Sparse Gaussian Process Variational Autoencoders

Large, multidimensional spatiotemporal 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 spatiotemporal 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. Increasing amounts of large, multidimensional datasets that exhibit strong spatiotemporal dependencies are arising from a wealth of domains, including earth, social and environmental sciences (Atluri et al., 2018). For example, consider modelling daily atmospheric measurements taken by weather stations situated across the globe. Such data are (1) large in number; (2) subject to strong spatiotemporal dependencies; (3) multidimensional; and (4) non-Gaussian with complex dependencies across outputs.