Stochastic variational inference for scalable non-stationary Gaussian process regression

A natural extension to standard Gaussian process (GP) regression is the use of non-stationary Gaussian processes, an approach where the parameters of the covariance kernel are allowed to vary in time or space. The non-stationary GP is a flexible model that relaxes the strong prior assumption of standard GP regression, that the covariance properties of the inferred functions are constant across the input space. Non-stationary GPs typically model varying covariance kernel parameters as further lower-level GPs, thereby enabling sampling-based inference. However, due to the high computational costs and inherently sequential nature of MCMC sampling, these methods do not scale to large datasets. Here we develop a variational inference approach to fitting non-stationary GPs that combines sparse GP regression methods with a trajectory segmentation technique. Our method is scalable to large datasets containing potentially millions of data points. We demonstrate the effectiveness of our approach on both synthetic and real world datasets.

Automated summary

A natural extension to standard Gaussian process regression is the use of non-stationary Gaussian processes, which allows parameters of the covariance kernel to vary in time or space. However, existing methods for fitting non-stationary GPs are not scalable to large datasets due to high computational costs. In this study, we propose a variational inference approach that combines sparse GP regression methods with a trajectory segmentation technique to fit non-stationary GPs on large datasets. The effectiveness of our approach is demonstrated on both synthetic and real world datasets.