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In recent years important progress has been achieved towards proving the validity of the replica predictions for the (asymptotic) mutual information (or "free energy") in Bayesian inference problems.
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L. Pastur and M. Shcherbina · 1991
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L. Pastur, M. Shcherbina, and B. Tirozzi · 1994
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M. Shcherbina · 1997
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Y. Iba · 1999
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H. Nishimori · 2001
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Statistical Physics of Spin Glasses and Information Processing: an Introduction
H. Nishimori · 2001
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Quadratic replica coupling in the Sherrington- Kirkpatrick mean field spin glass model
F. Guerra and F. Toninelli · 2002
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The thermodynamic limit in mean field spin glass models
F. Guerra and F. L. Toninelli · 2002
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Spin glasses: a challenge for mathematicians: cavity and mean field models
M. Talagrand · 2003
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Replica broken bounds in the mean field spin glass model
F. Guerra · 2003
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Replica bounds for optimization problems and diluted spin systems
S. Franz and M. Leone · 2003
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Replica bounds for diluted non-poissonian spin systems
S. Franz, M. Leone, and F. Toninelli · 2003
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Extended variational principle for the sherrington-kirkpatrick spin-glass model
M. Aizenman, R. Sims, and S. L. Starr · 2003
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The infinite volume limit in generalised mean field disordered models
F. Guerra and F. Toninelli · 2003
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Bounds for diluted mean-field spin glass models
D. Panchenko and M. Talagrand · 2004
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Concentration inequalities
S. Boucheron, G. Lugosi, and O. Bousquet · 2004
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Tight bounds for LDPC and LDGM codes under map decoding
A. Montanari · 2005
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The Parisi formula
M. Talagrand · 2006
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Griffith Kelly Sherman correlation inequalities: A useful tool in the theory of error correcting codes
N. Macris · 2007
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Sharp bounds on generalized exit functions
N. Macris · 2007
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On the capacity of a code division multiple access system
S. B. Korada and N. Macris · 2007
Cited alongside, same era.
Sharp bounds for optimal decoding of low-density parity-check codes
Mutual information in rank-one matrix estimation
F. Krzakala, J. Xu, and L. Zdeborová · 2016
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Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula
J. Barbier, M. Dia, N. Macris, F. Krzakala, T. Lesieur, and L. Zdeborová · 2016
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Spatial coupling as a proof technique and three applications
A. Giurgiu, N. Macris, and R. Urbanke · 2016
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The replica-symmetric prediction for compressed sensing with gaussian matrices is exact
G. Reeves and H. D. Pfister · 2016
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The replica-symmetric prediction for compressed sensing with gaussian matrices is exact
G. Reeves and H. D. Pfister · 2016
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S. Kudekar and N. Macris · 2009
Cited alongside, same era.
Exact solution of the gauge symmetric p-spin glass model on a complete graph
S. B. Korada and N. Macris · 2009
Cited alongside, same era.
Information, Physics and Computation
M. Mézard and A. Montanari · 2009
Cited alongside, same era.
Information, physics and computation
M. Mezard and A. Montanari · 2009
Cited alongside, same era.
Tight bounds on the capacity of binary input random CDMA systems
S. B. Korada and N. Macris · 2010
Cited alongside, same era.
Mean Field Models for Spin Glasses. Volume I: Basic Examples
M. Talagrand · 2011
Cited alongside, same era.
A. Coja-Oghlan, F. Krzakala, W. Perkins, and L. Zdeborova · 2016
Later among the works it cites.
Asymptotic mutual information for the binary stochastic block model
Y. Deshpande, E. Abbe, and A. Montanari · 2016
Later among the works it cites.
I-MMSE relations in random linear estimation and a sub-extensive interpolation method
J. Barbier and N. Macris · 2017
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Statistical and computational phase transitions in spiked tensor estimation
T. Lesieur, L. Miolane, M. Lelarge, F. Krzakala, and L. Zdeborová · 2017
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Fundamental limits of low-rank matrix estimation: The non-symmetric case
L. Miolane · 2017
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The Layered Structure of Tensor Estimation and its Mutual Information
J. Barbier, N. Macris, and L. Miolane · 2017
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Phase transitions, optimal errors and optimality of message-passing in generalized linear models
J. Barbier, F. Krzakala, N. Macris, L. Miolane, and L. Zdeborová · 2017
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Constrained low-rank matrix estimation: phase transitions, approximate message passing and applications
T. Lesieur, F. Krzakala, and L. Zdeborová · 2017
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Fundamental limits of symmetric low-rank matrix estimation
M. Lelarge and L. Miolane · 2018
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Entropy and mutual information in models of deep neural networks
M. Gabrié, A. Manoel, C. Luneau, J. Barbier, N. Macris, F. Krzakala, and L. Zdeborová · 2018
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The committee machine: Computational to statistical gaps in learning a two-layers neural network
B. Aubin, A. Maillard, J. Barbier, N. Macris, F. Krzakala, and L. Zdeborová · 2018
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The Mutual Information in Random Linear Estimation Beyond i.i.d. Matrices
J. Barbier, N. Macris, A. Maillard, and F. Krzakala · 2018
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Adaptive Path Interpolation for Sparse Systems: Application to a Simple Censored Block Model
J. Barbier, C.-L. Chan, and N. Macris · 2018
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