IDEAS home Printed from https://ideas.repec.org/a/jss/jstsof/v072i01.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.jstatsoft.org/index.php/jss/article/view/v072i01/v72i01.pdf
    Download Restriction: no
    File URL: https://www.jstatsoft.org/index.php/jss/article/downloadSuppFile/v072i01/laGP_1.3.tar.gz
    Download Restriction: no
    File URL: https://www.jstatsoft.org/index.php/jss/article/downloadSuppFile/v072i01/v72i01.R
    Download Restriction: no
    File URL: https://libkey.io/http://hdl.handle.net/10.18637/jss.v072.i01?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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. 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).
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. K. Shuvo Bakar & Nicholas Biddle & Philip Kokic & Huidong Jin, 2020. "A Bayesian spatial categorical model for prediction to overlapping geographical areas in sample surveys," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(2), pages 535-563, February.
    2. Matthias Katzfuss & Joseph Guinness & Wenlong Gong & Daniel Zilber, 2020. "Vecchia Approximations of Gaussian-Process Predictions," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(3), pages 383-414, September.
    3. Ranadeep Daw & Christopher K. Wikle, 2023. "REDS: Random ensemble deep spatial prediction," Environmetrics, John Wiley & Sons, Ltd., vol. 34(1), February.
    4. Aikaterini P. Kyprioti & Alexandros A. Taflanidis & Matthew Plumlee & Taylor G. Asher & Elaine Spiller & Richard A. Luettich & Brian Blanton & Tracy L. Kijewski-Correa & Andrew Kennedy & Lauren Schmie, 2021. "Improvements in storm surge surrogate modeling for synthetic storm parameterization, node condition classification and implementation to small size databases," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 109(2), pages 1349-1386, November.
    5. Jonathan R. Bradley & Christopher K. Wikle & Scott H. Holan, 2017. "Regionalization of multiscale spatial processes by using a criterion for spatial aggregation error," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 815-832, June.
    6. Andrew Finley & Sudipto Banerjee & Alan Gelfand, 2012. "Bayesian dynamic modeling for large space-time datasets using Gaussian predictive processes," Journal of Geographical Systems, Springer, vol. 14(1), pages 29-47, January.
    7. Sierra Pugh & Matthew J. Heaton & Jeff Svedin & Neil Hansen, 2019. "Spatiotemporal Lagged Models for Variable Rate Irrigation in Agriculture," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(4), pages 634-650, December.
    8. Zammit-Mangion, Andrew & Rougier, Jonathan, 2018. "A sparse linear algebra algorithm for fast computation of prediction variances with Gaussian Markov random fields," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 116-130.
    9. Marchetti, Yuliya & Nguyen, Hai & Braverman, Amy & Cressie, Noel, 2018. "Spatial data compression via adaptive dispersion clustering," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 138-153.
    10. Montero, José-María & Fernández-Avilés, Gema, 2015. "Functional Kriging Prediction of Pollution Series: The Geostatistical Alternative for Spatially-fixed Data/Predicción de series de contaminación mediante kriging funcional. La alternativa geoestadísti," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 33, pages 145-179, Enero.
    11. Chandra, Hukum & Salvati, Nicola & Chambers, Ray & Tzavidis, Nikos, 2012. "Small area estimation under spatial nonstationarity," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2875-2888.
    12. Kenneth K. Lopiano & Linda J. Young & Carol A. Gotway, 2014. "A pseudo-penalized quasi-likelihood approach to the spatial misalignment problem with non-normal data," Biometrics, The International Biometric Society, vol. 70(3), pages 648-660, September.
    13. Jonathan Bradley & Noel Cressie & Tao Shi, 2015. "Comparing and selecting spatial predictors using local criteria," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 1-28, March.
    14. Hang Zhang & Yong Liu & Dongyang Yang & Guanpeng Dong, 2022. "PM 2.5 Concentrations Variability in North China Explored with a Multi-Scale Spatial Random Effect Model," IJERPH, MDPI, vol. 19(17), pages 1-14, August.
    15. Sameh Abdulah & Yuxiao Li & Jian Cao & Hatem Ltaief & David E. Keyes & Marc G. Genton & Ying Sun, 2023. "Large‐scale environmental data science with ExaGeoStatR," Environmetrics, John Wiley & Sons, Ltd., vol. 34(1), February.
    16. Mahdi Hosseinpouri & Majid Jafari Khaledi, 2019. "An area-specific stick breaking process for spatial data," Statistical Papers, Springer, vol. 60(1), pages 199-221, February.
    17. Li, Yang & Zhu, Zhengyuan, 2016. "Modeling nonstationary covariance function with convolution on sphere," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 233-246.
    18. Huang Huang & Sameh Abdulah & Ying Sun & Hatem Ltaief & David E. Keyes & Marc G. Genton, 2021. "Competition on Spatial Statistics for Large Datasets," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(4), pages 580-595, December.
    19. Furrer, Reinhard & Bachoc, François & Du, Juan, 2016. "Asymptotic properties of multivariate tapering for estimation and prediction," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 177-191.
    20. Yang, Dazhi & Gueymard, Christian A., 2019. "Producing high-quality solar resource maps by integrating high- and low-accuracy measurements using Gaussian processes," Renewable and Sustainable Energy Reviews, Elsevier, vol. 113(C), pages 1-1.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:jss:jstsof:v:072:i01. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Christopher F. Baum (email available below). General contact details of provider: http://www.jstatsoft.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.