Reviews: Sparse PCA from Sparse Linear Regression

The paper proposes an approach to reduce solving a special sparse PCA to a sparse linear regression (SLR) problem (treated as a black-box solution). It uses the spiked covariance model [17] and assumes that the number of nonzero components of the direction (u) is known, plus some technical conditions such as a restricted eigenvalue property. The authors propose algorithms for both hypothesis testing and support recovery, as well as provide theoretical performance guarantees for them. Finally, the paper argues that the approach is robust to rescaling and presents some numerical experiments comparing two variants of the method (based on SLR methods FoBa and LASSO) with two alternatives (diagonal thresholding and covariance thresholding). Strengths: - The addressed problem (sparse PCA) is interesting and important.