212 citations · 1.4k across the 61 of their papers we have counts for
11 papers · 2 filters
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…
Displacement Convexity in Spatially Coupled Scalar Recursions
Rafah El-Khatib, Nicolas Macris, Tom Richardson +1
We introduce a technique for the analysis of general spatially coupled systems that are governed by scalar recursions. Such systems can be expressed in variational form in terms of…
The Velocity of the Propagating Wave for Spatially Coupled Systems with Applications to LDPC Codes
Rafah El-Khatib, Nicolas Macris
We consider the dynamics of message passing for spatially coupled codes and, in particular, the set of density evolution equations that tracks the profile of decoding errors along…
Analysis of Coupled Scalar Systems by Displacement Convexity
Rafah El-Khatib, Nicolas Macris, Tom Richardson +1
Potential functionals have been introduced recently as an important tool for the analysis of coupled scalar systems (e.g. density evolution equations). In this contribution, we inv…
The Velocity of the Decoding Wave for Spatially Coupled Codes on BMS Channels
Rafah El-Khatib, Nicolas Macris
We consider the dynamics of belief propagation decoding of spatially coupled Low-Density Parity-Check codes. It has been conjectured that after a short transient phase, the profile…
The Velocity of the Propagating Wave for General Coupled Scalar Systems
Rafah El-Khatib, Nicolas Macris
We consider spatially coupled systems governed by a set of scalar density evolution equations. Such equations track the behavior of message-passing algorithms used, for example, in…
Mutual Information and Optimality of Approximate Message-Passing in Random Linear Estimation
Jean Barbier, Nicolas Macris, Mohamad Dia +1
We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections. A few examples where this problem is relevant are compressed sensing, spa…