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We consider a broad class of Approximate Message Passing (AMP) algorithms defined as a Lipschitzian functional iteration in terms of an $n\times n$ random symmetric matrix $A$.
Solvable model of a spin-glass
D. Sherrington and S. Kirkpatrick · 1975
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On the distribution of the largest eigenvalue in principal components analysis
I. M. Johnstone · 2001
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Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
J. Baik, G. Ben Arous, and S. Péché · 2005
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Eigenvalues of large sample covariance matrices of spiked population models
J. Baik and J. W. Silverstein · 2006
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The largest eigenvalue of small rank perturbations of Hermitian random matrices
S. Péché · 2006
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The largest eigenvalue of rank one deformation of large Wigner matrices
D. Féra and S. Péché · 2007
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Asymptotics of the leading sample eigenvalues for a spiked covariance model
D. Paul · 2007
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The largest eigenvalues of finite rank deformation of large Wigner matrices: convergence and nonuniversality of the fluctuations
M. Capitaine, C. Donati-Martin, and D. Féral · 2009
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Message-passing algorithms for compressed sensing
D. L. Donoho, A. Maleki, and A. Montanari · 2009
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Message passing algorithms for compressed sensing: I. motivation and construction
D. L. Donoho, A. Maleki, and A. Montanari · 2010
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The dynamics of message passing on dense graphs, with applications to compressed sensing
M. Bayati and A. Montanari · 2011
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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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The singular values and vectors of low rank perturbations of large rectangular random matrices
F. Benaych-Georges and R. R. Nadakuditi · 2012
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Iterative estimation of constrained rank-one matrices in noise
S. Rangan and A. K. Fletcher · 2012
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Information-theoretically optimal compressed sensing via spatial coupling and approximate message passing
D. L. Donoho, A. Javanmard, and A. Montanari · 2013
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Accurate prediction of phase transitions in compressed sensing via a connection to minimax denoising
D. L. Donoho, I. Johnstone, and A. Montanari · 2013
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State evolution for general approximate message passing algorithms, with applications to spatial coupling
A. Javanmard and A. Montanari · 2013
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The isotropic semicircle law and deformation of Wigner matrices
A. Knowles and J. Yin · 2013
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Information-theoretically optimal sparse PCA
Phase transitions and sample complexity in Bayes-optimal matrix factorization
Y. Kabashima, F. Krzakala, M. Mézard, A. Sakata, and L. Zdeborová · 2016
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Mutual information in rank-one matrix estimation
F. Krzakala, J. Xu, and L. Zdeborová · 2016
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Non-negative principal component analysis: message passing algorithms and sharp asymptotics
A. Montanari and E. Richard · 2016
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State evolution for approximate message passing with non-separable functions
R. Berthier, A. Montanari, and P.-M. Nguyen · 2017
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Asymptotic mutual information for the balanced binary stochastic block model
Y. Deshpande, E. Abbe, and A. Montanari · 2017
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Y. Deshpande and A. Montanari · 2014
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Bilinear generalized approximate message passing—Part I: Derivation
J. T. Parker, P. Schniter, and V. Cevher · 2014
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Bilinear generalized approximate message passing—Part II: Applications
J. T. Parker, P. Schniter, and V. Cevher · 2014
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Universality in polytope phase transitions and message passing algorithms
M. Bayati, M. Lelarge, and A. Montanari · 2015
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Finding hidden cliques of size
Y. Deshpande and A. Montanari · 2015
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Hyperspectral unmixing via turbo bilinear approximate message passing
J. Vila, P. Schniter, and J. Meola · 2015
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Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula
J. Barbier, M. Dia, N. Macris, F. Krzakala, T. Lesieur, and L. Zdeborová · 2016
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M. Lelarge and L. Miolane · 2017
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Constrained low-rank matrix estimation: phase transitions, approximate message passing and applications
T. Lesieur, F. Krzakala, and L. Zdeborová · 2017
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Fundamental limits of symmetric low-rank matrix estimation: the non-symmetric case
L. Miolane · 2017
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Estimation of law-rank matrices via approximate message passing
A. Montanari and R. Venkataramanan · 2017
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High-dimensional probability
R. Vershynin · 2018
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Optimization of the sherrington-kirkpatrick hamiltonian
A. Montanari · 2019
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Optimization of mean-field spin glasses
A. El Alaoui, A. Montanari, and M. Sellke · 2020
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