A0309
Title: Radial neighbors for provably accurate scalable approximations of Gaussian processes
Authors: Yichen Zhu - Duke University (United States) [presenting]
Abstract: In geostatistical problems with massive sample sizes, Gaussian processes (GP) can be approximated using sparse-directed acyclic graphs to achieve scalable O(n) computational complexity. In these models, data at each location are typically assumed conditionally dependent on a small set of parents, which usually include a subset of the nearest neighbours. These methodologies often exhibit excellent empirical performance, but the lack of theoretical validation leads to unclear guidance in specifying the underlying graphical model. It may result in sensitivity to graph choice. These issues are addressed by introducing radial neighbours Gaussian processes and corresponding theoretical guarantees. The method proposes to approximate GPs using a sparse directed acyclic graph in which a directed edge connects every location to its neighbours within a predetermined radius. Using our novel construction, it is shown that one can accurately approximate a Gaussian process in Wasserstein-2 distance, with an error rate determined by the approximation radius, the spatial covariance function, and the spatial dispersion of samples. The method is also insensitive to specific graphical model choices. Further empirical validation of our approach is offered via applications on simulated and real-world data showing state-of-the-art performance in the posterior inference of spatial random effects.
