Scalable Exact Inference in MultiOutput Gaussian Processes
Abstract
Multioutput Gaussian processes (MOGPs) leverage the flexibility and interpretability of GPs while capturing structure across outputs, which is desirable, for example, in spatiotemporal modelling. The key problem with MOGPs is the cubic computational scaling in the number of both inputs (e.g., time points or locations), n, and outputs, p. Current methods reduce this to O(n^3 m^3), where m < p is the desired degrees of freedom. This computational cost, however, is still prohibitive in many applications. To address this limitation, we present the Orthogonal Linear Mixing Model (OLMM), an MOGP in which exact inference scales linearly in m: O(n^3 m). This advance opens up a wide range of realworld tasks and can be combined with existing GP approximations in a plugandplay way as demonstrated in the paper. Additionally, the paper organises the existing disparate literature on MOGP models into a simple taxonomy called the Mixing Model Hierarchy (MMH).
 Publication:

arXiv eprints
 Pub Date:
 November 2019
 arXiv:
 arXiv:1911.06287
 Bibcode:
 2019arXiv191106287B
 Keywords:

 Statistics  Machine Learning;
 Computer Science  Machine Learning
 EPrint:
 19 pages, 9 figures, includes appendix