TY - JOUR
T1 - Deep Compositional Spatial Models
AU - Zammit-Mangion, Andrew
AU - Ng, Tin Lok James
AU - Vu, Quan
AU - Filippone, Maurizio
N1 - Publisher Copyright:
© 2021 American Statistical Association.
PY - 2022
Y1 - 2022
N2 - Spatial processes with nonstationary and anisotropic covariance structure are often used when modeling, analyzing, and predicting complex environmental phenomena. Such processes may often be expressed as ones that have stationary and isotropic covariance structure on a warped spatial domain. However, the warping function is generally difficult to fit and not constrained to be injective, often resulting in “space-folding.” Here, we propose modeling an injective warping function through a composition of multiple elemental injective functions in a deep-learning framework. We consider two cases; first, when these functions are known up to some weights that need to be estimated, and, second, when the weights in each layer are random. Inspired by recent methodological and technological advances in deep learning and deep Gaussian processes, we employ approximate Bayesian methods to make inference with these models using graphics processing units. Through simulation studies in one and two dimensions we show that the deep compositional spatial models are quick to fit, and are able to provide better predictions and uncertainty quantification than other deep stochastic models of similar complexity. We also show their remarkable capacity to model nonstationary, anisotropic spatial data using radiances from the MODIS instrument aboard the Aqua satellite.
AB - Spatial processes with nonstationary and anisotropic covariance structure are often used when modeling, analyzing, and predicting complex environmental phenomena. Such processes may often be expressed as ones that have stationary and isotropic covariance structure on a warped spatial domain. However, the warping function is generally difficult to fit and not constrained to be injective, often resulting in “space-folding.” Here, we propose modeling an injective warping function through a composition of multiple elemental injective functions in a deep-learning framework. We consider two cases; first, when these functions are known up to some weights that need to be estimated, and, second, when the weights in each layer are random. Inspired by recent methodological and technological advances in deep learning and deep Gaussian processes, we employ approximate Bayesian methods to make inference with these models using graphics processing units. Through simulation studies in one and two dimensions we show that the deep compositional spatial models are quick to fit, and are able to provide better predictions and uncertainty quantification than other deep stochastic models of similar complexity. We also show their remarkable capacity to model nonstationary, anisotropic spatial data using radiances from the MODIS instrument aboard the Aqua satellite.
KW - Deep models
KW - Nonstationarity
KW - Spatial statistics
KW - Stochastic processes
KW - Variational Bayes
UR - http://www.scopus.com/inward/record.url?scp=85104090622&partnerID=8YFLogxK
U2 - 10.1080/01621459.2021.1887741
DO - 10.1080/01621459.2021.1887741
M3 - Article
AN - SCOPUS:85104090622
SN - 0162-1459
VL - 117
SP - 1787
EP - 1808
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 540
ER -