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Activity Number: 354 - Multivariate Analysis and Graphical Models
Type: Contributed
Date/Time: Wednesday, August 5, 2020 : 10:00 AM to 2:00 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #313168
Title: Sparse Generalized Correlation Analysis and Thresholded Gradient Descent
Author(s): Sheng Gao* and Zongming Ma
Companies: University of Pennsylvania and University of Pennsylvania
Keywords: Sparse CCA (SCCA); Sparse GCA (SGCA); Minimax Rates; Thresholded Gradient Descent; Convex Relaxation; High Dimension Statistics

Generalized Correlation Analysis (GCA) is a technique for finding highly correlation variation patterns across multiple datasets. It includes PCA and CCA as special cases. In this presentation, we discuss the estimation of leading sparse generalized correlation loading vectors in high dimensions, which can be called sparse GCA. Sparse GCA has found applications in multi-omics and multi-modal imaging where ambient dimensions of datasets are high. We first postulate a latent variable model in order to understand what the target of estimation is. Then we propose an efficient algorithm based on thresholded gradient descent of a non-convex objective function. With proper initialization, the algorithm is shown to achieve optimal estimation error rates. Time permitting, we also discuss the numerical performance of the algorithm on simulated and real datasets.

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

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