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Sparse PCA from Sparse Linear Regression

Sparse Principal Component Analysis (SPCA) and Sparse Linear Regression (SLR) have a wide range of applications and have attracted attention as canonical examples of statistical problems in high dimension. A variety of algorithms have been proposed for both SPCA and SLR, but an explicit connection between the two had not been made. This paper shows how to efficiently transform a black-box solver for SLR into an algorithm for SPCA.