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Approximate Message Passing (AMP) algorithms provide a valuable tool for studying mean-field approximations and dynamics in a variety of applications.
Multidimensional scaling of measures of distance between partitions
Phipps Arabie and Scott A Boorman · 1973
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Metrics on spaces of finite trees
Scott A Boorman and Donald C Olivier · 1973
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Free random variables
Dan V Voiculescu, Ken J Dykema, and Alexandru Nica · 1992
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Probability and measure
Patrick Billingsley · 1995
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A CDMA multiuser detection algorithm on the basis of belief propagation
Yoshiyuki Kabashima · 2003
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Neighborliness of randomly projected simplices in high dimensions
David L Donoho and Jared Tanner · 2005
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Maxima of entries of haar distributed matrices
Tiefeng Jiang · 2005
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A CLT for a band matrix model
Greg W Anderson and Ofer Zeitouni · 2006
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Integration with respect to the haar measure on unitary, orthogonal and symplectic group
Benoît Collins and Piotr Śniady · 2006
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Lectures on the combinatorics of free probability
Alexandru Nica and Roland Speicher · 2006
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Message-passing algorithms for compressed sensing
David L Donoho, Arian Maleki, and Andrea Montanari · 2009
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Observed universality of phase transitions in high-dimensional geometry, with implications for modern data analysis and signal processing
David Donoho and Jared Tanner · 2009
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Optimal transport: old and new
Cédric Villani · 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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The dynamics of message passing on dense graphs, with applications to compressed sensing
Mohsen Bayati and Andrea Montanari · 2011
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Generalized approximate message passing for estimation with random linear mixing
Sundeep Rangan · 2011
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Bulk universality for generalized Wigner matrices
László Erdős, Horng-Tzer Yau, and Jun Yin · 2012
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Rigidity of eigenvalues of generalized Wigner matrices
László Erdős, Horng-Tzer Yau, and Jun Yin · 2012
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Sharp bounds for sums associated to graphs of matrices
James A Mingo and Roland Speicher · 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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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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Deterministic matrices matching the compressed sensing phase transitions of gaussian random matrices
Hatef Monajemi, Sina Jafarpour, Matan Gavish, et al · 2013
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Asymptotically liberating sequences of random unitary matrices
Greg W Anderson and Brendan Farrell · 2014
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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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S-AMP: Approximate message passing for general matrix ensembles
Burak Cakmak, Ole Winther, and Bernard H Fleury · 2014
Cited alongside, same era.
Universality in polytope phase transitions and message passing algorithms
Mohsen Bayati, Marc Lelarge, and Andrea Montanari · 2015
Cited alongside, same era.
Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula
Jean Barbier, Mohamad Dia, Nicolas Macris, Florent Krzakala, Thibault Lesieur, and Lenka Zdeborová · 2016
Cited alongside, same era.
High dimensional robust m-estimation: Asymptotic variance via approximate message passing
David Donoho and Andrea Montanari · 2016
Cited alongside, same era.
A theory of solving tap equations for ising models with general invariant random matrices
Manfred Opper, Burak Cakmak, and Ole Winther · 2016
Cited alongside, same era.
Vector approximate message passing for the generalized linear model
Traffic distributions and independence: permutation invariant random matrices and the three notions of independence
Camille Male · 2020
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Convolutional approximate message-passing
Keigo Takeuchi · 2020
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Freeness over the diagonal for large random matrices
Benson Au, Guillaume Cébron, Antoine Dahlqvist, Franck Gabriel, and Camille Male · 2021
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Gardner formula for Ising perceptron models at small densities
Erwin Bolthausen, Shuta Nakajima, Nike Sun, and Changji Xu · 2021
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The high-dimensional asymptotics of first order methods with random data
Michael Celentano, Chen Cheng, and Andrea Montanari · 2021
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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
Cited alongside, same era.
Orthogonal amp
Junjie Ma and Li Ping · 2017
Cited alongside, same era.
Free probability and random matrices
James A Mingo and Roland Speicher · 2017
Cited alongside, same era.
The moment problem
Konrad Schmüdgen · 2017
Cited alongside, same era.
Rigorous dynamics of expectation-propagation-based signal recovery from unitarily invariant measurements
Keigo Takeuchi · 2017
Cited alongside, same era.
A Morita type proof of the replica-symmetric formula for SK
Erwin Bolthausen · 2018
Cited alongside, same era.
Universality of approximate message passing algorithms
Wei-Kuo Chen and Wai-Kit Lam · 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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Graph-based approximate message passing iterations
Cédric Gerbelot and Raphaël Berthier · 2021
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Memory approximate message passing
Lei Liu, Shunqi Huang, and Brian M Kurkoski · 2021
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Minimum ℓ 1 \ell_{1} -norm interpolators: Precise asymptotics and multiple descent
Yue Li and Yuting Wei · 2021
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Biwhitening reveals the rank of a count matrix
Boris Landa, Thomas TCK Zhang, and Yuval Kluger · 2021
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Optimization of the Sherrington–Kirkpatrick Hamiltonian
Andrea Montanari · 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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Separating measurement and expression models clarifies confusion in single-cell RNA sequencing analysis
Abhishek Sarkar and Matthew Stephens · 2021
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Bayes-optimal convolutional AMP
Keigo Takeuchi · 2021
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Xinyi Zhong, Tianhao Wang, and Zhou Fan · 2021
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Universality of approximate message passing with semi-random matrices
Rishabh Dudeja, Yue M Lu, and Subhabrata Sen · 2022
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Spectral universality of regularized linear regression with nearly deterministic sensing matrices
Rishabh Dudeja, Subhabrata Sen, and Yue M Lu · 2022
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Approximate message passing algorithms for rotationally invariant matrices
Zhou Fan · 2022
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Tap equations for orthogonally invariant spin glasses at high temperature
Zhou Fan, Yufan Li, and Subhabrata Sen · 2022
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A unifying tutorial on approximate message passing
Oliver Y. Feng, Ramji Venkataramanan, Cynthia Rush, and Richard J. Samworth · 2022
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A non-asymptotic framework for approximate message passing in spiked models
Gen Li and Yuting Wei · 2022
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Collin Cademartori and Cynthia Rush · 2023
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Gen Li, Wei Fan, and Yuting Wei · 2023
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