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

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.