Nonconvex Statistical Learning for the Dimensionality Reduction of High-Dimensional Data

• Activity Number: 150 - Recent Advances in Nonparametric Statistical Methods for Complex Data
• Type: Invited
• Date/Time: Monday, July 29, 2019 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Lingzhou Xue* and Shiqian Ma and Hui Zou
• Companies: Penn State University and National Institute of Statistical Sciences and University of California, Davis and University of Minnesota
• Keywords: Sparse PCA; Statistical Learning; Dimension Reduction; Proximal Gradient Descent; Manifold Gradient Descent; Nonconvex Optimization

Abstract

In this talk, we revisit the classic sparse principal component analysis (SPCA) proposed by Zou, Hastie, and Tibshirani (2006). After a decade, it is still an open question to efficiently solve the challenging nonsmooth manifold optimization problem of SPCA with provable guarantees. To close this gap, we introduce a novel alternating Manifold gradient descent and proximal gradient descent, which solves the SPCA with provable convergence guarantees. In the end, we will demonstrate the numerical properties of the proposed nonconvex algorithms in both simulation studies and real applications.