Generalized method of moments approach to hyperparameter estimation for Gaussian Markov random fields

Eunhye Song, Yi Dong

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

When a Gaussian Markov random field (GMRF) is used as a metamodel of an unknown response surface for a discrete optimization via simulation (DOvS) problem, the hyperparameters of the GMRF are estimated based on a few initial design points in a large feasible solution space. Although the maximum likelihood estimators (MLEs) are most commonly adopted to estimate these hyperparameters, its computation time increases polynomially in the size of the feasible solution space. We introduce new generalized method of moments (GMM) estimators of the hyperparameters of GMRFs and their initial sampling schemes, and show they are consistent under some conditions. Unlike MLEs, the computation time for these GMM estimators does not depend on the size of the feasible solution space. We show empirically that the GMM estimators have smaller biases and standard errors than MLE for a wide range of initial simulation budget while requiring orders of magnitude smaller computation time.

Original languageEnglish (US)
Title of host publicationWSC 2018 - 2018 Winter Simulation Conference
Subtitle of host publicationSimulation for a Noble Cause
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1790-1801
Number of pages12
ISBN (Electronic)9781538665725
DOIs
StatePublished - Jan 31 2019
Event2018 Winter Simulation Conference, WSC 2018 - Gothenburg, Sweden
Duration: Dec 9 2018Dec 12 2018

Publication series

NameProceedings - Winter Simulation Conference
Volume2018-December
ISSN (Print)0891-7736

Conference

Conference2018 Winter Simulation Conference, WSC 2018
CountrySweden
CityGothenburg
Period12/9/1812/12/18

All Science Journal Classification (ASJC) codes

  • Software
  • Modeling and Simulation
  • Computer Science Applications

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  • Cite this

    Song, E., & Dong, Y. (2019). Generalized method of moments approach to hyperparameter estimation for Gaussian Markov random fields. In WSC 2018 - 2018 Winter Simulation Conference: Simulation for a Noble Cause (pp. 1790-1801). [8632275] (Proceedings - Winter Simulation Conference; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/WSC.2018.8632275