  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.
