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Consider the problem of estimating a low-rank matrix when its entries are perturbed by Gaussian noise.
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2010
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Florent Benaych-Georges and Raj Rao Nadakuditi, The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices , Advances in Mathematics 227
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David L Donoho, Iain Johnstone, and Andrea Montanari, Accurate prediction of phase transitions in compressed sensing via a connection to minimax denoising , IEEE transactions on information theory 59
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Adel Javanmard and Andrea Montanari, State evolution for general approximate message passing algorithms, with applications to spatial coupling , Information and Inference (2013), iat004
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Antti Knowles and Jun Yin, The isotropic semicircle law and deformation of wigner matrices , Communications on Pure and Applied Mathematics (2013)
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2017
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Thibault Lesieur, Florent Krzakala, and Lenka Zdeborová, Constrained low-rank matrix estimation: Phase transitions, approximate message passing and applications , Journal of Statistical Mechanics: Theory and Experiment (2017)
2017
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Léo Miolane, Fundamental limits of low-rank matrix estimation , arXiv:1702.00473
2017
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2017
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Emmanuel Abbe, Community detection and stochastic block models: Recent developments , Journal of Machine Learning Research 18
2018
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Yuxin Chen and Emmanuel J Candès, The projected power method: An efficient algorithm for joint alignment from pairwise differences , Communications on Pure and Applied Mathematics 71
2018
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Alyson K Fletcher and Sundeep Rangan, Iterative reconstruction of rank-one matrices in noise , Information and Inference: A Journal of the IMA 7
2018
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Raphael Berthier, Andrea Montanari, and Phan-Minh Nguyen, State evolution for approximate message passing with non-separable functions , Information and Inference: A Journal of the IMA (2019)
2019
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Marc Lelarge and Léo Miolane, Fundamental limits of symmetric low-rank matrix estimation , Probability Theory and Related Fields 173
2019
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