Posterior contraction in Gaussian process regression using Wasserstein approximations
Anirban Bhattacharya, Debdeep Pati · Information and Inference A Journal of the IMA · 2017
We study posterior rates of contraction in Gaussian process regression with potentially unbounded covariate domain. Our argument relies on developing a Gaussian approximation to the posterior of the leading coefficients of a Karhunen–Loève expansion of the Gaussian process. The salient feature of our result is deriving such an approximation in the |$L^2$| Wasserstein distance and relating the speed of the approximation to the posterior contraction rate using a coupling argument. Specific illustrations are provided for the Gaussian (or squared exponential) and Matérn covariance kernels.