Efficient Canonical Correlation Analysis with Sparsity

TL;DR

This paper presents ECCAR, a fast, scalable, and provably consistent sparse CCA algorithm that effectively balances computational efficiency and statistical accuracy in high-dimensional data analysis.

Contribution

Introduces ECCAR, a novel sparse CCA method formulated as a reduced-rank regression, eliminating the need for complex projections and enabling practical large-scale applications.

Findings

ECCAR is significantly faster than existing methods.

It provides reliable, interpretable associations in biological datasets.

The method is validated through extensive simulations and real data applications.

Abstract

In high-dimensional settings, Canonical Correlation Analysis (CCA) often fails, and existing sparse methods force an untenable choice between computational speed and statistical rigor. This work introduces a fast and provably consistent sparse CCA algorithm (ECCAR) that resolves this trade-off. We formulate CCA as a high-dimensional reduced-rank regression problem, which allows us to derive consistent estimators with high-probability error bounds without relying on computationally expensive techniques like Fantope projections. The resulting algorithm is scalable, projection-free, and significantly faster than its competitors. We validate our method through extensive simulations and demonstrate its power to uncover reliable and interpretable associations in two complex biological datasets, as well as in an ML interpretability task. Our work makes sparse CCA a practical and trustworthy tool for large-scale multimodal data analysis. A companion R package has been made available.