212 citations · 1.4k across the 61 of their papers we have counts for
44 papers · 1 filter
Bayesian Extensive-Rank Matrix Factorization with Rotational Invariant Priors
Farzad Pourkamali, Nicolas Macris
We consider a statistical model for matrix factorization in a regime where the rank of the two hidden matrix factors grows linearly with their dimension and their product is corrup…
Matrix Inference in Growing Rank Regimes
Farzad Pourkamali, Jean Barbier, Nicolas Macris
The inference of a large symmetric signal-matrix corrupted by additive Gaussian noise, is considered for two regimes of growth of the rank $…
Rectangular Rotational Invariant Estimator for General Additive Noise Matrices
Farzad Pourkamali, Nicolas Macris
We propose a rectangular rotational invariant estimator to recover a real matrix from noisy matrix observations coming from an arbitrary additive rotational invariant perturbation,…
Statistical limits of dictionary learning: random matrix theory and the spectral replica method
Jean Barbier, Nicolas Macris
We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank…
Mismatched Estimation of rank-one symmetric matrices under Gaussian noise
Farzad Pourkamali, Nicolas Macris
We consider the estimation of an n-dimensional vector s from the noisy element-wise measurements of , a generic problem that arises in statistics and machin…
Tensor estimation with structured priors
Clément Luneau, Nicolas Macris
We consider rank-one symmetric tensor estimation when the tensor is corrupted by Gaussian noise and the spike forming the tensor is a structured signal coming from a generalized li…
Information theoretic limits of learning a sparse rule
Clément Luneau, Jean Barbier, Nicolas Macris
We consider generalized linear models in regimes where the number of nonzero components of the signal and accessible data points are sublinear with respect to the size of the signa…
All-or-nothing statistical and computational phase transitions in sparse spiked matrix estimation
Jean Barbier, Nicolas Macris, Cynthia Rush
We determine statistical and computational limits for estimation of a rank-one matrix (the spike) corrupted by an additive gaussian noise matrix, in a sparse limit, where the under…
0-1 phase transitions in sparse spiked matrix estimation
Jean Barbier, Nicolas Macris
We consider statistical models of estimation of a rank-one matrix (the spike) corrupted by an additive gaussian noise matrix in the sparse limit. In this limit the underlying hidde…
Mutual information for low-rank even-order symmetric tensor estimation
Clément Luneau, Jean Barbier, Nicolas Macris
We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its asymptotic mutual information when the tenso…
Mutual Information for the Stochastic Block Model by the Adaptive Interpolation Method
Jean Barbier, Chun Lam Chan, Nicolas Macris
We rigorously derive a single-letter variational expression for the mutual information of the asymmetric two-groups stochastic block model in the dense graph regime. Existing proof…
Rank-one matrix estimation: analysis of algorithmic and information theoretic limits by the spatial coupling method
Jean Barbier, Mohamad Dia, Nicolas Macris +2
Factorizing low-rank matrices is a problem with many applications in machine learning and statistics, ranging from sparse PCA to community detection and sub-matrix localization. Fo…
Adaptive Path Interpolation for Sparse Systems: Application to a Simple Censored Block Model
Jean Barbier, Chun Lam Chan, Nicolas Macris
Recently a new adaptive path interpolation method has been developed as a simple and versatile scheme to calculate exactly the asymptotic mutual information of Bayesian inference p…
The Mutual Information in Random Linear Estimation Beyond i.i.d. Matrices
Jean Barbier, Nicolas Macris, Antoine Maillard +1
There has been definite progress recently in proving the variational single-letter formula given by the heuristic replica method for various estimation problems. In particular, the…
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…