Sparse CCA via Precision Adjusted Iterative Thresholding
arXiv:1311.6186
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.
References in corpus (3)
Cited by in corpus (12)
- Sparse CCA: Adaptive Estimation and Computational Barriers
- Minimax estimation in sparse canonical correlation analysis
- Rate-Optimal Perturbation Bounds for Singular Subspaces with Applications to High-Dimensional Statistics
- Stochastic Canonical Correlation Analysis
- An Alternating Manifold Proximal Gradient Method for Sparse PCA and Sparse CCA
- Subspace Perspective on Canonical Correlation Analysis: Dimension Reduction and Minimax Rates
- Sparse GCA and Thresholded Gradient Descent
- Sparse Generalized Eigenvalue Problem: Optimal Statistical Rates via Truncated Rayleigh Flow
- Joint association and classification analysis of multi-view data
- -based Sparse Canonical Correlation Analysis
- Sparse Generalized Canonical Correlation Analysis: Distributed Alternating Iteration based Approach
- Eigenvector-based sparse canonical correlation analysis: Fast computation for estimation of multiple canonical vectors