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Efficient Gaussian process regression for large datasets

Publication ,  Journal Article
Banerjee, A; Dunson, DB; Tokdar, ST
Published in: Biometrika
2013

Gaussian processes are widely used in nonparametric regression, classification and spatiotemporal modelling, facilitated in part by a rich literature on their theoretical properties. However, one of their practical limitations is expensive computation, typically on the order of n3 where n is the number of data points, in performing the necessary matrix inversions. For large datasets, storage and processing also lead to computational bottlenecks, and numerical stability of the estimates and predicted values degrades with increasing n. Various methods have been proposed to address these problems, including predictive processes in spatial data analysis and the subset-of-regressors technique in machine learning. The idea underlying these approaches is to use a subset of the data, but this raises questions concerning sensitivity to the choice of subset and limitations in estimating fine-scale structure in regions that are not well covered by the subset. Motivated by the literature on compressive sensing, we propose an alternative approach that involves linear projection of all the data points onto a lower-dimensional subspace. We demonstrate the superiority of this approach from a theoretical perspective and through simulated and real data examples. © 2012 Biometrika Trust.

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Published In

Biometrika

DOI

ISSN

0006-3444

Publication Date

2013

Volume

100

Issue

1

Start / End Page

75 / 89

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1403 Econometrics
  • 0104 Statistics
  • 0103 Numerical and Computational Mathematics
 

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Banerjee, A., Dunson, D. B., & Tokdar, S. T. (2013). Efficient Gaussian process regression for large datasets. Biometrika, 100(1), 75–89. https://doi.org/10.1093/biomet/ass068
Banerjee, A., D. B. Dunson, and S. T. Tokdar. “Efficient Gaussian process regression for large datasets.” Biometrika 100, no. 1 (2013): 75–89. https://doi.org/10.1093/biomet/ass068.
Banerjee A, Dunson DB, Tokdar ST. Efficient Gaussian process regression for large datasets. Biometrika. 2013;100(1):75–89.
Banerjee, A., et al. “Efficient Gaussian process regression for large datasets.” Biometrika, vol. 100, no. 1, 2013, pp. 75–89. Scival, doi:10.1093/biomet/ass068.
Banerjee A, Dunson DB, Tokdar ST. Efficient Gaussian process regression for large datasets. Biometrika. 2013;100(1):75–89.
Journal cover image

Published In

Biometrika

DOI

ISSN

0006-3444

Publication Date

2013

Volume

100

Issue

1

Start / End Page

75 / 89

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1403 Econometrics
  • 0104 Statistics
  • 0103 Numerical and Computational Mathematics