Fast Gaussian Processes for Bayesian non-parametric inference: How smooth is your latent process?
Conference
64th ISI World Statistics Congress - Ottawa, Canada
Format: IPS Abstract
Keywords: "bayesian, gaussian-process
Session: IPS 192 - Advancing environmental statistics through online collaborative groups
Monday 17 July 2 p.m. - 3:40 p.m. (Canada/Eastern)
Abstract
Gaussian Processes (GP) are flexible regression tools used in various applied contexts, including spatial regression and machine learning. Due to the computational complexities of matrix inversion, the use of GPs is often limited to modeling data with fewer than a thousand observations. Due to this bottleneck, an extensive literature has developed on fast, accurate GP approximation methods. Though comparisons of these approaches exist, it is difficult to know which approach to use for a given context because the literature does not seek to understand why one method is superior in that set of simulation studies. To study this problem, we look at three proposed Bayesian solutions to the GP approximation approach, and through an extensive simulation study, we find that the smoothness of the observed process is essential to understanding which method should be used in each context. In this presentation, we show which method is superior and when. We conclude by showing that it is essential to understand how the latent process is expected to behave (in terms of smoothness) before using a particular approach.