Scalable Partial Least Squares Regression on Grammar-Compressed Data Matrices

TL;DR

This paper introduces a scalable, interpretable partial least squares regression algorithm called cPLS, which efficiently handles massive high-dimensional data by using grammar compression, significantly reducing computational costs while maintaining high accuracy.

Contribution

The paper presents a novel grammar-compressed data representation and a scalable cPLS algorithm that improves efficiency and interpretability for large high-dimensional datasets.

Findings

cPLS outperforms existing methods in prediction accuracy

cPLS significantly reduces computational time and memory usage

cPLS maintains high interpretability in models learned from massive data

Abstract

With massive high-dimensional data now commonplace in research and industry, there is a strong and growing demand for more scalable computational techniques for data analysis and knowledge discovery. Key to turning these data into knowledge is the ability to learn statistical models with high interpretability. Current methods for learning statistical models either produce models that are not interpretable or have prohibitive computational costs when applied to massive data. In this paper we address this need by presenting a scalable algorithm for partial least squares regression (PLS), which we call compression-based PLS (cPLS), to learn predictive linear models with a high interpretability from massive high-dimensional data. We propose a novel grammar-compressed representation of data matrices that supports fast row and column access while the data matrix is in a compressed form. The original data matrix is grammar-compressed and then the linear model in PLS is learned on the compressed data matrix, which results in a significant reduction in working space, greatly improving scalability. We experimentally test cPLS on its ability to learn linear models for classification, regression and feature extraction with various massive high-dimensional data, and show that cPLS performs superiorly in terms of prediction accuracy, computational efficiency, and interpretability.