Variational properties of the square root LASSO: well-posedness, Lipschitz stability and numerical consequences

Aaron Berk^1, Simone Brugiapaglia^2 and Tim Hoheisel^1

1. Department of Mathematics & Statistics, McGill University, Montreal, Canada
2. Department of Mathematics & Statistics, Concordia University, Montreal, Canada

Repository contents

A detailed description of elementary components of the experimental setup (like support computation, matrix rank computation, etc.) are furnished in numerical implementation details (PDF).

The scripts for generating Figures 1a and 1b are:

• figure_1a.py
• figure_1b.py

The two main scripts in this repository, used to generate Figures 5 and 6, respectively, are:

• srlasso_inexact_empirical_uniqueness_sufficiency_crosssection.py
• srlasso_inexact_empirical_uniqueness_sufficiency_experiment.py

The final figure was created using:

• lipschitzness_srlasso.py

The supporting code for these scripts is distributed amongst:

• solve.py
• solve_utils.py
• uclasso_utils.py
• utils.py
• viz.py