
Statistical limits of dictionary learning: random matrix theory and the spectral replica method
We consider increasingly complex models of matrix denoising and dictiona...
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Performance of Bayesian linear regression in a model with mismatch
For a model of highdimensional linear regression with random design, we...
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Highdimensional inference: a statistical mechanics perspective
Statistical inference is the science of drawing conclusions about some s...
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Strong replica symmetry for highdimensional disordered logconcave Gibbs measures
We consider a generic class of logconcave, possibly random, (Gibbs) mea...
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Information theoretic limits of learning a sparse rule
We consider generalized linear models in regimes where the number of non...
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Allornothing statistical and computational phase transitions in sparse spiked matrix estimation
We determine statistical and computational limits for estimation of a ra...
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Informationtheoretic limits of a multiview lowrank symmetric spiked matrix model
We consider a generalization of an important class of highdimensional i...
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Strong replica symmetry in highdimensional optimal Bayesian inference
We consider generic optimal Bayesian inference, namely, models of signal...
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Highdimensional rankone nonsymmetric matrix decomposition: the spherical case
We consider the problem of estimating a rankone nonsymmetric matrix und...
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01 phase transitions in sparse spiked matrix estimation
We consider statistical models of estimation of a rankone matrix (the s...
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Blind calibration for compressed sensing: State evolution and an online algorithm
Compressed sensing, allows to acquire compressible signals with a small ...
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Concentration of the matrixvalued minimum meansquare error in optimal Bayesian inference
We consider Bayesian inference of signals with vectorvalued entries. Ex...
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Mutual Information for LowRank EvenOrder Symmetric Tensor Factorization
We consider a statistical model for finiterank symmetric tensor factori...
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Overlap matrix concentration in optimal Bayesian inference
We consider models of Bayesian inference of signals with vectorial compo...
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Mutual Information for the Stochastic Block Model by the Adaptive Interpolation Method
We rigorously derive a singleletter variational expression for the mutu...
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The adaptive interpolation method for proving replica formulas. Applications to the CurieWeiss and Wigner spike models
In this contribution we give a pedagogic introduction to the newly intro...
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Rankone matrix estimation: analysis of algorithmic and information theoretic limits by the spatial coupling method
Factorizing lowrank matrices is a problem with many applications in mac...
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The committee machine: Computational to statistical gaps in learning a twolayers neural network
Heuristic tools from statistical physics have been used in the past to l...
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Adaptive Path Interpolation for Sparse Systems: Application to a Simple Censored Block Model
A new adaptive path interpolation method has been recently developed as ...
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Entropy and mutual information in models of deep neural networks
We examine a class of deep learning models with a tractable method to co...
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The Mutual Information in Random Linear Estimation Beyond i.i.d. Matrices
There has been definite progress recently in proving the variational sin...
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Phase Transitions, Optimal Errors and Optimality of MessagePassing in Generalized Linear Models
We consider generalized linear models (GLMs) where an unknown ndimensio...
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Jean Barbier
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