The well-known Kalman filters model dynamical systems by relying on state-space representations with the next state updated, and its uncertainty controlled, by fresh information associated with newly observed system outputs. This paper generalizes, for the first time in the literature, Kalman and extended Kalman filters to discrete-time settings where inputs, states, and outputs are represented as attributed graphs whose topology and attributes can change with time. The setup allows us to adapt the framework to cases where the output is a vector or a scalar too (node/graph level tasks). Within the proposed theoretical framework, the unknown state-transition and the readout functions are learned end-to-end along with the downstream prediction task.

翻译：著名的卡尔曼滤波器通过依赖状态空间表示来建模动态系统，其中下一状态由新观测到的系统输出所携带的新信息进行更新，且其不确定性受此信息控制。本文首次在文献中将卡尔曼滤波器和扩展卡尔曼滤波器推广到离散时间环境，其中输入、状态和输出均表示为属性图，其拓扑结构和属性可随时间变化。该设定使我们能够将框架适应于输出为向量或标量的情况（节点级/图级任务）。在所提出的理论框架内，未知的状态转移函数和读出函数与下游预测任务一起进行端到端学习。