Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula

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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An introduction to mean field spin glass theory: methods and results

F. Guerra · 2005

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Mutual information and minimum mean-square error in gaussian channels

D. Guo, S. Shamai, and S. Verdú · 2005

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Sparse principal component analysis

H. Zou, T. Hastie, and R. Tibshirani · 2006

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A direct formulation for sparse pca using semidefinite programming

A. d’Aspremont, L. El Ghaoui, M.I. Jordan, and G.RG. Lanckriet · 2007

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High-dimensional analysis of semidefinite relaxations for sparse principal components

A.A. Amini and M.J. Wainwright · 2008

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Exact matrix completion via convex optimization

E.J. Candès and B. Recht · 2009

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Exact solution of the gauge symmetric p-spin glass model on a complete graph

S.B. Korada and N. Macris · 2009

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Coupled graphical models and their thresholds

S.H. Hassani, N. Macris, and R. Urbanke · 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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Threshold saturation via spatial coupling: Why convolutional ldpc ensembles perform so well over the bec

S. Kudekar, T.J. Richardson, and R. Urbanke · 2011

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On consistency and sparsity for principal components analysis in high dimensions

I.M. Johnstone and A.Y. Lu · 2012

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Iterative estimation of constrained rank-one matrices in noise

S. Rangan and A.K. Fletcher · 2012

State evolution for general approximate message passing algorithms, with applications to spatial coupling

A. Javanmard and A. Montanari · 2013

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Information-theoretically optimal sparse pca

Y. Deshpande and A. Montanari · 2014

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A simple proof of maxwell saturation for coupled scalar recursions

A. Yedla, Y.Y. Jian, P.S. Nguyen, and H.D. Pfister · 2014

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Finding hidden cliques of size N / e \sqrt{N/e} in nearly linear time

Y. Deshpande and A. Montanari · 2015

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Asymptotic mutual information for the two-groups stochastic block model

Original

Y. Deshpande, E. Abbe, and A. Montanari · 2015

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Threshold saturation of spatially coupled sparse superposition codes for all memoryless channels