Publications related to The Mutual Information in Random Linear Estimation Beyond i.i.d. Matrices

Mutual Information and Optimality of Approximate Message-Passing in Random Linear Estimation

Nicolas Macris, Florent Gérard Krzakala, Jean François Emmanuel Barbier, Mohamad Baker Dia

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, sparse superposition codes, and code division multiple access. There has been a ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Liouville Measure As A Multiplicative Cascade Via Level Sets Of The Gaussian Free Field

Juhan Aru

We provide new constructions of the subcritical and critical Gaussian multiplicative chaos (GMC) measures corresponding to the 2D Gaussian free field (GFF). As a special case we recover E. Aidekon's construction of random measures using nested conformally ...

ANNALES INST FOURIER2020

Global eigenvalue distribution of matrices defined by the skew-shift

Marius Christopher Lemm

We consider large Hermitian matrices whose entries are defined by evaluating the exponential function along orbits of the skew-shift

\binom{j}{2} \omega+jy+x \mod 1

for irrational

\omega

. We prove that the eigenvalue distribution of these matrices conv ...

2019

MATHICSE Technical Report: A posteriori error estimation for the stochastic collocation finite element approximation of the heat equation with random coefficients

Fabio Nobile, Eva Vidlicková

In this work we present a residual based a posteriori error estimation for a heat equation with a random forcing term and a random diffusion coefficient which is assumed to depend affinely on a finite number of independent random variables. The problem is ...

MATHICSE2019

Statistical Applications of Random Matrix Theory: Comparison of Two Populations

Rémy Mariétan

During the last twenty years, Random matrix theory (RMT) has produced numerous results that allow a better understanding of large random matrices. These advances have enabled interesting applications in the domain of communication. Although this theory can ...

EPFL2019

Optimal errors and phase transitions in high-dimensional generalized linear models

Nicolas Macris, Florent Gérard Krzakala, Lenka Zdeborová, Jean François Emmanuel Barbier

Generalized linear models (GLMs) are used in high-dimensional machine learning, statistics, communications, and signal processing. In this paper we analyze GLMs when the data matrix is random, as relevant in problems such as compressed sensing, error-corre ...

PNAS2019

The adaptive interpolation method: a simple scheme to prove replica formulas in Bayesian inference

Nicolas Macris, Jean François Emmanuel Barbier

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 inference problems. The proof techniques that have emerged appear to be quite ...

SPRINGER HEIDELBERG2019

A Posteriori Error Estimation for the Stochastic Collocation Finite Element Method

Fabio Nobile, Diane Sylvie Guignard

In this work, we consider an elliptic partial differential equation (PDE) with a random coefficient solved with the stochastic collocation finite element method (SC-FEM). The random diffusion coefficient is assumed to depend in an affine way on independent ...

2018

A posteriori error estimation for the steady Navier-Stokes equations in random domains

Fabio Nobile, Marco Picasso, Diane Sylvie Guignard

We consider finite element error approximations of the steady incompressible Navier-Stokes equations defined on a randomly perturbed domain, the perturbation being small. Introducing a random mapping, these equations are transformed into PDEs on a fixed re ...

Elsevier2017

MATHICSE Technical Report : A posteriori error estimation for the stochastic collocation finite element method

Fabio Nobile, Diane Sylvie Guignard

In this work, we consider an elliptic partial differential equation with a random coefficient solved with the stochastic collocation finite element method. The random diffusion coefficient is assumed to depend in an affine way on independent random variabl ...

MATHICSE2017

The Mutual Information in Random Linear Estimation Beyond i.i.d. Matrices

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Mutual Information and Optimality of Approximate Message-Passing in Random Linear Estimation

Liouville Measure As A Multiplicative Cascade Via Level Sets Of The Gaussian Free Field

Global eigenvalue distribution of matrices defined by the skew-shift

MATHICSE Technical Report: A posteriori error estimation for the stochastic collocation finite element approximation of the heat equation with random coefficients

Statistical Applications of Random Matrix Theory: Comparison of Two Populations

Optimal errors and phase transitions in high-dimensional generalized linear models

The adaptive interpolation method: a simple scheme to prove replica formulas in Bayesian inference

A Posteriori Error Estimation for the Stochastic Collocation Finite Element Method

A posteriori error estimation for the steady Navier-Stokes equations in random domains

MATHICSE Technical Report : A posteriori error estimation for the stochastic collocation finite element method

Global eigenvalue distribution of matrices defined by the skew-shift

Liouville Measure As A Multiplicative Cascade Via Level Sets Of The Gaussian Free Field

Statistical Applications of Random Matrix Theory: Comparison of Two Populations

Mutual Information and Optimality of Approximate Message-Passing in Random Linear Estimation

MATHICSE Technical Report: A posteriori error estimation for the stochastic collocation finite element approximation of the heat equation with random coefficients

The adaptive interpolation method: a simple scheme to prove replica formulas in Bayesian inference

A Posteriori Error Estimation for the Stochastic Collocation Finite Element Method

Optimal errors and phase transitions in high-dimensional generalized linear models

A posteriori error estimation for the steady Navier-Stokes equations in random domains

MATHICSE Technical Report : A posteriori error estimation for the stochastic collocation finite element method