KernelMatmul: Scaling Gaussian Processes to Large Time Series

Proceedings of the AAAI Conference on Artificial Intelligence, vol. 39, pp. 17223–17230

Abstract

Time series forecasting requires reliable uncertainty estimates. Gaussian process regression provides a powerful framework for modelling this in a probabilistic fashion. However, its application to large time series is challenging, due to its cubic time complexity and quadratic memory requirement. In this work, we present KernelMatmul, a novel method that accelerates Gaussian process inference and thus facilitates scaling of Gaussian process regression to large, irregularly sampled and multi-output time series. Leveraging conjugate gradients in combination with sparsity approximation, KernelMatmul achieves time and memory complexity linear in the number of samples. We thoroughly benchmark our new method against multiple baselines to demonstrate its benefits and limitations, both in efficiency and accuracy.

Authors 3

1. Tilman Hoffbauer Aachen Chair for AI Methodology (AIM)

   RWTH Aachen University

   Affiliation as printed

   Chair for AI Methodology, RWTH Aachen University, Germany

2. Holger H. Hoos Aachen Chair for AI Methodology

   RWTH Aachen University · Leiden University · University of British Columbia

   Affiliation as printed

   Chair for AI Methodology, RWTH Aachen University, Germany Leiden Institute of Advanced Computer Science, Leiden University, The Netherlands University of British Columbia, Canada

3. Jakob Bossek

   Paderborn University

   Affiliation as printed

   Chair for Machine Learning and Optimisation, Paderborn University, Germany