Full scale multi-output Gaussian process emulator with nonseparable auto-covariance functions

Zhang, Bohai; Konomi, Bledar A.; Sang, Huiyan; Karagiannis, Georgios; Lin, Guang

doi:10.1016/j.jcp.2015.08.006

Cited by 15 publications

(11 citation statements)

References 35 publications

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“…Basically, the BLHS guarantees a good mix of short and long pairwise distances. The method is similar in flavor to so-called full scale approximation (Sang and Huang, 2012;Zhang et al, 2015). It also has aspects in common with composite likelihood approaches (Varin et al, 2011;Gu and Berger, 2016).…”

Section: Bootstrapped Block Latin Hypercube Subsamplesmentioning

confidence: 99%

Emulating Satellite Drag from Large Simulation Experiments

Sun¹,

Gramacy²,

Haaland³

et al. 2019

SIAM/ASA J. Uncertainty Quantification

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Obtaining accurate estimates of satellite drag coefficients in low Earth orbit is a crucial component in positioning and collision avoidance. Simulators can produce accurate estimates, but their computational expense is much too large for real-time application. A pilot study by Mehta et al. (2014b) showed that Gaussian process (GP) surrogate models could accurately emulate simulations. However, cubic runtime for training GPs means that they could only be applied to a narrow range of input configurations to achieve the desired level of accuracy. In this paper we show how extensions to the local approximate GP (laGP) method allow accurate full-scale emulation. The new methodological contributions, which involve a multilevel global/local modeling approach, and a setwise approach to local subset selection, are shown to perform well in benchmark and synthetic data settings. We conclude by demonstrating that our method achieves the desired level of accuracy, besting simpler viable (i.e., computationally tractable) global and local modeling approaches, when trained on seventy thousand core hours of drag simulations for two real-world satellites: the Hubble space telescope (HST) and the gravity recovery and climate experiment (GRACE).

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Section: Bootstrapped Block Latin Hypercube Subsamplesmentioning

confidence: 99%

Emulating Satellite Drag from Large Simulation Experiments

Sun¹,

Gramacy²,

Haaland³

et al. 2019

SIAM/ASA J. Uncertainty Quantification

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show abstract

“…With sparse approximation, storing and manipulating directly the training data for inference as in standard GP [1] is no longer necessary, instead, we need only to utilize the posterior of the inducing points. In future works, it would be interesting to compare p(y t |D 0:t−1 ) in (22) with the true predictive distribution of the model outputs y t , which can be derived from the joint distribution of y t and D 0:t−1 . This could provide insights into the approximation error introduced by the use of the inducing point assumption.…”

Section: A Model Predictionmentioning

confidence: 99%

“…This could provide insights into the approximation error introduced by the use of the inducing point assumption. Substituting (10) and (20) into (22) and following the computations in the prediction step of the standard Kalman filter yield [53]…”

Section: A Model Predictionmentioning

confidence: 99%

“…The standard GP model assumes a single output variable only. However, in practice, multi-output functions arise widely in geostatistics [16], robotics [17], sensor networks [18], chemometrics [19], traffic flow forecasting [20] and computational physics [21], [22], just to name a few. A typical example of multi-output regression is the robot inverse dynamics problem [17], [23].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Online Sparse Multi-Output Gaussian Process Regression and Learning

Yang

Wang

Mihaylova

2019

IEEE Trans. on Signal and Inf. Process. over Networks

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This paper proposes an approach for online training of a sparse multi-output Gaussian process (GP) model using sequentially obtained data. The considered model combines linearly multiple latent sparse GPs to produce correlated output variables. Each latent GP has its own set of inducing points to achieve sparsity. We show that given the model hyperparameters, the posterior over the inducing points is Gaussian under Gaussian noise since they are linearly related to the model outputs. However, the inducing points from different latent GPs would become correlated, leading to a full covariance matrix cumbersome to handle. Variational inference is thus applied and an approximate regression technique is obtained, with which the posteriors over different inducing point sets can always factorize. As the model outputs are non-linearly dependent on the hyperparameters, a novel marginalized particle filer (MPF)-based algorithm is proposed for the online inference of the inducing point values and hyperparameters. The approximate regression technique is incorporated in the MPF and its distributed realization is presented. Algorithm validation using synthetic and real data is conducted, and promising results are obtained.

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“…MTGPs model temporal or spatial relationships among infinitely many random variables, as scalar GPs, but also account for the statistical dependence across different sources of data (or tasks) [3,4,5,6,7,8,9]. How to choose an appropriate kernel to jointly model the cross covariance between tasks and auto-covariance within each task is the core aspect of MTGPs design [3,10,11,12,5,13,14].…”

Section: Introductionmentioning

confidence: 99%

Generalized Convolution Spectral Mixture for Multi-Task Gaussian Processes

Chen¹,

Laarhoven²,

Groot³

et al. 2018

Preprint

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Multi-Task Gaussian processes (MTGPs) have shown a significant progress both in expressiveness and interpretation of the relatedness between different tasks: from linear combinations of independent single-output Gaussian processes (GPs), through the direct modeling of the cross-covariances such as spectral mixture kernels with phase shift, to the design of multivariate covariance functions based on spectral mixture kernels which model delays among tasks in addition to phase differences, and which provide a parametric interpretation of the relatedness across tasks. In this paper we further extend expressiveness and interpretability of MTGPs models and introduce a new family of kernels capable to model nonlinear correlations between tasks as well as dependencies between component, including time and phase delay. Specifically, we use generalized convolution spectral mixture kernels for modeling dependencies at component level, and coupling coregionalization for discovering task level correlations. The proposed kernels for MTGP are validated on artificial data and compared with existing MTGPs methods on three real-world experiments. Results indicate the benefits of our more expressive representation with respect to performance and interpretability.

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Full scale multi-output Gaussian process emulator with nonseparable auto-covariance functions

Cited by 15 publications

References 35 publications

Emulating Satellite Drag from Large Simulation Experiments

Emulating Satellite Drag from Large Simulation Experiments

Online Sparse Multi-Output Gaussian Process Regression and Learning

Generalized Convolution Spectral Mixture for Multi-Task Gaussian Processes

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