Block-Enhanced Precision Matrix Estimation for Large-Scale Datasets
Additional information
Authors
Type
Journal Article
Year
2021
Language
English
Abstract
The L1 -regularized Gaussian maximum likelihood method is a common approach for sparse precision matrix estimation, but one that poses a computational challenge for high-dimensional datasets. We present a novel L1-regularized maximum likelihood method for performant large-scale sparse precision matrix estimation utilizing the block structures in the underlying computations. We identify the computational bottlenecks and contribute a block coordinate descent update as well as a block approximate matrix inversion routine, which is then parallelize
using a shared-memory scheme. We demonstrate the effectiveness, accuracy, and performance of these algorithms. Our numerical examples and comparative results with various modern open-source packages reveal that these precision matrix estimation methods can accelerate the computation of covariance matrices by two to three orders of magnitude, while keeping memory requirements modest. Furthermore, we conduct large-scale case studies for applications from finance and medicine with several thousand random variables to demonstrate applicability for real-world datasets.
Journal
Journal of Computational Science
Volume
53
Start page number
1
End page number
39
Keywords
covariance matrices, graphical model, optimization, Gaussian Markov random field, machine learning application
