Title: An iterative penalized least squares approach to sparse canonical correlation analysis
Authors: Qing Mai - Florida State University (United States) [presenting]
Abstract: It is of increasing interest to model the relationship between two sets of measurements when both of them are high-dimensional. Canonical correlation analysis (CCA) is a classical tool that explores the dependency of two multivariate random variables and extracts canonical pairs of linear combinations that are highly correlated. Many recent studies aim to generalize the classical CCA to high-dimensional settings. However, most of the existing CCA methods either rely on strong assumptions on the covariance matrices, or do not produce nested solutions. We propose a new sparse CCA (SCCA) method that recasts high-dimensional CCA as an iterative penalized least squares problem. Thanks to the new penalized least squares formulation, our SCCA method directly penalizes and estimates the sparse CCA directions with efficient algorithms. Therefore, in contrast to some existing methods, the new SCCA does not impose any sparsity assumptions on the covariance matrices. The proposed SCCA is also very flexible in the sense that it can be easily combined with properly chosen penalty functions to perform structured variable selection or to incorporate prior information. Moreover, our proposal of SCCA produces nested solutions, which provides great convenient in practice. Theoretical results show that SCCA can consistently estimate the true canonical pairs with an overwhelming probability in ultra-high dimensions. Numerical results also demonstrate the competitive performance of SCCA.