Exact Gaussian Processes on a Million Data Points

Gaussian processes (GPs) are flexible non-parametric models, with a capacity that grows with the available data. However, computational constraints with standard inference procedures have limited exact GPs to problems with fewer than about ten thousand training points, necessitating approximations for larger datasets. In this paper, we develop a scalable approach for exact GPs that leverages multi-GPU parallelization and methods like linear conjugate gradients, accessing the kernel matrix only through matrix multiplication. By partitioning and distributing kernel matrix multiplies, we demonstrate that an exact GP can be trained on over a million points, a task previously thought to be impossible with current computing hardware. Moreover, our approach is generally applicable, without constraints to grid data or specific kernel classes. Enabled by this scalability, we perform the first-ever comparison of exact GPs against scalable GP approximations on datasets with $10^4 \! -\! 10^6$ data points, showing dramatic performance improvements.

Authors

• Ke Wang School of Astronautics, Beihang University; Tianmushan Laboratory, Beihang University
• Geoff Pleiss
• Jacob Gardner University of Pennsylvania
• Stephen Tyree NVIDIA
• Kilian Weinberger
• Andrew Gordon Wilson

Keywords

No keywords are indexed for this paper.