Unconstrained Stochastic CCA: Unifying Multiview and Self-Supervised Learning

TL;DR

This paper introduces fast stochastic algorithms for CCA and PLS that outperform previous methods in speed and accuracy, enabling large-scale biomedical data analysis and enhancing self-supervised learning performance.

Contribution

The paper proposes a novel unconstrained objective and stochastic gradient algorithms for CCA, PLS, and Deep CCA, unifying multiview and self-supervised learning with improved efficiency.

Findings

Faster convergence and higher correlation recovery than previous methods.

Successful large-scale biomedical data analysis with over 33,000 individuals.

Matching SSL methods' performance on CIFAR datasets with minimal tuning.

Abstract

The Canonical Correlation Analysis (CCA) family of methods is foundational in multiview learning. Regularised linear CCA methods can be seen to generalise Partial Least Squares (PLS) and be unified with a Generalized Eigenvalue Problem (GEP) framework. However, classical algorithms for these linear methods are computationally infeasible for large-scale data. Extensions to Deep CCA show great promise, but current training procedures are slow and complicated. First we propose a novel unconstrained objective that characterizes the top subspace of GEPs. Our core contribution is a family of fast algorithms for stochastic PLS, stochastic CCA, and Deep CCA, simply obtained by applying stochastic gradient descent (SGD) to the corresponding CCA objectives. Our algorithms show far faster convergence and recover higher correlations than the previous state-of-the-art on all standard CCA and Deep CCA benchmarks. These improvements allow us to perform a first-of-its-kind PLS analysis of an extremely large biomedical dataset from the UK Biobank, with over 33,000 individuals and 500,000 features. Finally, we apply our algorithms to match the performance of `CCA-family' Self-Supervised Learning (SSL) methods on CIFAR-10 and CIFAR-100 with minimal hyper-parameter tuning, and also present theory to clarify the links between these methods and classical CCA, laying the groundwork for future insights.