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We consider generic optimal Bayesian inference, namely, models of signal reconstruction where the posterior distribution and all hyperparameters are known.
Solvable model of a spin glass
D. Sherrington and S. Kirkpatrick · 1975
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Infinite number of order parameters for spin-glasses
G. Parisi · 1979
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A sequence of approximated solutions to the SK model for spin glasses
Giorgio Parisi · 1980
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Representations for partially exchangeable arrays of random variables
D. Aldous · 1981
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Row-column exchangeability and a generalized model for probability
D. Hoover · 1982
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Order parameter for spin glasses
G. Parisi · 1983
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Spin-Glass Theory and Beyond
M. Mézard, G. Parisi, and M. A. Virasoro · 1987
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Optimal storage properties of neural network models
E. Gardner and B. Derrida · 1988
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The absence of the selfaverageness of the order parameter in the Sherrington-Kirkpatrick model
L. Pastur and M. Shcherbina · 1991
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The replica symmetric solution without replica trick for the Hopfield model
L. Pastur, M. Shcherbina, and B. Tirozzi · 1994
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On the stability of the quenched state in mean-field spin-glass models
M. Aizenman and P. Contucci · 1998
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General properties of overlap probability distributions in disordered spin systems. towards Parisi ultrametricity
S. Ghirlanda and F. Guerra · 1998
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The Sherrington-Kirkpatrick model: A challenge for mathematicians
M. Talagrand · 1998
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On the distribution of the largest eigenvalue in principal components analysis
I. M. Johnstone · 2001
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The Bethe lattice spin glass revisited
M. Mézard and G. Parisi · 2001
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Statistical Physics of Spin Glasses and Information Processing: an Introduction
H. Nishimori · 2001
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The high temperature case for the random k k -sat problem
M. Talagrand · 2001
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The thermodynamic limit in mean field spin glass models
F. Guerra and F. Toninelli · 2002
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Analytic and algorithmic solution of random satisfiability problems
M. Mézard, G. Parisi, and R. Zecchina · 2002
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Extended variational principle for the Sherrington-Kirkpatrick spin-glass model
M. Aizenman, R. Sims, and S. Starr · 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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Replica broken bounds in the mean field spin glass model
F. Guerra · 2003
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Bounds for diluted mean-field spin glass models
D. Panchenko and M. Talagrand · 2004
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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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Mutual information and minimum mean-square error in Gaussian channels
D. Guo, S. Shamai, and S. Verdu · 2005
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Counting good truth assignments of random k k -sat formulae
A. Montanari and D. Shah · 2006
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The Parisi formula
M. Talagrand · 2006
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Stability properties and probability distributions of multi-overlaps in dilute spin glasses
A. Barra and L. De Sanctis · 2007
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Gibbs states and the set of solutions of random constraint satisfaction problems
F. Krzakala, A. Montanari, F. Ricci-Tersenghi, G. Semerjian, and L. Zdeborová · 2007
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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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Estimating random variables from random sparse observations
A. Montanari · 2008
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Modern coding theory
T. Richardson and R. Urbanke · 2008
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On the structure of quasi-stationary competing particles systems
L.-P. Arguin and M. Aizenman · 2009
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Spin glass identities and the Nishimori line
P. Contucci, C. Giardina, and H. Nishimori · 2009
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Self-averaging identities for random spin systems
L. de Sanctis and S. Franz · 2009
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Message-passing algorithms for compressed sensing
D. Donoho, A. Maleki, and A. Montanari · 2009
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Sparse principal components analysis
I. M. Johnstone and A. Y. Lu · 2009
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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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Inference in Deep Networks in High Dimensions
