Balancing Statistical and Computational Precision: A General Theory and Applications to Sparse Regression

TL;DR

This paper introduces a unified approach to balance statistical accuracy and computational efficiency in regularized estimation, specifically improving sparse and group-sparse regression methods.

Contribution

It presents a general theory that integrates statistical and computational considerations, enhancing existing sparse regression techniques.

Findings

Improved statistical performance over standard methods.

Enhanced computational efficiency in sparse regression.

Applicable to both sparse and group-sparse models.

Abstract

Modern technologies are generating ever-increasing amounts of data. Making use of these data requires methods that are both statistically sound and computationally efficient. Typically, the statistical and computational aspects are treated separately. In this paper, we propose an approach to entangle these two aspects in the context of regularized estimation. Applying our approach to sparse and group-sparse regression, we show that it can improve on standard pipelines both statistically and computationally.