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

翻译：高维状态空间模型中的概率推理在计算上极具挑战性。然而，对于许多时空系统而言，状态变量依赖结构的先验知识是可获得的。我们利用这种结构开发了一种计算高效的方法，用于在具有（部分）未知动力学和有限历史数据的图结构状态空间模型中进行状态估计与学习。基于近期将深度学习理念与高斯马尔可夫随机场（GMRF）中的原则性推理相结合的方法，我们将图结构状态空间模型重新表述为深度GMRF，其由简单的空间和时间图层次定义。这产生了一种灵活的时空先验，可通过变分推理从单个时间序列中高效学习。在线性高斯假设下，我们保留了闭式后验，并可利用共轭梯度法高效采样，其计算规模相较于经典的卡尔曼滤波方法更具优势。