A. K. Fletcher and S. Rangan · 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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Multi-layer generalized linear estimation
A. Manoel, F. Krzakala, M. Mézard, and L. Zdeborová · 2017
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Fundamental limits of low-rank matrix estimation: the non-symmetric case
Léo Miolane · 2017
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Hiding quiet solutions in random constraint satisfaction problems
F. Krzakala and L. Zdeborová · 2009
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Sharp bounds for optimal decoding of low-density parity-check codes
S. Kudekar and N. Macris · 2009
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Information, Physics and Computation
M. Mézard and A. Montanari · 2009
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Toward fast reliable communication at rates near capacity with gaussian noise
A. R. Barron and A. Joseph · 2010
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Tight bounds on the capacity of binary input random CDMA systems
S. B. Korada and N. Macris · 2010
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A connection between the Ghirlanda–Guerra identities and ultrametricity
D. Panchenko · 2010
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Additivity of Information in Multilayer Networks via Additive Gaussian Noise Transforms
G. Reeves · 2017
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Capacity-achieving sparse superposition codes via approximate message passing decoding
C. Rush, A. Greig, and R. Venkataramanan · 2017
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The committee machine: computational to statistical gaps in learning a two-layers neural network
B. Aubin, A. Maillard, J. Barbier, F. Krzakala, N. Macris, and L. Zdeborová · 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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The mutual information in random linear estimation beyond iid matrices
J. Barbier, N. Macris, A. Maillard, and F. Krzakala · 2018
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Phase transition in random tensors with multiple spikes
W.-K. Chen, M. Handschy, and G. Lerman · 2018
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Charting the replica symmetric phase
A. Coja-Oghlan, C. Efthymiou, N. Jaafari, M. Kang, and T. Kapetanopoulos · 2018
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The replica symmetric phase of random constraint satisfaction problems
A. Coja-Oghlan, T. Kapetanopoulos, and N. Müller · 2018
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Information-theoretic thresholds from the cavity method
A. Coja-Oghlan, F. Krzakala, W. Perkins, and L. Zdeborová · 2018
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Estimation in the spiked wigner model: a short proof of the replica formula
A. El Alaoui and F. Krzakala · 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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Entropy and mutual information in models of deep neural networks
Marylou Gabrié, Andre Manoel, Clément Luneau, Jean Barbier, Nicolas Macris, Florent Krzakala, and Lenka Zdeborová · 2018
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Fundamental limits of symmetric low-rank matrix estimation
M. Lelarge and L. Miolane · 2018
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Free energy in the mixed p p -spin models with vector spins
D. Panchenko · 2018
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Free energy in the Potts spin glass
D. Panchenko · 2018
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Optimality and sub-optimality of PCA I: Spiked random matrix models
A. Perry, A. Wein, A. Bandeira, and A. Moitra · 2018
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The spiked matrix model with generative priors
Benjamin Aubin, Bruno Loureiro, Antoine Maillard, Florent Krzakala, and Lenka Zdeborová · 2019
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Overlap matrix concentration in optimal Bayesian inference
J. Barbier · 2019
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Concentration of multi-overlaps for random ferromagnetic spin models
J. Barbier, C.-L. Chan, and N. Macris · 2019
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Optimal errors and phase transitions in high-dimensional generalized linear models
J. Barbier, F. Krzakala, N. Macris, L. Miolane, and L. Zdeborová · 2019
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0-1 phase transitions in sparse spiked matrix estimation
J. Barbier and N. Macris · 2019
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The adaptive interpolation method: a simple scheme to prove replica formulas in Bayesian inference
J. Barbier and N. Macris · 2019
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The adaptive interpolation method for proving replica formulas. Applications to the Curie–Weiss and Wigner spike models
J. Barbier and N. Macris · 2019
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Phase transition in the spiked random tensor with Rademacher prior
W.-K. Chen · 2019
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Asymptotics of MAP inference in deep networks
Parthe Pandit, Mojtaba Sahraee, Sundeep Rangan, and Alyson K. Fletcher · 2019
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Statistical limits of spiked tensor models
A. Perry, A. Wein, and A. Bandeira · 2020
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