Hierarchical Inducing Point Gaussian Process for Inter-domain Observations
This addresses a scalability bottleneck in inter-domain GPs for researchers and practitioners in machine learning, though it is incremental as it builds on existing GP methods with specific assumptions.
The authors tackled the problem of scalable inference for inter-domain Gaussian Processes (GPs) where observations and realizations are on different domains, introducing HIP-GP to enable millions of inducing points and improve approximation accuracy for low-dimensional problems.
We examine the general problem of inter-domain Gaussian Processes (GPs): problems where the GP realization and the noisy observations of that realization lie on different domains. When the mapping between those domains is linear, such as integration or differentiation, inference is still closed form. However, many of the scaling and approximation techniques that our community has developed do not apply to this setting. In this work, we introduce the hierarchical inducing point GP (HIP-GP), a scalable inter-domain GP inference method that enables us to improve the approximation accuracy by increasing the number of inducing points to the millions. HIP-GP, which relies on inducing points with grid structure and a stationary kernel assumption, is suitable for low-dimensional problems. In developing HIP-GP, we introduce (1) a fast whitening strategy, and (2) a novel preconditioner for conjugate gradients which can be helpful in general GP settings. Our code is available at https: //github.com/cunningham-lab/hipgp.