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We study the problem of detecting a structured, low-rank signal matrix corrupted with additive Gaussian noise.
On the problem of the most efficient tests of statistical hypotheses
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Mutual information and minimum mean-square error in gaussian channels
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The largest eigenvalue of small rank perturbations of hermitian random matrices
S. Péché · 2006
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An investigation of computational and informational limits in gaussian mixture clustering
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Asymptotics of sample eigenstructure for a large dimensional spiked covariance model
D. Paul · 2007
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The spectral method for general mixture models
R. Kannan, H. Salmasian, and S. Vempala · 2008
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High-dimensional analysis of semidefinite relaxations for sparse principal components
A. A. Amini and M. J. Wainwright · 2009
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On consistency and sparsity for principal components analysis in high dimensions
I. M. Johnstone and A. Y. Lu · 2009
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Spectral algorithms
R. Kannan and S. Vempala · 2009
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Spectral analysis of large dimensional random matrices
Z. Bai and J. W. Silverstein · 2010
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Introduction to the non-asymptotic analysis of random matrices
R. Vershynin · 2010
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The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices
F. Benaych-Georges and R. R. Nadakuditi · 2011
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Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications
A. Decelle, F. Krzakala, C. Moore, and L. Zdeborová · 2011
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Inference and phase transitions in the detection of modules in sparse networks
A. Decelle, F. Krzakala, C. Moore, and L. Zdeborová · 2011
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Non-backtracking spectrum of random graphs: Community detection and non-regular ramanujan graphs
C. Bordenave, M. Lelarge, and L. Massoulié · 2015
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Optimal estimation and rank detection for sparse spiked covariance matrices
T. Cai, Z. Ma, and Y. Wu · 2015
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Information limits for recovering a hidden community
B. Hajek, Y. Wu, and J. Xu · 2015
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Submatrix localization via message passing
B. Hajek, Y. Wu, and J. Xu · 2015
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Do semidefinite relaxations solve sparse PCA up to the information limit?
R. Krauthgamer, B. Nadler, and D. Vilenchik · 2015
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MMSE of probabilistic low-rank matrix estimation: Universality with respect to the output channel
T. Lesieur, F. Krzakala, and L. Zdeborová · 2015
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Detection of a sparse submatrix of a high-dimensional noisy matrix
C. Butucea and Y. I. Ingster · 2013
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Spectral redemption in clustering sparse networks
F. Krzakala, C. Moore, E. Mossel, J. Neeman, A. Sly, L. Zdeborová, and P. Zhang · 2013
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Community detection in sparse random networks
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Community detection in dense random networks
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Phase transitions in sparse PCA
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Reconstruction and estimation in the planted partition model
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Lecture Notes on Information Theory
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Information-theoretic thresholds for community detection in sparse networks
J. Banks, C. Moore, J. Neeman, and P. Netrapalli · 2016
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Mutual information in rank-one matrix estimation
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Fundamental limits of symmetric low-rank matrix estimation
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Phase transitions and optimal algorithms in high-dimensional gaussian mixture clustering
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Statistical limits of spiked tensor models
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Optimality and sub-optimality of PCA for spiked random matrices and synchronization
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