Speeding up Kriging through fast estimation of the hyperparameters in the frequency-domain

Baar, Jouke H. S. de; Dwight, Richard P.; Bijl, H.

doi:10.1016/j.cageo.2013.01.016

Cited by 15 publications

(11 citation statements)

References 21 publications

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“…Motivated by the application in the Stochastic Frontier Model [6] and Kriging problem [11], the Fast Fourier Transform (FFT) can be a promising method to deal with this complexity. As mentioned before, the kernel function is a positive-definite function, then the Fourier Transform makes it possible to transform this kernel to bring the computation from the spatialtemporal domain into frequency domain.…”

Section: Hyper-parameter Learning Phasementioning

confidence: 99%

Complexity reduction for Gaussian process regression in spatio-temporal prediction

Bui

Huynh‐The

Lee

et al. 2015

2015 International Conference on Advanced Technologies for Communications (ATC)

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To deal with inference and reasoning problems, Gaussian process has been considered as a promising tool due to the robustness and flexibility features. Especially, solving the regression and classification, Gaussian process coupling with Bayesian learning is one of the most appropriate supervised learning approaches in terms of accuracy and tractability. Unfortunately, this combination tolerates high complexity from computation and data storage. Obviously, this limitation makes Gaussian process ill-equipped to deal with the systems requiring fast response time. In this paper, the research focuses on analyzing the performance issue of Gaussian process, developing a method to reduce the complexity and implementing to predict CPU utilization, which is used as a factor to predict the status of computing node. Subsequently, a migration mechanism is applied so as to migrate the system-level processes between CPU cores and turn off the idle ones in order to save the energy while still maintaining the performance.

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Section: Hyper-parameter Learning Phasementioning

confidence: 99%

Complexity reduction for Gaussian process regression in spatio-temporal prediction

Bui

Huynh‐The

Lee

et al. 2015

2015 International Conference on Advanced Technologies for Communications (ATC)

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“…In section 2.3 we present the basic steps in performing learning via MLE and highlight the bottlenecks introduced by high dimensions and big data. In section 2.3.2 we provide an overview of the frequency-domain approach of De Baar, Dwight, and Bijl [19] that bypasses the shortcomings of MLE and enables fast learning from massive data-sets. Subsequently, in section 3 we elaborate on kernel design in high dimensions.…”

Section: B523mentioning

confidence: 99%

“…Following the approach of De Baar, Dwight, and Bijl [19] we employ the Wiener-Khinchin theorem to fit the autocorrelation function of a wide-sense stationary random field to the power spectrum of the data. The latter contains sufficient information for extracting the second-order statistics that fully describe the Gaussian predictor Z t (x).…”

Section: Frequency-domain Sample Variogram Fittingmentioning

confidence: 99%

Multifidelity Information Fusion Algorithms for High-Dimensional Systems and Massive Data sets

Perdikaris¹,

Venturi²,

Karniadakis³

2016

SIAM J. Sci. Comput.

117

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Abstract. We develop a framework for multifidelity information fusion and predictive inference in high-dimensional input spaces and in the presence of massive data sets. Hence, we tackle simultaneously the "big N" problem for big data and the curse of dimensionality in multivariate parametric problems. The proposed methodology establishes a new paradigm for constructing response surfaces of high-dimensional stochastic dynamical systems, simultaneously accounting for multifidelity in physical models as well as multifidelity in probability space. Scaling to high dimensions is achieved by data-driven dimensionality reduction techniques based on hierarchical functional decompositions and a graph-theoretic approach for encoding custom autocorrelation structure in Gaussian process priors. Multifidelity information fusion is facilitated through stochastic autoregressive schemes and frequency-domain machine learning algorithms that scale linearly with the data. Taking together these new developments leads to linear complexity algorithms as demonstrated in benchmark problems involving deterministic and stochastic fields in up to 10 5 input dimensions and 10 5 training points on a standard desktop computer.

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“…Possible reasons for the discrepancies are: 1) for Fn > 0.5 the hull starts planing, 2) for Fn > 0. 5 we might see ventilation and 3) the flow shows separation at the transom.…”

Section: Uncertainty Quantificationmentioning

confidence: 99%

“…Kuya et al [23] use multi-fidelity Kriging to augment wind-tunnel data with CFD results. de Baar et al [5] develop a fast way to estimate the hyperparameters of large data sets, which they incorporate into multi-fidelity Kriging to augment satelite data with F-16-acquired terrain elevation data. In a recent paper, Toal [35] presents a best practise for the application of multi-fidelity…”

Section: Introductionmentioning

confidence: 99%

Uncertainty quantification for a sailing yacht hull, using multi-fidelity kriging

et al. 2015

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Uncertainty Quantification (UQ) for CFD-based ship design can require a large number of simulations, resulting in significant overall computational cost. Presently, we use an existing method, multi-fidelity Kriging, to reduce the number of simulations required for the UQ analysis of the performance of a sailing yacht hull, considering uncertainties in the tank blockage, mass and centre of gravity. We compare the UQ results with experimental values.

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Speeding up Kriging through fast estimation of the hyperparameters in the frequency-domain

Cited by 15 publications

References 21 publications

Complexity reduction for Gaussian process regression in spatio-temporal prediction

Complexity reduction for Gaussian process regression in spatio-temporal prediction

Multifidelity Information Fusion Algorithms for High-Dimensional Systems and Massive Data sets

Uncertainty quantification for a sailing yacht hull, using multi-fidelity kriging

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