Deep Gaussian Markov Random Fields for Graph-Structured Dynamical Systems
This work addresses computational challenges in spatiotemporal systems for domains like sensor networks or environmental modeling, but it is incremental as it builds on existing deep learning and GMRF methods.
The paper tackles probabilistic inference in high-dimensional graph-structured state-space models by developing Deep Gaussian Markov Random Fields (GMRFs) as a flexible spatiotemporal prior, resulting in efficient state estimation and learning that scales favorably compared to classical Kalman filter approaches.
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