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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.
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