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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
Abstract #300574
Title: Nonconvex Statistical Learning for the Dimensionality Reduction of High-Dimensional Data
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

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.

Authors who are presenting talks have a * after their name.

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