Publications by Nicolas Macris

Rectangular rotational invariant estimator for high-rank matrix estimation

We consider estimating a matrix from noisy observations coming from an arbitrary additive bi-rotational invariant perturbation. We propose an estimator, which we conjecture is optimal among the class of rectangular rotational invariant estimators and can b ...

Oxford University Press (OUP)2025

On the Convergence to the Non-equilibrium Steady State of a Langevin Dynamics with Widely Separated Time Scales and Different Temperatures

Nicolas Macris, Emanuele Mingione, Diego Alberici

We study the solution of the two-temperature Fokker-Planck equation and rigorously analyse its convergence towards an explicit non-equilibrium stationary measure for long time and two widely separated time scales. The exponential rates of convergence are e ...

Springer Int Publ Ag2024

Matrix Inference in Growing Rank Regimes

Nicolas Macris, Farzad Pourkamali

The inference of a large symmetric signal-matrix S ϵ RN × N corrupted by additive Gaussian noise, is considered for two regimes of growth of the rank M as a function of N. For sub-linear ranks M=Θ (Nα) with α in (0,1) the mutual information and minimum mea ...

2024

Solving Non-linear Kolmogorov Equations in Large Dimensions by Using Deep Learning: A Numerical Comparison of Discretization Schemes

Nicolas Macris

Non-linear partial differential Kolmogorov equations are successfully used to describe a wide range of time dependent phenomena, in natural sciences, engineering or even finance. For example, in physical systems, the Allen-Cahn equation describes pattern f ...

SPRINGER/PLENUM PUBLISHERS2023

Statistical limits of dictionary learning: Random matrix theory and the spectral replica method

Nicolas Macris, Jean François Emmanuel Barbier

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 growing linearly with the system size. This is in contrast with most existin ...

AMER PHYSICAL SOC2022

Mismatched Estimation of Non-Symmetric Rank-One Matrices Under Gaussian Noise

Nicolas Macris, Farzad Pourkamali

We consider the estimation of a nxm matrix uv(T) observed through an additive Gaussian noise channel, a problem that frequently arises in statistics and machine learning. We investigate a scenario involving mismatched Bayesian inference in which the stat ...

IEEE2022

Information theoretic limits of learning a sparse rule

Nicolas Macris, Clément Dominique Luneau

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 signal. We prove a variational formula for the asymptotic mutual information per ...

IOP Publishing Ltd2022

Adaptive Path Interpolation Method for Sparse Systems: Application to a Censored Block Model

Nicolas Macris, Jean François Emmanuel Barbier, Chun Lam Chan

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 problems defined on dense factor graphs. These include random linear and gen ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

Bell Diagonal and Werner State Generation: Entanglement, Non-Locality, Steering and Discord on the IBM Quantum Computer

Nicolas Macris, Su Yeon Chang, Marc-André Dupertuis, Chun Lam Chan, Samuel Bosch, Nicolas Schwaller, Frédéric Gessler

We propose the first correct special-purpose quantum circuits for preparation of Bell diagonal states (BDS), and implement them on the IBM Quantum computer, characterizing and testing complex aspects of their quantum correlations in the full parameter spac ...

2021

Mutual information for low-rank even-order symmetric tensor estimation

Nicolas Macris, Jean François Emmanuel Barbier, Clément Dominique Luneau

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 tensor is of even order. The proof applies the adaptive interpolation method orig ...

OXFORD UNIV PRESS2021