Research Article
Variance Reduction for Matrix Computations with Applications to Gaussian Processes
@INPROCEEDINGS{10.1007/978-3-030-92511-6_16, author={Anant Mathur and Sarat Moka and Zdravko Botev}, title={Variance Reduction for Matrix Computations with Applications to Gaussian Processes}, proceedings={Performance Evaluation Methodologies and Tools. 14th EAI International Conference, VALUETOOLS 2021, Virtual Event, October 30--31, 2021, Proceedings}, proceedings_a={VALUETOOLS}, year={2021}, month={12}, keywords={stochastic simulation Variance reduction Gaussian processes}, doi={10.1007/978-3-030-92511-6_16} }- Anant Mathur
Sarat Moka
Zdravko Botev
Year: 2021
Variance Reduction for Matrix Computations with Applications to Gaussian Processes
VALUETOOLS
Springer
DOI: 10.1007/978-3-030-92511-6_16
Abstract
In addition to recent developments in computing speed and memory, methodological advances have contributed to significant gains in the performance of stochastic simulation. In this paper we focus on variance reduction for matrix computations via matrix factorization. We provide insights into existing variance reduction methods for estimating the entries of large matrices. Popular methods do not exploit the reduction in variance that is possible when the matrix is factorized. We show how computing the square root factorization of the matrix can achieve in some important cases arbitrarily better stochastic performance. In addition, we detail a factorized estimator for the trace of a product of matrices and numerically demonstrate that the estimator can be up to 1,000 times more efficient on certain problems of estimating the log-likelihood of a Gaussian process. Additionally, we provide a new estimator of the log-determinant of a positive semi-definite matrix where the log-determinant is treated as a normalizing constant of a probability density.
