  Probabilistic inference in high-dimensional state-space models is
computationally challenging. For many spatiotemporal systems, however, prior
knowledge about the dependency structure of state variables is available. We
leverage this structure to develop a computationally efficient approach to
state estimation and learning in graph-structured state-space models with
(partially) unknown dynamics and limited historical data. Building on recent
methods that combine ideas from deep learning with principled inference in
Gaussian Markov random fields (GMRF), we reformulate graph-structured
state-space models as Deep GMRFs defined by simple spatial and temporal graph
layers. This results in a flexible spatiotemporal prior that can be learned
efficiently from a single time sequence via variational inference. Under linear
Gaussian assumptions, we retain a closed-form posterior, which can be sampled
efficiently using the conjugate gradient method, scaling favourably compared to
classical Kalman filter based approaches
