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Gaussian random field approximation via Stein's method with applications to wide random neural networks
May 2, 2024, 4:43 a.m. | Krishnakumar Balasubramanian, Larry Goldstein, Nathan Ross, Adil Salim
cs.LG updates on arXiv.org arxiv.org
Abstract: We derive upper bounds on the Wasserstein distance ($W_1$), with respect to $\sup$-norm, between any continuous $\mathbb{R}^d$ valued random field indexed by the $n$-sphere and the Gaussian, based on Stein's method. We develop a novel Gaussian smoothing technique that allows us to transfer a bound in a smoother metric to the $W_1$ distance. The smoothing is based on covariance functions constructed using powers of Laplacian operators, designed so that the associated Gaussian process has a …
abstract applications approximation arxiv continuous cs.lg math.pr math.st networks neural networks norm novel random sphere stat.ml stat.th type via
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