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.
Original language | English |
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Title of host publication | Performance evaluation methodologies and tools |
Subtitle of host publication | 14th EAI International Conference, VALUETOOLS 2021, Virtual Event, October 30–31, 2021: proceedings |
Editors | Qianchuan Zhao, Li Xia |
Place of Publication | Cham, Switzerland |
Publisher | Springer, Springer Nature |
Pages | 243-261 |
Number of pages | 19 |
ISBN (Electronic) | 9783030925116 |
ISBN (Print) | 9783030925109 |
DOIs | |
Publication status | Published - 2021 |
Event | European Alliance for Innovation (EAI) International Conference on Performance Evaluation Methodologies and Tools (14th : 2021) - Online Duration: 30 Oct 2021 → 31 Oct 2021 Conference number: 14th |
Publication series
Name | Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering |
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Volume | 404 |
ISSN (Print) | 1867-8211 |
ISSN (Electronic) | 1867-822X |
Conference
Conference | European Alliance for Innovation (EAI) International Conference on Performance Evaluation Methodologies and Tools (14th : 2021) |
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Abbreviated title | VALUETOOLS 2021 |
City | Online |
Period | 30/10/21 → 31/10/21 |
Keywords
- stochastic simulation
- Variance reduction
- Gaussian processes