Parameter estimation in high dimensional Gaussian distributions

TL;DR

This paper introduces an innovative iterative method for efficiently computing the log-likelihood of high-dimensional Gaussian models by leveraging matrix functions, Krylov subspaces, and probing vectors, addressing memory limitations of traditional methods.

Contribution

The paper presents a novel approach that enables efficient likelihood computation in large Gaussian models using matrix functions and Krylov subspace techniques.

Findings

Method reduces memory requirements for large models.

Efficiently computes log-likelihood with fast matrix-vector products.

Applicable to high-dimensional spatial Gaussian models.

Abstract

In order to compute the log-likelihood for high dimensional spatial Gaussian models, it is necessary to compute the determinant of the large, sparse, symmetric positive definite precision matrix, Q. Traditional methods for evaluating the log-likelihood for very large models may fail due to the massive memory requirements. We present a novel approach for evaluating such likelihoods when the matrix-vector product, Qv, is fast to compute. In this approach we utilise matrix functions, Krylov subspaces, and probing vectors to construct an iterative method for computing the log-likelihood.