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laGP: Large-Scale Spatial Modeling via Local Approximate Gaussian Processes in R

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  • Gramacy, Robert B.

Abstract

Gaussian process (GP) regression models make for powerful predictors in out of sample exercises, but cubic runtimes for dense matrix decompositions severely limit the size of data - training and testing - on which they can be deployed. That means that in computer experiment, spatial/geo-physical, and machine learning contexts, GPs no longer enjoy privileged status as data sets continue to balloon in size. We discuss an implementation of local approximate Gaussian process models, in the laGP package for R, that offers a particular sparse-matrix remedy uniquely positioned to leverage modern parallel computing architectures. The laGP approach can be seen as an update on the spatial statistical method of local kriging neighborhoods. We briefly review the method, and provide extensive illustrations of the features in the package through worked-code examples. The appendix covers custom building options for symmetric multi-processor and graphical processing units, and built-in wrapper routines that automate distribution over a simple network of workstations.

Suggested Citation

  • Gramacy, Robert B., 2016. "laGP: Large-Scale Spatial Modeling via Local Approximate Gaussian Processes in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 72(i01).
    • Handle: RePEc:jss:jstsof:v:072:i01
    DOI: http://hdl.handle.net/10.18637/jss.v072.i01
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    References listed on IDEAS

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    1. Abhirup Datta & Sudipto Banerjee & Andrew O. Finley & Alan E. Gelfand, 2016. "Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 800-812, April.
    2. Noel Cressie & Gardar Johannesson, 2008. "Fixed rank kriging for very large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 209-226, February.
    3. Finley, Andrew O. & Banerjee, Sudipto & Carlin, Bradley P., 2007. "spBayes: An R Package for Univariate and Multivariate Hierarchical Point-referenced Spatial Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 19(i04).
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    1. Monterrubio-Gómez, Karla & Roininen, Lassi & Wade, Sara & Damoulas, Theodoros & Girolami, Mark, 2020. "Posterior inference for sparse hierarchical non-stationary models," Computational Statistics & Data Analysis, Elsevier, vol. 148(C).
    2. Yiping Hong & Yan Song & Sameh Abdulah & Ying Sun & Hatem Ltaief & David E. Keyes & Marc G. Genton, 2023. "The Third Competition on Spatial Statistics for Large Datasets," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(4), pages 618-635, December.
    3. Cole, D. Austin & Gramacy, Robert B. & Ludkovski, Mike, 2022. "Large-scale local surrogate modeling of stochastic simulation experiments," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    4. Mostafa Reisi Gahrooei & Hao Yan & Kamran Paynabar, 2020. "Comments on: On Active Learning Methods for Manifold Data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 38-41, March.
    5. Jack P. C. Kleijnen & Wim C. M. van Beers, 2022. "Statistical Tests for Cross-Validation of Kriging Models," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 607-621, January.
    6. Kleijnen, J.P.C. & van Beers, W.C.M., 2018. "Prediction for Big Data through Kriging : Small Sequential and One-Shot Designs," Other publications TiSEM b0504930-f518-44f7-908c-6, Tilburg University, School of Economics and Management.
    7. Daniel W. Gladish & Daniel E. Pagendam & Luk J. M. Peeters & Petra M. Kuhnert & Jai Vaze, 2018. "Emulation Engines: Choice and Quantification of Uncertainty for Complex Hydrological Models," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(1), pages 39-62, March.
    8. Stefano Blasi & Maryam Bahrami & Elmar Engels & Alexander Gepperth, 2024. "Safe contextual Bayesian optimization integrated in industrial control for self-learning machines," Journal of Intelligent Manufacturing, Springer, vol. 35(2), pages 885-903, February.
    9. Matthew J. Heaton & Abhirup Datta & Andrew O. Finley & Reinhard Furrer & Joseph Guinness & Rajarshi Guhaniyogi & Florian Gerber & Robert B. Gramacy & Dorit Hammerling & Matthias Katzfuss & Finn Lindgr, 2019. "A Case Study Competition Among Methods for Analyzing Large Spatial Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(3), pages 398-425, September.
    10. Sudipto Banerjee, 2023. "Discussion of “Saving Storage in Climate Ensembles: A Model-Based Stochastic Approach” by Huang Huang, Stefano Castruccio, Allison H. Baker and Marc Genton," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(2), pages 365-369, June.
    11. Raju Chowdhury & Neelesh S. Upadhye, 2025. "Addressing mixed constraints: an improved framework for black-box optimization," Journal of Global Optimization, Springer, vol. 92(4), pages 889-908, August.
    12. Xuefei Lu & Alessandro Rudi & Emanuele Borgonovo & Lorenzo Rosasco, 2020. "Faster Kriging: Facing High-Dimensional Simulators," Operations Research, INFORMS, vol. 68(1), pages 233-249, January.
    13. Hans Olav Vogt Myklebust & Jo Eidsvik & Iver Bakken Sperstad & Debarun Bhattacharjya, 2020. "Value of Information Analysis for Complex Simulator Models: Application to Wind Farm Maintenance," Decision Analysis, INFORMS, vol. 17(2), pages 134-153, June.
    14. Nathan Wycoff & John W. Smith Jr. & Annie S. Booth & Robert B. Gramacy, 2026. "Voronoi candidates for Bayesian optimization," Journal of Global Optimization, Springer, vol. 94(1), pages 175-201, January.

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