Gaussian random field approximation via Stein's method with applications to wide random neural networks

arXiv:2306.16308v2 Announce Type: replace-cross
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