Statistics Department Hosted Seminar Series by Professor Yves Atchade: Vincent Q. Vu, A new approach to sparse PCA
Professor Yves Atchade is hosting a bi-weekly seminar series called "Statistical Computing" which will discuss how statistical methods are implemented, and to explore computational techniques with potential applications in statistics.
Sparse PCA is a type of methodology for simultaneous dimension reduction and variable selection in high-dimensional data analysis. It has attracted much attention over the past 10 years, but there have been few theoretical insights until recently. This talk will report some recent developments in sparse PCA with a special focus on subspace estimation. The results include minimax rates of estimation and a new convex relaxation based on a semidefinite program called Fantope Projection and Selection (FPS). FPS can be computed efficiently by alternating direction method of multipliers and it has near-optimal statistical properties. A key tenet of the new methodology is that sparse PCA should be viewed as projection matrix estimation problem. The utility of this viewpoint will be demonstrated with an application to a large collection of articles from the New York Times.