  Large, multi-dimensional spatio-temporal datasets are omnipresent in modern
science and engineering. An effective framework for handling such data are
Gaussian process deep generative models (GP-DGMs), which employ GP priors over
the latent variables of DGMs. Existing approaches for performing inference in
GP-DGMs do not support sparse GP approximations based on inducing points, which
are essential for the computational efficiency of GPs, nor do they handle
missing data -- a natural occurrence in many spatio-temporal datasets -- in a
principled manner. We address these shortcomings with the development of the
sparse Gaussian process variational autoencoder (SGP-VAE), characterised by the
use of partial inference networks for parameterising sparse GP approximations.
Leveraging the benefits of amortised variational inference, the SGP-VAE enables
inference in multi-output sparse GPs on previously unobserved data with no
additional training. The SGP-VAE is evaluated in a variety of experiments where
it outperforms alternative approaches including multi-output GPs and structured
VAEs.
