212 citations · 1.1k across the 42 of their papers we have counts for
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The Layered Structure of Tensor Estimation and its Mutual Information
Jean Barbier, Nicolas Macris, Léo Miolane
We consider rank-one non-symmetric tensor estimation and derive simple formulas for the mutual information. We start by the order 2 problem, namely matrix factorization. We treat i…
Optimal Errors and Phase Transitions in High-Dimensional Generalized Linear Models
Jean Barbier, Florent Krzakala, Nicolas Macris +2
Generalized linear models (GLMs) arise in high-dimensional machine learning, statistics, communications and signal processing. In this paper we analyze GLMs when the data matrix is…
Universal Sparse Superposition Codes with Spatial Coupling and GAMP Decoding
Jean Barbier, Mohamad Dia, Nicolas Macris
Sparse superposition codes, or sparse regression codes, constitute a new class of codes which was first introduced for communication over the additive white Gaussian noise (AWGN) c…
The adaptive interpolation method: A simple scheme to prove replica formulas in Bayesian inference
Jean Barbier, Nicolas Macris
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…
I-MMSE relations in random linear estimation and a sub-extensive interpolation method
Jean Barbier, Nicolas Macris
Consider random linear estimation with Gaussian measurement matrices and noise. One can compute infinitesimal variations of the mutual information under infinitesimal variations of…
Generalized Approximate Message-Passing Decoder for Universal Sparse Superposition Codes
Erdem Biyik, Jean Barbier, Mohamad Dia
Sparse superposition (SS) codes were originally proposed as a capacity-achieving communication scheme over the additive white Gaussian noise channel (AWGNC) [1]. Very recently, it…