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• W3197575530 abstract "The stochastic partial differential equation approach to Gaussian processes (GPs) represents Mat'ern GP priors in terms of $n$ finite element basis functions and Gaussian coefficients with sparse precision matrix. Such representations enhance the scalability of GP regression and classification to datasets of large size $N$ by setting $napprox N$ and exploiting sparsity. In this paper we reconsider the standard choice $n approx N$ through an analysis of the estimation performance. Our theory implies that, under certain smoothness assumptions, one can reduce the computation and memory cost without hindering the estimation accuracy by setting $n ll N$ in the large $N$ asymptotics. Numerical experiments illustrate the applicability of our theory and the effect of the prior lengthscale in the pre-asymptotic regime." @default.
• W3197575530 created "2021-09-13" @default.
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• W3197575530 date "2021-09-06" @default.
• W3197575530 modified "2023-10-03" @default.
• W3197575530 title "Finite Element Representations of Gaussian Processes: Balancing Numerical and Statistical Accuracy" @default.
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• W3197575530 doi "https://doi.org/10.48550/arxiv.2109.02777" @default.
• W3197575530 hasPublicationYear "2021" @default.
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