Canonical Correlation Analysis in High Dimensions with Structured Regularization

• Activity Number: 97 - New Methods for Structured Variable Selection
• Type: Topic Contributed
• Date/Time: Monday, August 8, 2022 : 8:30 AM to 10:20 AM
• Sponsor: SSC (Statistical Society of Canada)
• Author(s): Elena Tuzhilina* and Leonardo Tozzi and Trevor Hastie
• Companies: Stanford University and Stanford University and Stanford University
• Keywords: Canonical Correlation Analysis; Group regularization; Kernel trick

Abstract

Canonical correlation analysis (CCA) is a technique for measuring the association between two multivariate data matrices. A regularized modification of canonical correlation analysis (RCCA) which imposes an L2-penalty on the CCA coefficients is widely used in applications with high-dimensional data. One limitation of such regularization is that it ignores any data structure, treating all the features equally, which can be ill-suited for some applications. In this talk, we introduce several approaches to regularizing CCA that take the underlying data structure into account. In particular, the proposed group regularized canonical correlation analysis (GRCCA) is useful when the variables are correlated in groups. We illustrate some computational strategies to avoid excessive computations with regularized CCA in high dimensions. We demonstrate the application of these methods in a motivating application from neuroscience.