Variance reduction for matrix computations with applications to Gaussian processes

Anant Mathur*, Sarat Moka, Zdravko Botev

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

1 Citation (Scopus)

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 languageEnglish
Title of host publicationPerformance evaluation methodologies and tools
Subtitle of host publication14th EAI International Conference, VALUETOOLS 2021, Virtual Event, October 30–31, 2021: proceedings
EditorsQianchuan Zhao, Li Xia
Place of PublicationCham, Switzerland
PublisherSpringer, Springer Nature
Pages243-261
Number of pages19
ISBN (Electronic)9783030925116
ISBN (Print)9783030925109
DOIs
Publication statusPublished - 2021
EventEuropean Alliance for Innovation (EAI) International Conference on Performance Evaluation Methodologies and Tools (14th : 2021) - Online
Duration: 30 Oct 202131 Oct 2021
Conference number: 14th

Publication series

NameLecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering
Volume404
ISSN (Print)1867-8211
ISSN (Electronic)1867-822X

Conference

ConferenceEuropean Alliance for Innovation (EAI) International Conference on Performance Evaluation Methodologies and Tools (14th : 2021)
Abbreviated titleVALUETOOLS 2021
CityOnline
Period30/10/2131/10/21

Keywords

  • stochastic simulation
  • Variance reduction
  • Gaussian processes

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