Non-Stationary Spectral Kernels

TL;DR

This paper introduces non-stationary spectral kernels for Gaussian process regression, modeling input-dependent spectral densities to capture complex, non-stationary relationships in data such as time series and images.

Contribution

It presents a novel family of non-stationary kernels based on input-dependent spectral densities, enabling modeling of long-range, non-monotonic covariances.

Findings

Effective in modeling non-stationary time series

Improves performance on image and geospatial data

Requires efficient inference methods

Abstract

We propose non-stationary spectral kernels for Gaussian process regression. We propose to model the spectral density of a non-stationary kernel function as a mixture of input-dependent Gaussian process frequency density surfaces. We solve the generalised Fourier transform with such a model, and present a family of non-stationary and non-monotonic kernels that can learn input-dependent and potentially long-range, non-monotonic covariances between inputs. We derive efficient inference using model whitening and marginalized posterior, and show with case studies that these kernels are necessary when modelling even rather simple time series, image or geospatial data with non-stationary characteristics.