Imaging and Computing Seminar

Lie Wang , Department of Mathematics, MIT

Square-root Lasso: Pivotal Recovery of Sparse Signals via Conic Programming

We propose a pivotal method for estimating high-dimensional sparse linear regression models. The method is a modification of Lasso, called square-root Lasso. The method neither relies on the knowledge of the standard deviation of the regression errors nor does it need to pre-estimate it. Despite not knowing the standard deviation, square-root Lasso achieves near-oracle performance, attaining the prediction norm convergence rate, and thus matching the performance of the Lasso. Moreover, we show that these results are valid for both Gaussian and non-Gaussian errors, under some mild moment restrictions, using moderate deviation theory.