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We study a class of Approximate Message Passing (AMP) algorithms for symmetric and rectangular spiked random matrix models with orthogonally invariant noise.
A CDMA multiuser detection algorithm on the basis of belief propagation
Yoshiyuki Kabashima · 2003
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Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
Jinho Baik, Gérard Ben Arous, and Sandrine Péché · 2005
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Eigenvalues of large sample covariance matrices of spiked population models
Jinho Baik and Jack W Silverstein · 2006
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Asymptotics of sample eigenstructure for a large dimensional spiked covariance model
Debashis Paul · 2007
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Rectangular random matrices, related convolution
Florent Benaych-Georges · 2009
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Message-passing algorithms for compressed sensing
David L Donoho, Arian Maleki, and Andrea Montanari · 2009
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Message passing algorithms for compressed sensing: I. Motivation and construction
David L Donoho, Arian Maleki, and Andrea Montanari · 2010
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Message passing algorithms for compressed sensing: II. Analysis and validation
David L Donoho, Arian Maleki, and Andrea Montanari · 2010
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Approximate message passing algorithms for compressed sensing
Arian Maleki · 2010
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The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices
Florent Benaych-Georges and Raj Rao Nadakuditi · 2011
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The dynamics of message passing on dense graphs, with applications to compressed sensing
Mohsen Bayati and Andrea Montanari · 2011
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The LASSO risk for Gaussian matrices
Mohsen Bayati and Andrea Montanari · 2011
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The singular values and vectors of low rank perturbations of large rectangular random matrices
Florent Benaych-Georges and Raj Rao Nadakuditi · 2012
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Probabilistic reconstruction in compressed sensing: algorithms, phase diagrams, and threshold achieving matrices
Florent Krzakala, Marc Mézard, Francois Sausset, Yifan Sun, and Lenka Zdeborová · 2012
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Iterative estimation of constrained rank-one matrices in noise
Sundeep Rangan and Alyson K Fletcher · 2012
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Weakly differentiable functions: Sobolev spaces and functions of bounded variation
William P Ziemer · 2012
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Information-theoretically optimal compressed sensing via spatial coupling and approximate message passing
David L Donoho, Adel Javanmard, and Andrea Montanari · 2013
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State evolution for general approximate message passing algorithms, with applications to spatial coupling
Adel Javanmard and Andrea Montanari · 2013
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Asymptotic analysis of complex LASSO via complex approximate message passing (CAMP)
Arian Maleki, Laura Anitori, Zai Yang, and Richard G Baraniuk · 2013
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An iterative construction of solutions of the TAP equations for the Sherrington–Kirkpatrick model
Erwin Bolthausen · 2014
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Information-theoretically optimal sparse PCA
Yash Deshpande and Andrea Montanari · 2014
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Universality in polytope phase transitions and message passing algorithms
Mohsen Bayati, Marc Lelarge, and Andrea Montanari · 2015
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Adaptive damping and mean removal for the generalized approximate message passing algorithm
Jeremy Vila, Philip Schniter, Sundeep Rangan, Florent Krzakala, and Lenka Zdeborová · 2015
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High dimensional robust M-estimation: Asymptotic variance via approximate message passing
David Donoho and Andrea Montanari · 2016
Cited alongside, same era.
Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula
A unified framework of state evolution for message-passing algorithms
Keigo Takeuchi · 2019
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Algorithmic analysis and statistical estimation of SLOPE via approximate message passing
Zhiqi Bu, Jason M Klusowski, Cynthia Rush, and Weijie J Su · 2020
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Mutual information and optimality of approximate message-passing in random linear estimation
Jean Barbier, Nicolas Macris, Mohamad Dia, and Florent Krzakala · 2020
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State evolution for approximate message passing with non-separable functions
Raphael Berthier, Andrea Montanari, and Phan-Minh Nguyen · 2020
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A dynamical mean-field theory for learning in restricted Boltzmann machines
Burak Çakmak and Manfred Opper · 2020
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Approximate message passing algorithms for rotationally invariant matrices
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Mohamad Dia, Nicolas Macris, Florent Krzakala, Thibault Lesieur, and Lenka Zdeborová · 2016
Cited alongside, same era.
A theory of solving TAP equations for Ising models with general invariant random matrices
Manfred Opper, Burak Çakmak, and Ole Winther · 2016
Cited alongside, same era.
Vector approximate message passing for the generalized linear model
Philip Schniter, Sundeep Rangan, and Alyson K Fletcher · 2016
Cited alongside, same era.
Asymptotic mutual information for the balanced binary stochastic block model
Yash Deshpande, Emmanuel Abbe, and Andrea Montanari · 2017
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Orthogonal AMP
Junjie Ma and Li Ping · 2017
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Free probability and random matrices
James A Mingo and Roland Speicher · 2017
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False discoveries occur early on the lasso path
Weijie Su, Malgorzata Bogdan, and Emmanuel Candes · 2017
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Zhou Fan · 2020
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Bayes-optimal convolutional AMP
Keigo Takeuchi · 2020
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Convolutional approximate message-passing
Keigo Takeuchi · 2020
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Empirical bayes pca in high dimensions
Xinyi Zhong, Chang Su, and Zhou Fan · 2020
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Local convexity of the TAP free energy and AMP convergence for Z2-synchronization
Michael Celentano, Zhou Fan, and Song Mei · 2021
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Universality of approximate message passing algorithms
Wei-Kuo Chen and Wai-Kit Lam · 2021
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A unifying tutorial on Approximate Message Passing
Oliver Y Feng, Ramji Venkataramanan, Cynthia Rush, and Richard J Samworth · 2021
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The replica-symmetric free energy for Ising spin glasses with orthogonally invariant couplings
Zhou Fan and Yihong Wu · 2021
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Memory approximate message passing
Lei Liu, Shunqi Huang, and Brian M Kurkoski · 2021
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Approximate message passing with spectral initialization for generalized linear models
Marco Mondelli and Ramji Venkataramanan · 2021
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PCA initialization for Approximate Message Passing in rotationally invariant models
Marco Mondelli and Ramji Venkataramanan · 2021
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Estimation of low-rank matrices via approximate message passing
Andrea Montanari and Ramji Venkataramanan · 2021
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Estimation in rotationally invariant generalized linear models via approximate message passing
Ramji Venkataramanan, Kevin Kögler, and Marco Mondelli · 2022
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Fundamental limits in structured principal component analysis and how to reach them
Jean Barbier, Francesco Camilli, Marco Mondelli, and Manuel Sáenz · 2023
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