# Sparse CCA via Precision Adjusted Iterative Thresholding

arXiv: https://arxiv.org/abs/1311.6186 · HTML: https://mlsanity.com/paper/1311.6186/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Nov 2013.

## Built on by (most cited first, 4 of 4)

- [Sparse GCA and Thresholded Gradient Descent](https://mlsanity.com/paper/2107.00371/) (2021)
- [Generalized Eigenvalue Problems with Generative Priors](https://mlsanity.com/paper/2411.01326/) (2024)
- [ℓ1-norm constrained multi-block sparse canonical correlation analysis via proximal gradient descent](https://mlsanity.com/paper/2201.05289/) (2022)
- [Efficient Computation of Sparse and Robust Maximum Association Estimators](https://mlsanity.com/paper/2311.17563/) (2023)

## Abstract (arXiv)

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.