Sparse PCA from Sparse Linear Regression

Posted on November 27, 2018

Authors: Mӑdӑlina Persu (Two Sigma), Guy Bresler, Sung Min Park

To be presented at: 32nd Conference on Neural Information Processing Systems (NeurIPS 2018), Montréal, Canada

Abstract: Sparse Principal Component Analysis (SPCA) and Sparse Linear Regression (SLR) have a wide range of applications and have attracted a tremendous amount of attention in the last two decades 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. We show how to efficiently transform a black-box solver for SLR into an algorithm for SPCA: assuming the SLR solver satisfies prediction error guarantees achieved by existing efficient algorithms such as those based on the Lasso, the SPCA algorithm derived from it achieves near state of the art guarantees for testing and for support recovery for the single spiked covariance model as obtained by the current best polynomial time algorithms. Our reduction not only highlights the inherent similarity between the two problems, but also, from a practical standpoint, allows one to obtain a collection of algorithms for SPCA directly from known algorithms for SLR. We provide experimental results on simulated data comparing our proposed framework to other algorithms for SPCA.

Download PDF — 736.39 KB

This article is not an endorsement by Two Sigma of the papers discussed, their viewpoints or the companies discussed. The views expressed above reflect those of the authors and are not necessarily the views of Two Sigma Investments, LP or any of its affiliates (collectively, “Two Sigma”). The information presented above is only for informational and educational purposes and is not an offer to sell or the solicitation of an offer to buy any securities or other instruments. Additionally, the above information is not intended to provide, and should not be relied upon for investment, accounting, legal or tax advice. Two Sigma makes no representations, express or implied, regarding the accuracy or completeness of this information, and the reader accepts all risks in relying on the above information for any purpose whatsoever. Click here for other important disclaimers and disclosures.

Related Articles