LASSO reloaded: a variational analysis perspective with applications to compressed sensing
Optimization and Control
2023-06-16 v5 Information Theory
Numerical Analysis
math.IT
Numerical Analysis
Abstract
This paper provides a variational analysis of the unconstrained formulation of the LASSO problem, ubiquitous in statistical learning, signal processing, and inverse problems. In particular, we establish smoothness results for the optimal value as well as Lipschitz properties of the optimal solution as functions of the right-hand side (or measurement vector) and the regularization parameter. Moreover, we show how to apply the proposed variational analysis to study the sensitivity of the optimal solution to the tuning parameter in the context of compressed sensing with subgaussian measurements. Our theoretical findings are validated by numerical experiments.
Cite
@article{arxiv.2205.06872,
title = {LASSO reloaded: a variational analysis perspective with applications to compressed sensing},
author = {Aaron Berk and Simone Brugiapaglia and Tim Hoheisel},
journal= {arXiv preprint arXiv:2205.06872},
year = {2023}
}