Stochastic kriging with biased sample estimates

Chen, Xi; Kim, Kyoung-Kuk

doi:10.1145/2567893

Cited by 32 publications

(15 citation statements)

References 20 publications

(24 reference statements)

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“…. , k. Prediction then follows (4) and (6) upon obtaining the metamodel parameter estimates through maximizing the log-likelihood function formed under the standard assumption stipulated by GPR that (Y(w 0 ),Ȳ ⊤ ) ⊤ follows a multivariate normal distribution (see e.g., [14,18]).…”

Section: Gaussian Process Regression For Spatio-temporal Metamodelingmentioning

confidence: 99%

Multi-Resolution Sensitivity Analysis of Model of Immune Response to Helicobacter pylori Infection via Spatio-Temporal Metamodeling

Chen

Wang

Xie

et al. 2019

Front. Appl. Math. Stat.

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Section: Gaussian Process Regression For Spatio-temporal Metamodelingmentioning

confidence: 99%

Multi-Resolution Sensitivity Analysis of Model of Immune Response to Helicobacter pylori Infection via Spatio-Temporal Metamodeling

Chen

Wang

Xie

et al. 2019

Front. Appl. Math. Stat.

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“…Note that a constant term β is considered to represent the overall surface mean, instead of the trend term f (x) T β, because this model has shown to be the most useful in practice [1]. Moreover, the MSE of the stochastic kriging predictor (i.e., the stochastic kriging variance), denotedŝ 2 (x i ), is estimated as [8]:…”

Section: Stochastic Krigingmentioning

confidence: 99%

A Stochastic-Kriging-Based Multiobjective Simulation Optimization Algorithm

Rojas-Gonzalez

Jalali

Nieuwenhuyse

2018

2018 Winter Simulation Conference (WSC)

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We consider the multiobjective simulation optimization problem, where we seek to find the non-dominated set of designs evaluated using noisy simulation evaluations, in the context of numerically expensive simulators. We propose SK-MOCBA, a metamodel-based approach built upon the famous ParEGO algorithm. Our approach mainly differentiates from similar algorithms in that we use stochastic kriging, which explicitly characterizes both the extrinsic uncertainty of the unknown response surface, and the intrinsic uncertainty inherent in a stochastic simulation. We additionally integrate the Multiobjective Optimal Computing Budget Allocation (MOCBA) procedure in view of maximizing the probability of selecting systems with the true best expected performance. We evaluate the performance of the algorithm using standard test functions for multiobjective optimizers, perturbed by heterogeneous noise. The experimental results show that the proposed method outperforms its deterministic counterpart based on well-known quality indicators and the members of the true Pareto set found. In addition, we measure the impact of using MOCBA to improve the accuracy of the algorithm during the identification of the observed Pareto front.

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“…This randomness could be, for example, uncertainty in the input parameters or noise in the function response. For such cases, a more recent extension called Stochastic Kriging (SK) (Staum, 2009;Ankenman et al, 2010;Kleijnen and Mehdad, 2016;Kamiński, 2015;Chen and Kim, 2014;Plumlee and Tuo, 2014) was developed. Improvements and extensions emerged for both SK and deterministic Kriging in recent years.…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo integration with adaptive variance selection for improved stochastic efficient global optimization

Carraro

López

Miguel

et al. 2019

Struct Multidisc Optim

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In this paper, the minimization of computational cost on evaluating multi-dimensional integrals is explored. More specifically, a method based on an adaptive scheme for error variance selection in Monte Carlo integration (MCI) is presented. It uses a stochastic Efficient Global Optimization (sEGO) framework to guide the optimization search. The MCI is employed to approximate the integrals, because it provides the variance of the error in the integration. In the proposed approach, the variance of the integration error is included into a Stochastic Kriging framework by setting a target variance in the MCI. We show that the variance of the error of the MCI may be controlled by the designer and that its value strongly influences the computational cost and the exploration ability of the optimization process. Hence, we propose an adaptive scheme for automatic selection of the target variance during the sEGO search. The robustness and efficiency of the proposed adaptive approach were evaluated on global optimization stochastic benchmark functions as well as on a tuned mass damper design problem. The results showed that the proposed adaptive approach consistently outperformed the constant approach and a multi-start op-timization method. Moreover, the use of MCI enabled the method application in problems with high number of stochastic dimensions. On the other hand, the main limitation of the method is inherited from sEGO coupled with the Kriging metamodel: the efficiency of the approach is reduced when the number of design variables increases.

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Stochastic kriging with biased sample estimates

Cited by 32 publications

References 20 publications

Multi-Resolution Sensitivity Analysis of Model of Immune Response to Helicobacter pylori Infection via Spatio-Temporal Metamodeling

Multi-Resolution Sensitivity Analysis of Model of Immune Response to Helicobacter pylori Infection via Spatio-Temporal Metamodeling

A Stochastic-Kriging-Based Multiobjective Simulation Optimization Algorithm

Monte Carlo integration with adaptive variance selection for improved stochastic efficient global optimization

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