Sparse inversion for derivative of log determinant
This work addresses efficiency issues for researchers and practitioners using statistical models with sparse matrices, but it is incremental as it builds on existing sparse inversion methods.
The paper tackles the computational bottleneck of evaluating derivatives of log determinants in Gaussian process and likelihood methods by leveraging sparse inversion techniques, resulting in accelerated performance for sparse matrices.
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.