  The expressive power of Gaussian processes depends heavily on the choice of
kernel. In this work we propose the novel harmonizable mixture kernel (HMK), a
family of expressive, interpretable, non-stationary kernels derived from
mixture models on the generalized spectral representation. As a theoretically
sound treatment of non-stationary kernels, HMK supports harmonizable
covariances, a wide subset of kernels including all stationary and many
non-stationary covariances. We also propose variational Fourier features, an
inter-domain sparse GP inference framework that offers a representative set of
'inducing frequencies'. We show that harmonizable mixture kernels interpolate
between local patterns, and that variational Fourier features offers a robust
kernel learning framework for the new kernel family.
