Adaptive Randomized Dimension Reduction on Massive Data

TL;DR

This paper introduces an adaptive randomized dimension reduction method that leverages low-rank structures for scalable PCA and improves parameter estimation in large-scale linear mixed models, with demonstrated benefits in genomic data analysis.

Contribution

It develops a randomized low-rank approximation approach for PCA that enhances scalability and statistical accuracy in high-dimensional data analysis.

Findings

Efficient PCA implementation for massive datasets.

Improved parameter estimation in large-scale linear mixed models.

Enhanced performance demonstrated on genomic data.

Abstract

The scalability of statistical estimators is of increasing importance in modern applications. One approach to implementing scalable algorithms is to compress data into a low dimensional latent space using dimension reduction methods. In this paper we develop an approach for dimension reduction that exploits the assumption of low rank structure in high dimensional data to gain both computational and statistical advantages. We adapt recent randomized low-rank approximation algorithms to provide an efficient solution to principal component analysis (PCA), and we use this efficient solver to improve parameter estimation in large-scale linear mixed models (LMM) for association mapping in statistical and quantitative genomics. A key observation in this paper is that randomization serves a dual role, improving both computational and statistical performance by implicitly regularizing the covariance matrix estimate of the random effect in a LMM. These statistical and computational advantages are highlighted in our experiments on simulated data and large-scale genomic studies.