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07/11/2023
Fundamental limits of overparametrized shallow neural networks for supervised learning
We carry out an information-theoretical analysis of a two-layer neural n...
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06/02/2023
Matrix Inference in Growing Rank Regimes
The inference of a large symmetric signal-matrix 𝐒∈ℝ^N× N corrupted by a...
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03/15/2023
Capacity-Achieving Sparse Regression Codes via Vector Approximate Message Passing
Sparse regression codes (SPARCs) are a promising coding scheme that can ...
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02/07/2023
Mismatched estimation of non-symmetric rank-one matrices corrupted by structured noise
We study the performance of a Bayesian statistician who estimates a rank...
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10/03/2022
Bayes-optimal limits in structured PCA, and how to reach them
We study the paradigmatic spiked matrix model of principal components an...
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05/20/2022
The price of ignorance: how much does it cost to forget noise structure in low-rank matrix estimation?
We consider the problem of estimating a rank-1 signal corrupted by struc...
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05/18/2022
Sparse superposition codes with rotational invariant coding matrices for memoryless channels
We recently showed in [1] the superiority of certain structured coding m...
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05/02/2022
The mighty force: statistical inference and high-dimensional statistics
This is a review to appear as a contribution to the edited volume "Spin ...
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02/09/2022
Sparse superposition codes under VAMP decoding with generic rotational invariant coding matrices
Sparse superposition codes were originally proposed as a capacity-achiev...
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09/14/2021
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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07/14/2021
Performance of Bayesian linear regression in a model with mismatch
For a model of high-dimensional linear regression with random design, we...
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10/28/2020
High-dimensional inference: a statistical mechanics perspective
Statistical inference is the science of drawing conclusions about some s...
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09/27/2020
Strong replica symmetry for high-dimensional disordered log-concave Gibbs measures
We consider a generic class of log-concave, possibly random, (Gibbs) mea...
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06/19/2020
Information theoretic limits of learning a sparse rule
We consider generalized linear models in regimes where the number of non...
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06/14/2020
All-or-nothing 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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05/16/2020
Information-theoretic limits of a multiview low-rank symmetric spiked matrix model
We consider a generalization of an important class of high-dimensional i...
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05/06/2020
Strong replica symmetry in high-dimensional optimal Bayesian inference
We consider generic optimal Bayesian inference, namely, models of signal...
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04/15/2020
High-dimensional rank-one nonsymmetric matrix decomposition: the spherical case
We consider the problem of estimating a rank-one nonsymmetric matrix und...
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11/12/2019
0-1 phase transitions in sparse spiked matrix estimation
We consider statistical models of estimation of a rank-one matrix (the s...
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10/01/2019
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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07/15/2019
Concentration of the matrix-valued minimum mean-square error in optimal Bayesian inference
We consider Bayesian inference of signals with vector-valued entries. Ex...
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04/09/2019
Mutual Information for Low-Rank Even-Order Symmetric Tensor Factorization
We consider a statistical model for finite-rank symmetric tensor factori...
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04/04/2019
Overlap matrix concentration in optimal Bayesian inference
We consider models of Bayesian inference of signals with vectorial compo...
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02/19/2019
Mutual Information for the Stochastic Block Model by the Adaptive Interpolation Method
We rigorously derive a single-letter variational expression for the mutu...
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01/19/2019
The adaptive interpolation method for proving replica formulas. Applications to the Curie-Weiss and Wigner spike models
In this contribution we give a pedagogic introduction to the newly intro...
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12/06/2018
Rank-one matrix estimation: analysis of algorithmic and information theoretic limits by the spatial coupling method
Factorizing low-rank matrices is a problem with many applications in mac...
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06/14/2018
The committee machine: Computational to statistical gaps in learning a two-layers neural network
Heuristic tools from statistical physics have been used in the past to l...
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06/13/2018
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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05/24/2018
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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02/25/2018
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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08/10/2017