3 papers
math.ST2025
The Lasso error is bounded iff its active set size is bounded away from n in the proportional regime
Pierre C. Bellec
This note develops an analysis of the Lasso \( \hat b\) in linear models without any sparsity or L1 assumption on the true regression vector, in the proportional regime where dimen…
math.ST2025
Phase transitions for the existence of unregularized M-estimators in single index models
Takuya Koriyama, Pierre C. Bellec
This paper studies phase transitions for the existence of unregularized M-estimators under proportional asymptotics where the sample size and feature dimension grow proport…
math.ST2024
Estimating Generalization Performance Along the Trajectory of Proximal SGD in Robust Regression
Kai Tan, Pierre C. Bellec
This paper studies the generalization performance of iterates obtained by Gradient Descent (GD), Stochastic Gradient Descent (SGD) and their proximal variants in high-dimensional r…