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相关的新信息进行更新，其不确定性亦受此信息控制。本文首次在文献中，将卡尔曼滤波器与扩展卡尔曼滤波器推广至离散时间环境，在此环境中输入、状态和输出均表示为属性图，其拓扑结构与属性可随时间变化。该设定使框架可适应输出为向量或标量（节点级/图级任务）的情形。在所提出的理论框架内，未知的状态转移函数与读出函数与下游预测任务进行端到端的联合学习。