9 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…
Resolvent convergence for sample second-moment matrices with heterogeneous profiles under quadratic-form control
Cosme Louart
We study the resolvent \(G^z=\left(\frac{1}{n}XX^{\top}-zI_p\right)^{-1}\), where \(z\in\mathbb{C}\) satisfies \(\Im(z)>0\) and \(X=(x_1,\ldots,x_n)\in\mathbb{R}^{p\times n}\) is a…
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…
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…
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 tr…