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Efficient Gaussian process regression for large datasets.

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Date
2013-03
Authors
Banerjee, Anjishnu
Dunson, David B
Tokdar, Surya T
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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 n(3) 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.
Type
Journal article
Subject
Bayesian regression
Compressive sensing
Dimensionality reduction
Gaussian process
Random projection
Permalink
https://hdl.handle.net/10161/15591
Published Version (Please cite this version)
10.1093/biomet/ass068
Publication Info
Banerjee, Anjishnu; Dunson, David B; & Tokdar, Surya T (2013). Efficient Gaussian process regression for large datasets. Biometrika, 100(1). pp. 75-89. 10.1093/biomet/ass068. Retrieved from https://hdl.handle.net/10161/15591.
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Scholars@Duke

Dunson

David B. Dunson

Arts and Sciences Distinguished Professor of Statistical Science
My research focuses on developing new tools for probabilistic learning from complex data - methods development is directly motivated by challenging applications in ecology/biodiversity, neuroscience, environmental health, criminal justice/fairness, and more.  We seek to develop new modeling frameworks, algorithms and corresponding code that can be used routinely by scientists and decision makers.  We are also interested in new inference framework and in studying theoretical properties
Tokdar

Surya Tapas Tokdar

Professor of Statistical Science
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