Variance Reduction for Matrix Computations with Applications to Gaussian
Processes
- URL: http://arxiv.org/abs/2106.14565v3
- Date: Sun, 26 Mar 2023 08:32:01 GMT
- Title: Variance Reduction for Matrix Computations with Applications to Gaussian
Processes
- Authors: Anant Mathur, Sarat Moka and Zdravko Botev
- Abstract summary: We focus on variance reduction for matrix computations via matrix factorization.
We show how computing the square root factorization of the matrix can achieve in some important cases arbitrarily better performance.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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 propose 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.
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