Slope Meets Lasso in Sparse Linear Regression

• Activity Number: 16 - Recent Advances and Challenges in High-Dimensional Data Analysis
• Type: Topic Contributed
• Date/Time: Sunday, July 30, 2017 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Pierre Bellec*
• Companies: Rutgers University
• Keywords: sparity ; linear regression ; lasso ; p larger than n ; concentration ; convex regularization

Abstract

We will present some results in sparse linear regression on two convex regularized estimators, the Lasso and the recently introduced Slope estimator, in the high-dimensional setting where the number of covariates p is larger than the number of observations n. Novel theory that deepens our understanding of the performance of these convex regularized will be presented. This includes arguments that lead to new lower bounds as well as arguments that lead to more precise concentration bounds for these estimators. We will also explain how the theory can be extended to general convex regularized estimators.