Radial neighbours for provably accurate scalable approximations of Gaussian processes
提出径向邻居高斯过程（RadGP），通过有向无环图连接每个位置与其半径内所有邻居，证明其可在Wasserstein-2距离下精确逼近无限制高斯过程，误差率由半径、协方差函数和样本分散度决定，模拟和真实数据验证了其优秀性能。
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 neighbors. These methodologies often exhibit excellent empirical performance, but the lack of theoretical validation leads to unclear guidance in specifying the underlying graphical model and sensitivity to graph choice. We address these issues by introducing radial neighbors Gaussian processes (RadGP), a class of Gaussian processes based on directed acyclic graphs in which directed edges connect every location to all of its neighbors within a predetermined radius. We prove that any radial neighbors Gaussian process can accurately approximate the corresponding unrestricted 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. We offer further empirical validation of our approach via applications on simulated and real world data showing excellent performance in both prior and posterior approximations to the original Gaussian process.