École Nationale Supérieure de
Techniques Avancées

Résumé

This work extends the foundational research of Pr. Louart to establish a unique characterization of the solution for a general empirical risk minimization (ERM) problem in regression. Our analysis operates under a minimally restrictive setting, assuming neither a specific distribution for the data matrix 𝑋 nor a particular form for the regularizer 𝜌. Furthermore, the theoretical framework is specifically designed for the high-dimensional regime, where the number of samples 𝑛 and features 𝑝 are of comparable size.