Abstract

Partial Least Squares (PLS) is a ubiquitous statistical technique for bilinear factor analysis. It is used in many data analysis, machine learning, and information retrieval applications to model the covariance structure between a pair of data matrices. In this paper, we consider PLS for representation learning in a multiview setting where we have more than one view in data at training time. Furthermore, instead of framing PLS as a problem about a fixed given data set, we argue that PLS should be studied as a stochastic optimization problem, especially in a “big data” setting, with the goal of optimizing a population objective based on sample. This view suggests using Stochastic Approximation (SA) approaches, such as Stochastic Gradient Descent (SGD) and enables a rigorous analysis of their benefits. In this paper, we develop SA approaches to PLS and provide iteration complexity bounds for the proposed algorithms.