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.