Keywords: Convex optimization, multivariate response linear regression
We discuss the multivariate square-root lasso, a spectral analog of the square-root lasso (Belloni et al., 2011). This estimator has not gained popularity in the recent literature, partly because it is difficult to compute. In this talk, we propose two new algorithms for computing the multivariate square-root lasso estimator: one of which can be used when the number of samples is larger than the number of responses; the other of which can be applied in any scenario. We will also discuss some theoretical properties of the estimator — providing intuition and justification for its performance and use.