Non-Stationary Spectral Kernels
This addresses the challenge of handling non-stationary characteristics in data for practitioners in fields like time series analysis and geospatial modeling, though it appears incremental as it builds on existing kernel methods.
The authors tackled the problem of modeling non-stationary data in Gaussian process regression by proposing non-stationary spectral kernels, which learn input-dependent and non-monotonic covariances, and demonstrated their necessity in case studies on time series, image, and geospatial data.
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.