Math @ Duke

Publications [#304008] of David B. Dunson
search arxiv.org.Papers Published
 Banerjee, A; Dunson, DB; Tokdar, ST, Efficient Gaussian process regression for large datasets,
Biometrika, vol. 100 no. 1
(2013),
pp. 7589 [1106.5779v1], [doi]
(last updated on 2019/05/25)
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 subsetofregressors 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 finescale 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 lowerdimensional 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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