dc.contributor.author Li, Yuxiao dc.contributor.author Sun, Ying dc.contributor.author Reich, Brian J dc.date.accessioned 2020-07-29T08:59:11Z dc.date.available 2020-07-29T08:59:11Z dc.date.issued 2020-07-23 dc.identifier.uri http://hdl.handle.net/10754/664490 dc.description.abstract In spatial statistics, a common objective is to predict the values of a spatial process at unobserved locations by exploiting spatial dependence. In geostatistics, Kriging provides the best linear unbiased predictor using covariance functions and is often associated with Gaussian processes. However, when considering non-linear prediction for non-Gaussian and categorical data, the Kriging prediction is not necessarily optimal, and the associated variance is often overly optimistic. We propose to use deep neural networks (DNNs) for spatial prediction. Although DNNs are widely used for general classification and prediction, they have not been studied thoroughly for data with spatial dependence. In this work, we propose a novel neural network structure for spatial prediction by adding an embedding layer of spatial coordinates with basis functions. We show in theory that the proposed DeepKriging method has multiple advantages over Kriging and classical DNNs only with spatial coordinates as features. We also provide density prediction for uncertainty quantification without any distributional assumption and apply the method to PM$_{2.5}$ concentrations across the continental United States. dc.description.sponsorship This research is supported by King Abdullah University of Science and Technology (KAUST), Office of Sponsored Research (OSR) under Award No: OSR-2019-CRG7- 3800. dc.publisher arXiv dc.relation.url https://arxiv.org/pdf/2007.11972 dc.rights Archived with thanks to arXiv dc.title DeepKriging: Spatially Dependent Deep Neural Networks for Spatial Prediction dc.type Preprint dc.contributor.department Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division dc.contributor.department Environmental Statistics Group dc.contributor.department Statistics Program dc.eprint.version Pre-print dc.contributor.institution North Carolina State University, Department of Statistics, Campus Box 8203, 5212 SAS Hall, Raleigh, NC 27695. dc.identifier.arxivid 2007.11972 kaust.person Li, Yuxiao kaust.person Sun, Ying kaust.grant.number OSR-2019-CRG7- 3800. refterms.dateFOA 2020-07-29T08:59:56Z kaust.acknowledged.supportUnit Office of Sponsored Research (OSR)
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