Balancing Statistical and Computational Precision and Applications to Penalized Linear Regression with Group Sparsity

Due to technological advances, large and high-dimensional data have become the rule rather than the exception. Methods that allow for feature selection with s uch data are thus highly sought after, in particular, since standard methods, such as cro ss-validated lasso and group-lasso, can be challenging both computationally and mathematically. In this paper, we propose a novel approach to feature selection and group feature selection in linear regression. It consists of simple optimization steps and tests, which makes it com putationally more efficient than standard approaches and suitable even for very larg e data sets. Moreover, it satisfies sharp guarantees for estimation and feature selection in terms of oracle inequalities. We thus expect that our contribution can help to leverage the incre asing volume of data in Biology, Public Health, Astronomy, Economics, and other fields.