Deep Gaussian Markov Random Fields for Graph-Structured Dynamical Systems

Published: 21 Sept 2023, Last Modified: 22 Dec 2023NeurIPS 2023 posterEveryoneRevisionsBibTeX
Keywords: probabilistic inference, graphical models, spatiotemporal dynamical systems, state-space models
TL;DR: We propose an extension to Deep Gaussian Markov Random Fields for computationally efficient learning and inference in large spatiotemporal dynamical systems.
Abstract: 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.
Supplementary Material: pdf
Submission Number: 8314
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