Imaging and Computing Seminar
Lie Wang , Department of Mathematics, MIT
Title:
Square-root Lasso: Pivotal Recovery of Sparse Signals via Conic
Programming
Abstract:
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.