Spatio-Temporal Variational Gaussian Processes
This provides an efficient and accurate solution for large spatio-temporal problems in fields like environmental monitoring or sensor networks, though it appears incremental as it builds on existing variational GP methods.
The paper tackles the challenge of scaling Gaussian process inference for multivariate spatio-temporal data by introducing a method that combines spatio-temporal filtering with natural gradient variational inference, achieving linear scaling with time and logarithmic temporal span complexity through parallelization.
We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with respect to time. Our natural gradient approach enables application of parallel filtering and smoothing, further reducing the temporal span complexity to be logarithmic in the number of time steps. We derive a sparse approximation that constructs a state-space model over a reduced set of spatial inducing points, and show that for separable Markov kernels the full and sparse cases exactly recover the standard variational GP, whilst exhibiting favourable computational properties. To further improve the spatial scaling we propose a mean-field assumption of independence between spatial locations which, when coupled with sparsity and parallelisation, leads to an efficient and accurate method for large spatio-temporal problems.