  Recently, non-stationary spectral kernels have drawn much attention, owing to
its powerful feature representation ability in revealing long-range
correlations and input-dependent characteristics. However, non-stationary
spectral kernels are still shallow models, thus they are deficient to learn
both hierarchical features and local interdependence. In this paper, to obtain
hierarchical and local knowledge, we build an interpretable convolutional
spectral kernel network (\texttt{CSKN}) based on the inverse Fourier transform,
where we introduce deep architectures and convolutional filters into
non-stationary spectral kernel representations. Moreover, based on Rademacher
complexity, we derive the generalization error bounds and introduce two
regularizers to improve the performance. Combining the regularizers and recent
advancements on random initialization, we finally complete the learning
framework of \texttt{CSKN}. Extensive experiments results on real-world
datasets validate the effectiveness of the learning framework and coincide with
our theoretical findings.
