Sparse CCA via Precision Adjusted Iterative Thresholding

Summary. Sparse Canonical Correlation Analysis (CCA) has received considerable atten-tion in high-dimensional data analysis to study the relationship between two sets of ran-dom variables. However, there has been remarkably little theoretical statistical foundation on sparse CCA in high-dimensional settings despite active methodological and applied re-search activities. In this paper, we introduce an elementary sufficient and necessary charac-terization such that the solution of CCA is indeed sparse, propose a computationally efficient procedure, called CAPIT, to estimate the canonical directions, and show that the procedure is rate-optimal under various assumptions on nuisance parameters. The procedure is applied to a breast cancer dataset from The Cancer Genome Atlas project. We identify methyla-tion probes that are associated with genes, which have been previously characterized as prognosis signatures of the metastasis of breast cancer