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

Understand

We propose a pivotal method for estimating high-dimensional sparse linear regression models, where the overall number of regressors $p$ is large, possibly much larger than $n$, but only $s$ regressors are significant.

• The method is a modification of the lasso, called the square-root lasso.
• The method is pivotal in that it neither relies on the knowledge of the standard deviation $\sigma$ or nor does it need to pre-estimate $\sigma$.
• Moreover, the method does not rely on normality or sub-Gaussianity of noise.