectra from data with symmetry-breaking structure, Physical Review E, vol.69, issue.2, p.26124, 2004. ,
State evolution for general approximate message passing algorithms, with applications to spatial coupling, Information and Inference, vol.2, issue.2, p.4, 2013. ,
DOI : 10.1093/imaiai/iat004
URL : http://arxiv.org/abs/1211.5164
Sparse principal components analysis. Unpublished manuscript, 2004. ,
Phase Transitions and Sample Complexity in Bayes-Optimal Matrix Factorization, IEEE Transactions on Information Theory, vol.62, issue.7, pp.4228-4265, 2016. ,
DOI : 10.1109/TIT.2016.2556702
Boltzmann machine learning using mean field theory and linear response correction Advances in neural information processing systems, pp.280-286, 1998. ,
Spherical Model of a Spin-Glass, Physical Review Letters, vol.36, issue.20, p.1217, 1976. ,
DOI : 10.1103/PhysRevLett.36.1217
Do semidefinite relaxations solve sparse PCA up to the information limit? The Annals of Statistics, pp.1300-1322, 2015. ,
Variational free energies for compressed sensing, 2014 IEEE International Symposium on Information Theory, pp.1499-1503, 2014. ,
DOI : 10.1109/ISIT.2014.6875083
URL : http://arxiv.org/abs/1402.1384
Phase diagram and approximate message passing for blind calibration and dictionary learning, 2013 IEEE International Symposium on Information Theory, pp.659-663, 2013. ,
DOI : 10.1109/ISIT.2013.6620308
URL : https://hal.archives-ouvertes.fr/cea-01140799
Spectral redemption in clustering sparse networks, Proceedings of the National Academy of Sciences, vol.110, issue.52, pp.20935-20940, 2013. ,
DOI : 10.1073/pnas.1312486110
URL : https://hal.archives-ouvertes.fr/cea-01223434
Mutual information in rank-one matrix estimation, 2016 IEEE Information Theory Workshop (ITW), 2016. ,
DOI : 10.1109/ITW.2016.7606798
Deep learning, Nature, vol.9, issue.7553, pp.436-444, 2015. ,
DOI : 10.1007/s10994-013-5335-x
Phase transitions and optimal algorithms in high-dimensional Gaussian mixture clustering, 2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2016. ,
DOI : 10.1109/ALLERTON.2016.7852287
URL : https://hal.archives-ouvertes.fr/cea-01448112
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), pp.680-687, 2015. ,
DOI : 10.1109/ALLERTON.2015.7447070
URL : https://hal.archives-ouvertes.fr/cea-01222294
Phase transitions in sparse PCA, 2015 IEEE International Symposium on Information Theory (ISIT), pp.1635-1639, 2015. ,
DOI : 10.1109/ISIT.2015.7282733
URL : https://hal.archives-ouvertes.fr/cea-01140712
Least squares quantization in PCM, IEEE Transactions on Information Theory, vol.28, issue.2, pp.129-137, 1982. ,
DOI : 10.1109/TIT.1982.1056489
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.131.1338
Biclustering algorithms for biological data analysis: a survey, IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB), vol.1, issue.1, pp.24-45, 2004. ,
Fundamental limits of symmetric low-rank matrix estimation, 2016. ,
Low-rank matrix reconstruction and clustering via approximate message passing, Advances in Neural Information Processing Systems 26, pp.917-925, 2013. ,
Spin-Glass Theory and Beyond, Lecture Notes in Physics. World Scientific, vol.9, 1987. ,
Mean-field message-passing equations in the Hopfield model and its generalizations. arXiv preprint, 2016. ,
Estimating the principal components of correlation matrices from all their empirical eigenvectors, EPL (Europhysics Letters), vol.112, issue.5, p.50001, 2015. ,
DOI : 10.1209/0295-5075/112/50001
Finding One Community in a Sparse Graph, Journal of Statistical Physics, vol.92, issue.4, pp.273-299, 2015. ,
DOI : 10.1007/s10955-015-1338-2
Statistical Physics of Spin Glasses and Information Processing: An Introduction, 2001. ,
DOI : 10.1093/acprof:oso/9780198509417.001.0001
Absence of replica symmetry breaking in a region of the phase diagram of the Ising spin glass, AIP Conference Proceedings, pp.67-72, 2001. ,
DOI : 10.1063/1.1358165
Bilinear generalized approximate message passing part I: Derivation, IEEE Transactions on Signal Processing, vol.62, issue.22, pp.5839-5853, 2014. ,
Subspace clustering for high dimensional data, ACM SIGKDD Explorations Newsletter, vol.6, issue.1, pp.90-105, 2004. ,
DOI : 10.1145/1007730.1007731
Message-passing algorithms for synchronization problems over compact groups, 2016. ,
Optimality and sub-optimality of PCA for spiked random matrices and synchronization. arXiv preprint, 2016. ,
Convergence condition of the TAP equation for the infinite-ranged Ising spin glass model, Journal of Physics A: Mathematical and General, vol.15, issue.6, p.1971, 1982. ,
DOI : 10.1088/0305-4470/15/6/035
Estimation with random linear mixing, belief propagation and compressed sensing, 2010 44th Annual Conference on Information Sciences and Systems (CISS), pp.1-6, 2010. ,
DOI : 10.1109/CISS.2010.5464768
URL : http://arxiv.org/abs/1001.2228
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
Fixed points of generalized approximate message passing with arbitrary matrices, IEEE International Symposium on Information Theory Proceedings (ISIT), pp.664-668, 2013. ,
A statistical model for tensor PCA, Advances in Neural Information Processing Systems, pp.2897-2905, 2014. ,
Solvable Model of a Spin-Glass, Physical Review Letters, vol.35, issue.26, pp.1792-1796, 1975. ,
DOI : 10.1103/PhysRevLett.35.1792
Theory of a Heisenberg spin glass, Journal of Magnetism and Magnetic Materials, vol.22, issue.3, pp.267-270, 1981. ,
DOI : 10.1016/0304-8853(81)90032-9
Solution of 'Solvable model of a spin glass', Philosophical Magazine, vol.35, issue.3, pp.593-601, 1977. ,
DOI : 10.1103/PhysRevLett.35.1792
Inferring sparsity: Compressed sensing using generalized restricted Boltzmann machines, IEEE Information Theory Workshop (ITW), pp.265-269, 2016. ,
Emergence of compositional representations in restricted Boltzmann machines. arXiv preprint, 2016. ,
Adaptive damping and mean removal for the generalized approximate message passing algorithm, 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp.2021-2025, 2015. ,
DOI : 10.1109/ICASSP.2015.7178325
URL : https://hal.archives-ouvertes.fr/cea-01140721
All of statistics: a concise course in statistical inference, 2013. ,
DOI : 10.1007/978-0-387-21736-9
Optimal unsupervised learning, Journal of Physics A: Mathematical and General, vol.27, issue.6, p.1899, 1994. ,
DOI : 10.1088/0305-4470/27/6/016
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.127.3242
Exploring artificial intelligence in the new millennium. chapter Understanding Belief Propagation and Its Generalizations, pp.239-269, 2003. ,
Statistical physics of inference: thresholds and algorithms, Advances in Physics, vol.19, issue.5, pp.453-552, 2016. ,
DOI : 10.1214/009117905000000233
Sparse Principal Component Analysis, Journal of Computational and Graphical Statistics, vol.15, issue.2, pp.265-286, 2006. ,
DOI : 10.1198/106186006X113430