Efficient Globally Convergent Stochastic Optimization for Canonical Correlation Analysis

TL;DR

This paper introduces two globally convergent stochastic optimization algorithms for canonical correlation analysis, transforming the problem into sequences of least squares problems and demonstrating superior performance over previous methods.

Contribution

The paper proposes novel meta-algorithms for CCA that guarantee global convergence and improve time complexity using approximate least squares solutions.

Findings

Algorithms outperform previous stochastic methods in experiments.

The methods guarantee global convergence for nonconvex CCA optimization.

Time complexity is significantly improved over existing approaches.

Abstract

We study the stochastic optimization of canonical correlation analysis (CCA), whose objective is nonconvex and does not decouple over training samples. Although several stochastic gradient based optimization algorithms have been recently proposed to solve this problem, no global convergence guarantee was provided by any of them. Inspired by the alternating least squares/power iterations formulation of CCA, and the shift-and-invert preconditioning method for PCA, we propose two globally convergent meta-algorithms for CCA, both of which transform the original problem into sequences of least squares problems that need only be solved approximately. We instantiate the meta-algorithms with state-of-the-art SGD methods and obtain time complexities that significantly improve upon that of previous work. Experimental results demonstrate their superior performance.