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Gaussian Processes (GP) are a powerful framework for modeling expensive black-box functions and have thus been adopted for various challenging modeling and optimization problems. In GP-based modeling, we typically default to a stationary covariance kernel to model the underlying function over the input domain, but many real-world applications, such as controls and cyber-physical system safety, often require modeling and optimization of functions that are locally stationary and globally non-stationary across the domain; using standard GPs with a stationary kernel often yields poor modeling performance in such scenarios. In this paper, we propose a novel modeling technique called Class-GP (Class Gaussian Process) to model a class of heterogeneous functions, i.e., non-stationary functions which can be divided into locally stationary functions over the partitions of input space with one active stationary function in each partition. We provide theoretical insights into the modeling power of Class-GP and demonstrate its benefits over standard modeling techniques via extensive empirical evaluations.
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Spatio-Temporal Expanding Distance Asymptotic Framework for Locally Stationary Processes
Spatio-temporal data indexed by sampling locations and sampling time points are encountered in many scientific disciplines such as climatology, environ- mental sciences, and public health. Here, we propose a novel spatio-temporal expanding distance (STED) asymptotic framework for studying the proper- ties of statistical inference for nonstationary spatio-temporal models. In particular, to model spatio-temporal dependence, we develop a new class of locally stationary spatio-temporal covariance functions. The STED asymp- totic framework has a fixed spatio-temporal domain for spatio-temporal pro- cesses that are globally nonstationary in a rescaled fixed domain and locally stationary in a distance expanding domain. The utility of STED is illus- trated by establishing the asymptotic properties of the maximum likelihood estimation for a general class of spatio-temporal covariance functions. A simulation study suggests sound finite-sample properties and the method is applied to a sea-surface temperature dataset.
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- PAR ID:
- 10338200
- Date Published:
- Journal Name:
- Sankhya A
- ISSN:
- 0976-836X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s13171-020-00213-4
