Despite a large corpus of recent work on scaling up Gaussian processes, a stubborn trade-off between computational speed, prediction and uncertainty quantification accuracy, and customizability persists. This is because the vast majority of existing methodologies exploit various levels of approximations that lower accuracy and limit the flexibility of kernel and noise-model designs -- an unacceptable drawback at a time when expressive non-stationary kernels are on the rise in many fields. Here, we propose a methodology we term \emph{gp2Scale} that scales exact Gaussian processes to more than 10 million data points without relying on inducing points, kernel interpolation, or neighborhood-based approximations, and instead leveraging the existing capabilities of a GP: its kernel design. Highly flexible, compactly supported, and non-stationary kernels lead to the identification of naturally occurring sparse structure in the covariance matrix, which is then exploited for the calculations of the linear system solution and the log-determinant for training. We demonstrate our method's functionality on several real-world datasets and compare it with state-of-the-art approximation algorithms. Although we show superior approximation performance in many cases, the method's real power lies in its agnosticism toward arbitrary GP customizations -- core kernel design, noise, and mean functions -- and the type of input space, making it optimally suited for modern Gaussian process applications.

Machine learning for node classification on graphs is a prominent area driven by applications such as recommendation systems.

However, current methods are mostly limited to discrete graph filtering operations.

Neural Information Processing Systems http://nips.cc/

A typical way in which network data is recorded is to measure all interactions involving a specified set of core nodes, which produces a graph containing this core together with a potentially larger set of fringe nodes that link to the core.

Sparse training is a popular technique to reduce the overhead of training large models.

However, these results are limited to a single residual block (i.e., shallow ResNets),