  Inter-domain Gaussian processes (GPs) allow for high flexibility and low
computational cost when performing approximate inference in GP models. They are
particularly suitable for modeling data exhibiting global structure but are
limited to stationary covariance functions and thus fail to model
non-stationary data effectively. We propose Inter-domain Deep Gaussian
Processes, an extension of inter-domain shallow GPs that combines the
advantages of inter-domain and deep Gaussian processes (DGPs), and demonstrate
how to leverage existing approximate inference methods to perform simple and
scalable approximate inference using inter-domain features in DGPs. We assess
the performance of our method on a range of regression tasks and demonstrate
that it outperforms inter-domain shallow GPs and conventional DGPs on
challenging large-scale real-world datasets exhibiting both global structure as
well as a high-degree of non-stationarity.
