B1636
Title: Theoretical guarantees for sparse principal component analysis based on the elastic net
Authors: Teng Zhang - University of Central Florida (United States) [presenting]
Abstract: Sparse principal component analysis (SPCA) is widely used for dimensionality reduction and feature extraction in high-dimensional data analysis. Despite many methodological and theoretical developments in the past two decades, the theoretical guarantees of the popular SPCA algorithm proposed by a prior study are still unknown. The aim is to address this critical gap. The SPCA algorithm of a previous study is first revisited, and its implementation is presented. A computationally more efficient variant of the SPCA algorithm is also studied that can be considered the limiting case of SPCA. The guarantees of convergence are provided to a stationary point for both algorithms and prove that, under a sparse spiked covariance model, both algorithms can recover the principal subspace consistently under mild regularity conditions. It is shown that their estimation error bounds match the best available bounds of existing works or the minimax rates up to some logarithmic factors. Moreover, the competitive numerical performance of both algorithms is demonstrated in numerical studies.
