20 citations · 41 across the 15 of their papers we have counts for
16 papers
A Central Limit Theorem for Regularized M-Estimators
Cosme Louart
We prove a quantitative central limit theorem for linear functionals of regularized empirical-risk minimizers in the proportional-dimensional regime \(p=O(n)\). The data columns ar…
Characterization of Gaussian Universality Breakdown in High-Dimensional Empirical Risk Minimization
Chiheb Yaakoubi, Cosme Louart, Malik Tiomoko +1
We study high-dimensional convex empirical risk minimization (ERM) under general non-Gaussian data designs. By heuristically extending the Convex Gaussian Min-Max Theorem (CGMT) to…
Universal concentration for sums under arbitrary dependence
Cosme Louart, Sicheng Tan
We present a universal concentration bound for sums of random variables under arbitrary dependence, and we prove that it is asymptotically optimal for broad families of marginals a…
Generalization in Representation Models via Random Matrix Theory: Application to Recurrent Networks
Yessin Moakher, Malik Tiomoko, Cosme Louart +1
We first study the generalization error of models that use a fixed feature representation (frozen intermediate layers) followed by a trainable readout layer. This setting encompass…
A Random Matrix Perspective of Echo State Networks: From Precise Bias--Variance Characterization to Optimal Regularization
Yessin Moakher, Malik Tiomoko, Cosme Louart +1
We present a rigorous asymptotic analysis of Echo State Networks (ESNs) in a teacher student setting with a linear teacher with oracle weights. Leveraging random matrix theory, we…
High-Dimensional Analysis of Bootstrap Ensemble Classifiers
Malik Tiomoko, Hamza Cherkaoui, Mohamed El Amine Seddik +3
Bootstrap methods have long been the cornerstone of ensemble learning in machine learning. This paper presents a theoretical analysis of bootstrap techniques applied to the Least S…
Analysing Multi-Task Regression via Random Matrix Theory with Application to Time Series Forecasting
Romain Ilbert, Malik Tiomoko, Cosme Louart +4
In this paper, we introduce a novel theoretical framework for multi-task regression, applying random matrix theory to provide precise performance estimations, under high-dimensiona…
Operation with Concentration Inequalities
Cosme Louart
Following the concentration of the measure theory formalism, we consider the transformation of a random variable having a general concentration function . If the tran…
Sharp Bounds for the Concentration of the Resolvent in Convex Concentration Settings
Cosme Louart
Considering random matrix with independent columns satisfying the convex concentration properties issued from a famous theorem of Talagrand, we express the…
Resolvent convergence under heterogeneous second-moment profiles and quadratic-form control
Cosme Louart
Let have independent real columns with finite second moments, not necessarily centered or identically distributed. For $z\in\mathbb C\s…
Concentration of measure and generalized product of random vectors with an application to Hanson-Wright-like inequalities
Cosme Louart, Romain Couillet
Starting from concentration of measure hypotheses on random vectors , this article provides an expression of the concentration of functionals $ϕ(Z_1,\ldots, Z_…
A Concentration of Measure Framework to study convex problems and other implicit formulation problems in machine learning
Cosme Louart
This paper provides a framework to show the concentration of solutions to convex minimizing problem where the objective function depends on some random vector s…
A Concentration of Measure and Random Matrix Approach to Large Dimensional Robust Statistics
Cosme Louart, Romain Couillet
This article studies the \emph{robust covariance matrix estimation} of a data collection with , where is a \te…
Random Matrix Theory Proves that Deep Learning Representations of GAN-data Behave as Gaussian Mixtures
Mohamed El Amine Seddik, Cosme Louart, Mohamed Tamaazousti +1
This paper shows that deep learning (DL) representations of data produced by generative adversarial nets (GANs) are random vectors which fall within the class of so-called \textit{…
Concentration of Measure and Large Random Matrices with an application to Sample Covariance Matrices
Cosme Louart, Romain Couillet
The present work provides an original framework for random matrix analysis based on revisiting the concentration of measure theory from a probabilistic point of view. By providing…
A Random Matrix Approach to Neural Networks
Cosme Louart, Zhenyu Liao, Romain Couillet
This article studies the Gram random matrix model , , classically found in the analysis of random feature maps and random neural networks, where $X=[x…