Sparse inversion for derivative of log determinant

TL;DR

This paper presents a method to efficiently compute derivatives of log determinants in sparse matrices, leveraging selected inversion techniques to accelerate calculations in Gaussian process and likelihood models.

Contribution

It introduces a novel approach that exploits sparse matrix inversion to speed up derivative evaluations of log determinants in statistical models.

Findings

Significant reduction in computation time for derivatives in sparse matrices

Effective application to Gaussian process and likelihood methods

Demonstrated improved efficiency over traditional dense methods

Abstract

Algorithms for Gaussian process, marginal likelihood methods or restricted maximum likelihood methods often require derivatives of log determinant terms. These log determinants are usually parametric with variance parameters of the underlying statistical models. This paper demonstrates that, when the underlying matrix is sparse, how to take the advantage of sparse inversion---selected inversion which share the same sparsity as the original matrix---to accelerate evaluating the derivative of log determinant.