title: Efficient Gaussian process regression for large datasets.
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 ofn3wherenis 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 increasingn. 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.
authors.affiliation: Department of Statistical Science, Duke University, Box 90251, Durham, North Carolina 27708-0251, U.S.A.
authors.forename: Anjishnu
authors.initials: A
authors.lastname: Banerjee
authors.forename: David B
authors.initials: DB
authors.lastname: Dunson
authors.forename: Surya T
authors.initials: ST
authors.lastname: Tokdar
keywords: Bayesian regression; Compressive sensing; Dimensionality reduction; Gaussian process; Random projection