gp2Scale: A Class of Compactly-Supported Non-Stationary Kernels and Distributed Computing for Exact Gaussian Processes on 10 Million Data Points

TL;DR

gp2Scale enables exact Gaussian process inference on over 10 million data points by leveraging non-stationary kernels and distributed computing, avoiding common approximation methods and maintaining high accuracy and flexibility.

Contribution

The paper introduces gp2Scale, a novel scalable method for exact Gaussian processes that exploits kernel design and sparse structure without approximations, handling large datasets efficiently.

Findings

Successfully scales to over 10 million data points.

Outperforms state-of-the-art approximation algorithms in accuracy.

Maintains flexibility for various kernel and noise configurations.

Abstract

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.