Further Understanding of a Local Gaussian Process Approximation: Characterising Convergence in the Finite Regime

arXiv:2404.06200v1 Announce Type: cross
Abstract: We show that common choices of kernel functions for a highly accurate and massively scalable nearest-neighbour based GP regression model (GPnn: \cite{GPnn}) exhibit gradual convergence to asymptotic behaviour as dataset-size $n$ increases. For isotropic kernels such as Mat\'{e}rn and squared-exponential, an upper bound on the predictive MSE can be obtained as $O(n^{-\frac{p}{d}})$ for input dimension $d$, $p$ dictated by the kernel (and $d>p$) and fixed number of nearest-neighbours $m$ with minimal assumptions on the input …

abstract approximation arxiv convergence dataset functions kernel math.st process regression scalable show stat.ml stat.th type understanding