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We consider the problem of estimating a rank-one perturbation of a Wigner matrix in a setting of low signal-to-noise ratio.
Recipes for metastable states in spin glasses
Silvio Franz and Giorgio Parisi · 1995
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Effective potential in glassy systems: theory and simulations
Silvio Franz and Giorgio Parisi · 1998
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Sum rules for the free energy in the mean field spin glass model
Francesco Guerra · 2001
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On the distribution of the largest eigenvalue in principal components analysis
Iain M Johnstone · 2001
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Statistical physics of spin glasses and information processing: an introduction
Hidetoshi Nishimori · 2001
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The thermodynamic limit in mean field spin glass models
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Extended variational principle for the Sherrington-Kirkpatrick spin-glass model
Michael Aizenman, Robert Sims, and Shannon L Starr · 2003
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Jinho Baik, Gérard Ben Arous, and Sandrine Péché · 2005
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The largest eigenvalue of small rank perturbations of Hermitian random matrices
Sandrine Péché · 2006
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Emile Richard and Andrea Montanari · 2014
Asymptotic mutual information for the binary stochastic block model
Yash Deshpande, Emmanuel Abbé, and Andrea Montanari · 2016
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Mutual information in rank-one matrix estimation
Florent Krzakala, Jiaming Xu, and Lenka Zdeborová · 2016
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Fundamental limits of symmetric low-rank matrix estimation
Marc Lelarge and Léo Miolane · 2016
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Phase transitions, optimal errors and optimality of message-passing in generalized linear models
Jean Barbier, Florent Krzakala, Nicolas Macris, Léo Miolane, and Lenka Zdeborová · 2017
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The stochastic interpolation method: A simple scheme to prove replica formulas in bayesian inference
Jean Barbier and Nicolas Macris · 2017
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Phase transitions in sparse PCA
Thibault Lesieur, Florent Krzakala, and Lenka Zdeborová · 2015
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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
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The layered structure of tensor estimation and its mutual information
Jean Barbier, Nicolas Macris, and Léo Miolane · 2017
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Finite size corrections and likelihood ratio fluctuations in the spiked Wigner model
Ahmed El Alaoui, Florent Krzakala, and Michael I Jordan · 2017
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Statistical and computational phase transitions in spiked tensor estimation
Thibault Lesieur, Léo Miolane, Marc Lelarge, Florent Krzakala, and Lenka Zdeborová · 2017
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