Vecchia-Approximated Deep Gaussian Processes for Computer Experiments

Sauer, Annie; Cooper, Andrew I.; Gramacy, Robert B.

doi:10.1080/10618600.2022.2129662

Cited by 11 publications

(2 citation statements)

References 61 publications

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“…Other techniques for large‐scale GP, such as sparse approximation (Quiñonero‐Candela & Rasmussen, 2005; Sang & Huang, 2012), covariance tapering (Furrer et al, 2006), inducing inputs (Snelson & Ghahramani, 2006), and nearest neighbor GPs (Datta et al, 2016; Finley et al, 2019) (which has been utilized in Cheng et al (2021) for large‐scale calibration), as well as Vecchia‐approximated GPs/deep GPs (Katzfuss & Guinness, 2021; Sauer, Cooper, & Gramacy, 2023), are also worth exploring within the framework of KOH calibration. For a comprehensive review of large‐scale GP, refer to Liu et al (2020).…”

Section: Applications In Diverse Scenariosmentioning

confidence: 99%

A review on computer model calibration

Sung,

Tuo

2024

WIREs Computational Stats

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Model calibration is crucial for optimizing the performance of complex computer models across various disciplines. In the era of Industry 4.0, symbolizing rapid technological advancement through the integration of advanced digital technologies into industrial processes, model calibration plays a key role in advancing digital twin technology, ensuring alignment between digital representations and real‐world systems. This comprehensive review focuses on the Kennedy and O'Hagan (KOH) framework (Kennedy and O'Hagan, Journal of the Royal Statistical Society: Series B 2001; 63(3):425–464). In particular, we explore recent advancements addressing the challenges of the unidentifiability issue while accommodating model inadequacy within the KOH framework. In addition, we explore recent advancements in adapting the KOH framework to complex scenarios, including those involving multivariate outputs and functional calibration parameters. We also delve into experimental design strategies tailored to the unique demands of model calibration. By offering a comprehensive analysis of the KOH approach and its diverse applications, this review serves as a valuable resource for researchers and practitioners aiming to enhance the accuracy and reliability of their computer models.This article is categorized under: Statistical Models > Semiparametric Models Statistical Models > Simulation Models Statistical Models > Bayesian Models

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Section: Applications In Diverse Scenariosmentioning

confidence: 99%

A review on computer model calibration

Sung,

Tuo

2024

WIREs Computational Stats

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“…If the size of the neighbourhood is

n = scriptO false(N^{a} false)

, then the cost of each prediction is

scriptO false(N^{3 a} false)

, which can be tedious and inefficient when a large number of sequential predictions are required. We briefly note that a similar class of methods, based on Vecchia approximations (Vecchia, 1988), have recently become popular (Katzfuss et al, 2020; Katzfuss & Guinness, 2021; Sauer et al, 2022). These methods generally aim to construct a sparse approximation to the Cholesky factor of the covariance matrix in

scriptO false(n m^{3} false)

time.…”

Section: Introductionmentioning

confidence: 99%

A localized ensemble of approximate Gaussian processes for fast sequential emulation

Rumsey

Huerta

Tucker

2023

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More attention has been given to the computational cost associated with the fitting of an emulator. Substantially less attention is given to the computational cost of using that emulator for prediction. This is primarily because the cost of fitting an emulator is usually far greater than that of obtaining a single prediction, and predictions can often be obtained in parallel. In many settings, especially those requiring Markov Chain Monte Carlo, predictions may arrive sequentially and parallelization is not possible. In this case, using an emulator procedure which can produce accurate predictions efficiently can lead to substantial time savings in practice. In this paper, we propose a global model approximate Gaussian process framework via extension of a popular local approximate Gaussian process (laGP) framework. Our proposed emulator can be viewed as a treed Gaussian process where the leaf nodes are laGP models, and the tree structure is learned greedily as a function of the prediction stream. The suggested method (called leapGP) has interpretable tuning parameters which control the time‐memory trade‐off. One reasonable choice of settings leads to an emulator with a training cost and makes predictions rapidly with an asymptotic amortized cost of .

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