Generalized Sparse Precision Matrix Selection for Fitting Multivariate Gaussian Random Fields to Large Data Sets

TL;DR

This paper introduces a generalized sparse precision matrix selection method for fitting multivariate Gaussian Random Fields to large datasets, providing theoretical guarantees and practical validation.

Contribution

It extends the SPS algorithm to multivariate cases, establishing convergence rates and demonstrating effectiveness on simulated and real data.

Findings

The method accurately estimates covariance matrices and parameters.

Theoretical convergence rates are validated through numerical experiments.

Data segmentation enables handling of large datasets efficiently.

Abstract

We present a new method for estimating multivariate, second-order stationary Gaussian Random Field (GRF) models based on the Sparse Precision matrix Selection (SPS) algorithm, proposed by Davanloo et al. (2015) for estimating scalar GRF models. Theoretical convergence rates for the estimated between-response covariance matrix and for the estimated parameters of the underlying spatial correlation function are established. Numerical tests using simulated and real datasets validate our theoretical findings. Data segmentation is used to handle large data sets.