Sparse CCA via Precision Adjusted Iterative Thresholding

TL;DR

This paper introduces a new efficient method called CAPIT for sparse Canonical Correlation Analysis, providing theoretical guarantees and applying it to breast cancer data to identify relevant genetic markers.

Contribution

It offers a novel characterization for sparse CCA solutions, proposes a rate-optimal estimation procedure, and demonstrates its effectiveness on real high-dimensional biological data.

Findings

CAPIT is computationally efficient and rate-optimal.

Successfully identified methylation probes linked to breast cancer prognosis.

Provides theoretical foundations for sparse CCA in high-dimensional settings.

Abstract

Sparse Canonical Correlation Analysis (CCA) has received considerable attention in high-dimensional data analysis to study the relationship between two sets of random variables. However, there has been remarkably little theoretical statistical foundation on sparse CCA in high-dimensional settings despite active methodological and applied research activities. In this paper, we introduce an elementary sufficient and necessary characterization 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 methylation probes that are associated with genes, which have been previously characterized as prognosis signatures of the metastasis of breast cancer.