TY - JOUR
T1 - Learning Temporal Evolution of Spatial Dependence with Generalized Spatiotemporal Gaussian Process Models
AU - Lan, Shiwei
N1 - Funding Information:
SL is supported by NSF grant DMS-2134256. Data collection and sharing for this project was funded by the Alzheimer’s Disease Neuroimaging Initiative (ADNI) (National Institutes of Health Grant U01 AG024904) and DOD ADNI (Department of Defense award number W81XWH-12-2-0012). ADNI is funded by the National Institute on Aging, the National Institute of Biomedical Imaging and Bioengineering, and through generous contributions from the following: AbbVie, Alzheimer’s Association; Alzheimer’s Drug Discovery Foundation; Araclon Biotech; BioClinica, Inc.; Biogen; Bristol-Myers Squibb Company;
Publisher Copyright:
©2022 Shiwei Lan.
PY - 2022/8/1
Y1 - 2022/8/1
N2 - A large number of scientific studies involve high-dimensional spatiotemporal data with complicated relationships. In this paper, we focus on a type of space-time interaction named temporal evolution of spatial dependence (TESD), which is a zero time-lag spatiotemporal covariance. For this purpose, we propose a novel Bayesian nonparametric method based on non-stationary spatiotemporal Gaussian process (STGP). The classic STGP has a covariance kernel separable in space and time, failed to characterize TESD. More recent works on non-separable STGP treat location and time together as a joint variable, which is unnecessarily inefficient. We generalize STGP (gSTGP) to introduce time-dependence to the spatial kernel by varying its eigenvalues over time in the Mercer’s representation. The resulting non-stationary non-separable covariance model bares a quasi Kronecker sum structure. Finally, a hierarchical Bayesian model for the joint covariance is proposed to allow for full flexibility in learning TESD. A simulation study and a longitudinal neuroimaging analysis on Alzheimer’s patients demonstrate that the proposed methodology is (statistically) effective and (computationally) efficient in characterizing TESD. Theoretic properties of gSTGP including posterior contraction (for covariance) are also studied.
AB - A large number of scientific studies involve high-dimensional spatiotemporal data with complicated relationships. In this paper, we focus on a type of space-time interaction named temporal evolution of spatial dependence (TESD), which is a zero time-lag spatiotemporal covariance. For this purpose, we propose a novel Bayesian nonparametric method based on non-stationary spatiotemporal Gaussian process (STGP). The classic STGP has a covariance kernel separable in space and time, failed to characterize TESD. More recent works on non-separable STGP treat location and time together as a joint variable, which is unnecessarily inefficient. We generalize STGP (gSTGP) to introduce time-dependence to the spatial kernel by varying its eigenvalues over time in the Mercer’s representation. The resulting non-stationary non-separable covariance model bares a quasi Kronecker sum structure. Finally, a hierarchical Bayesian model for the joint covariance is proposed to allow for full flexibility in learning TESD. A simulation study and a longitudinal neuroimaging analysis on Alzheimer’s patients demonstrate that the proposed methodology is (statistically) effective and (computationally) efficient in characterizing TESD. Theoretic properties of gSTGP including posterior contraction (for covariance) are also studied.
KW - Non-stationary Non-separable Kernel
KW - Nonparametric Spatiotemporal Covariance Model
KW - Quasi Kronecker Product/Sum Structure
KW - Spatiotemporal Gaussian process
KW - Temporal Evolution of Spatial Dependence
UR - http://www.scopus.com/inward/record.url?scp=85140420671&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85140420671&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:85140420671
SN - 1532-4435
VL - 23
JO - Journal of Machine Learning Research
JF - Journal of Machine Learning Research
ER -