Time: 2021/10/27 10:00-11:00 AM

Form: Tencent Meeting (ID: 939263154)

Topic: Canonical correlation analysis (CCA) in high dimensions

Abstract:

CCA is a classical tool to study the relationship between two sets of variables. We will discuss two closely related problems in high-dimensional CCA: sparse estimation of the directions and significance testing of the correlation. The first part of this talk discusses a new sparse CCA (SCCA) method that recasts high-dimensional CCA as an iterative penalized least squares problem. The new iterative penalized least squares formulation leads to a direct penalized estimation approach to the sparse CCA problem and efficient algorithms. In contrast to some existing methods, the new SCCA does not impose any sparsity assumptions on the covariance matrices and consistently estimates the true CCA directions with an overwhelming probability in ultra-high dimensions. In the second part of the talk, we discuss the problem of testing for the presence of linear relationships between large sets of random variables based on a post-selection inference approach to CCA. The challenge is to adjust for the selection of subsets of variables having linear combinations with maximal sample correlation. To this end, we construct a stabilized one-step estimator of the square root of Pillai`s trace maximized over subsets of variables of pre-specified cardinality. This estimator is shown to be consistent for its target parameter and asymptotically normal, provided the dimensions of the variables do not grow too quickly with sample size. We also develop a greedy search algorithm to accurately compute the estimator, leading to a computationally tractable omnibus test for the global null hypothesis that there are no linear relationships between any subsets of variables having the pre-specified cardinality.

Resume:

Xin (Henry) Zhang is an Associate Professor in Statistics at the Florida State University. He received his B.S. degree in Applied Physics from the University of Science and Technology of China in 2008 and a Ph.D. degree in Statistics from the University of Minnesota in 2014. His current research interests include tensor analysis, multivariate and computational statistics, medical imaging, dimension reduction, and envelope models. Background on his works can be found at https://ani.stat.fsu.edu/~henry/research.html