TY - GEN
T1 - Generalized method of moments approach to hyperparameter estimation for Gaussian Markov random fields
AU - Song, Eunhye
AU - Dong, Yi
N1 - Funding Information:
The authors thank Xinmeng Wang for testing the full-GMM and slim-GMM estimation algorithms as a part of her M.S. degree paper at the Penn State University. Computations for this research were performed on the Penn State University's Institute for CyberScience Advanced CyberInfrastructure (ICS-ACI).
Publisher Copyright:
© 2018 IEEE
PY - 2019/1/31
Y1 - 2019/1/31
N2 - 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.
AB - 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.
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U2 - 10.1109/WSC.2018.8632275
DO - 10.1109/WSC.2018.8632275
M3 - Conference contribution
AN - SCOPUS:85062631966
T3 - Proceedings - Winter Simulation Conference
SP - 1790
EP - 1801
BT - WSC 2018 - 2018 Winter Simulation Conference
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2018 Winter Simulation Conference, WSC 2018
Y2 - 9 December 2018 through 12 December 2018
ER -