A decomposed multi-fidelity covariance formulation allows Vecchia approximation on latent processes and GLS mean removal to deliver scalable, fully likelihood-based fusion of noisy low-fidelity and accurate high-fidelity spatio-temporal data.
An accuracy-runtime trade-off comparison of scalable Gaussian process approximations for spatial data
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abstract
Gaussian processes (GPs) are flexible, probabilistic, nonparametric models widely used in fields such as spatial statistics and machine learning. A drawback of Gaussian processes is their computational cost, with $O(N^3)$ time and $O(N^2)$ memory complexity, which makes them prohibitive for large data sets. Numerous approximation techniques have been proposed to address this limitation. In this work, we systematically compare the accuracy of different Gaussian process approximations with respect to likelihood evaluation, parameter estimation, and prediction, explicitly accounting for the computational time required. We analyze the trade-off between accuracy and runtime on multiple simulated and large-scale real-world data sets and find that Vecchia approximations consistently provide the best accuracy-runtime trade-off across most settings considered.
representative citing papers
VIF approximations combine inducing points and Vecchia methods with an efficient neighbor search to deliver computationally efficient, accurate, and stable Gaussian process inference on large data.
citing papers explorer
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A new framework for non-stationary spatio-temporal data fusion of multi-fidelity models
A decomposed multi-fidelity covariance formulation allows Vecchia approximation on latent processes and GLS mean removal to deliver scalable, fully likelihood-based fusion of noisy low-fidelity and accurate high-fidelity spatio-temporal data.
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Vecchia-Inducing-Points Full-Scale Approximations for Gaussian Processes
VIF approximations combine inducing points and Vecchia methods with an efficient neighbor search to deliver computationally efficient, accurate, and stable Gaussian process inference on large data.