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Efficient Gaussian process regression for large datasets. Biometrika 2013 Mar;100(1):75-89

Date

07/23/2013

Pubmed ID

23869109

Pubmed Central ID

PMC3712798

DOI

10.1093/biomet/ass068

Scopus ID

2-s2.0-84874776816 (requires institutional sign-in at Scopus site)   95 Citations

Abstract

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.

Author List

Banerjee A, Dunson DB, Tokdar ST

Author

Anjishnu Banerjee PhD Associate Professor in the Data Science Institute department at Medical College of Wisconsin