# Stochastic Canonical Correlation Analysis

arXiv: https://arxiv.org/abs/1702.06533 · HTML: https://mlsanity.com/paper/1702.06533/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2017.

## Built on by (most cited first, 7 of 7)

- [On the Versatile Uses of Partial Distance Correlation in Deep Learning](https://mlsanity.com/paper/2207.09684/) (2022)
- [An Online Riemannian PCA for Stochastic Canonical Correlation Analysis](https://mlsanity.com/paper/2106.07479/) (2021)
- [Optimization without Retraction on the Random Generalized Stiefel Manifold](https://mlsanity.com/paper/2405.01702/) (2024)
- [Nonconvex Stochastic Scaled-Gradient Descent and Generalized Eigenvector Problems](https://mlsanity.com/paper/2112.14738/) (2021)
- [The Symmetric Generalized Eigenvalue Problem as a Nash Equilibrium](https://mlsanity.com/paper/2206.04993/) (2022)
- [Sliding Window Informative Canonical Correlation Analysis](https://mlsanity.com/paper/2507.17921/) (2025)
- [When Does Dense Retrieval Need Asymmetric Geometry? A Bias-Variance Theory of Shared and Dual Projections](https://mlsanity.com/paper/2609.32488/) (2026)

## Abstract (arXiv)

We study the sample complexity of canonical correlation analysis (CCA), ie, the number of samples needed to estimate the population canonical correlation and directions up to arbitrarily small error. With mild assumptions on the data distribution, we show that in order to achieve ε-suboptimality in a properly defined measure of alignment between the estimated canonical directions and the population solution, we can solve the empirical objective exactly with N(ε, Delta, γ) samples, where Delta is the singular value gap of the whitened cross-covariance matrix and 1/γ is an upper bound of the condition number of auto-covariance matrices. Moreover, we can achieve the same learning accuracy by drawing the same level of samples and solving the empirical objective approximately with a stochastic optimization algorithm; this algorithm is based on the shift-and-invert power iterations and only needs to process the dataset for Oleft(log frac1ε right) passes. Finally, we show that, given an estimate of the canonical correlation, the streaming version of the shift-and-invert power iterations achieves the same learning accuracy with the same level of sample complexity, by processing the data only once.