  Learning Granger causality from event sequences is a challenging but
essential task across various applications. Most existing methods rely on the
assumption that event sequences are independent and identically distributed
(i.i.d.). However, this i.i.d. assumption is often violated due to the inherent
dependencies among the event sequences. Fortunately, in practice, we find these
dependencies can be modeled by a topological network, suggesting a potential
solution to the non-i.i.d. problem by introducing the prior topological network
into Granger causal discovery. This observation prompts us to tackle two
ensuing challenges: 1) how to model the event sequences while incorporating
both the prior topological network and the latent Granger causal structure, and
2) how to learn the Granger causal structure. To this end, we devise a unified
topological neural Poisson auto-regressive model with two processes. In the
generation process, we employ a variant of the neural Poisson process to model
the event sequences, considering influences from both the topological network
and the Granger causal structure. In the inference process, we formulate an
amortized inference algorithm to infer the latent Granger causal structure. We
encapsulate these two processes within a unified likelihood function, providing
an end-to-end framework for this task. Experiments on simulated and real-world
data demonstrate the effectiveness of our approach.
