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The dynamics of message passing on dense graphs, with applications to compressed sensing

https://doi.org/10.1109/isit.2010.5513529
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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For most large underdetermined systems of equations, the minimal 𝓁 1 ‐norm near‐solution approximates the sparsest near‐solution
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The ζ(2) limit in the random assignment problem
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Mean Field Models for Spin Glasses
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The Objective Method: Probabilistic Combinatorial Optimization and Local Weak Convergence
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Minimax risk overl p -balls forl p -error
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Modern Coding Theory
inferredcites →https://doi.org/10.1070/sm1967v001n04abeh001994openalex-snapshot
DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES
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Neighborliness of randomly projected simplices in high dimensions
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Message-passing algorithms for compressed sensing
inferredcites →https://doi.org/10.1088/0305-4470/36/43/030openalex-snapshot
A CDMA multiuser detection algorithm on the basis of belief propagation
inferredcites →https://doi.org/10.1090/s0894-0347-08-00600-0openalex-snapshot
Counting faces of randomly projected polytopes when the projection radically lowers dimension
inferredcites →https://doi.org/10.1093/acprof:oso/9780198570837.001.0001openalex-snapshot
Information, Physics, and Computation
inferredcites →https://doi.org/10.1109/18.749007openalex-snapshot
Spectral efficiency of CDMA with random spreading
inferredcites →https://doi.org/10.1109/18.749008openalex-snapshot
Linear multiuser receivers: effective interference, effective bandwidth and user capacity
inferredcites →https://doi.org/10.1109/allerton.2009.5394838openalex-snapshot
A single-letter characterization of optimal noisy compressed sensing
inferredcites →https://doi.org/10.1109/isit.2010.5513529openalex-snapshot
The dynamics of message passing on dense graphs, with applications to compressed sensing
inferredcites →https://doi.org/10.1109/itw.2006.1633802openalex-snapshot
Analysis of Belief Propagation for Non-Linear Problems: The Example of CDMA (or: How to Prove Tanaka's Formula)
inferredcites →https://doi.org/10.1109/itw2.2006.323786openalex-snapshot
Asymptotic Mean-Square Optimality of Belief Propagation for Sparse Linear Systems
inferredcites →https://doi.org/10.1109/itwksps.2010.5503193openalex-snapshot
Message passing algorithms for compressed sensing: I. motivation and construction
inferredcites →https://doi.org/10.1109/tit.2002.804053openalex-snapshot
A statistical-mechanics approach to large-system analysis of CDMA multiuser detectors
inferredcites →https://doi.org/10.1109/tit.2004.840887openalex-snapshot
Approximate Belief Propagation, Density Evolution, and Statistical Neurodynamics for CDMA Multiuser Detection
inferredcites →https://doi.org/10.1109/tit.2005.847700openalex-snapshot
Randomly Spread CDMA: Asymptotics Via Statistical Physics
inferredcites →https://doi.org/10.1109/tit.2011.2165823openalex-snapshot
The Noise-Sensitivity Phase Transition in Compressed Sensing
inferredcites →https://doi.org/10.1109/tit.2011.2174612openalex-snapshot
The LASSO Risk for Gaussian Matrices
inferredcites →https://doi.org/10.1109/tit.2011.2177575openalex-snapshot
Asymptotic Analysis of MAP Estimation via the Replica Method and Applications to Compressed Sensing
inferredcites →https://doi.org/10.1143/ptps.157.176openalex-snapshot
Statistical Physics of Information Processing in Mobile Communications
inferredcites →https://doi.org/10.1155/s0161171297000483openalex-snapshot
On the strong law for arrays and for the bootstrap mean and variance
inferredcites →https://doi.org/10.1209/epl/i2005-10148-5openalex-snapshot
Improved message passing for inference in densely connected systems
inferredcites →https://doi.org/10.1214/aop/1020107771openalex-snapshot
On the High Temperature Phase of the Sherrington-Kirkpatrick Model
inferredcites →https://doi.org/10.1214/ecp.v1-978openalex-snapshot
Percolation Beyond $Z^d$, Many Questions And a Few Answers
inferredcites →https://doi.org/10.1525/9780520423671-036openalex-snapshot
A Bound for the Error in the Normal Approximation to the Distribution of a Sum of Dependent Random Variables

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Optimal errors and phase transitions in high-dimensional generalized linear models
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Perturbative construction of mean-field equations in extensive-rank matrix factorization and denoising
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Statistical mechanics analysis of generalized multi-dimensional knapsack problems
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Statistical estimation: from denoising to sparse regression and hidden cliques
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