  We propose a novel framework for modeling multiple multivariate point
processes, each with heterogeneous event types that share an underlying space
and obey the same generative mechanism. Focusing on Hawkes processes and their
variants that are associated with Granger causality graphs, our model leverages
an uncountable event type space and samples the graphs with different sizes
from a nonparametric model called {\it graphon}. Given those graphs, we can
generate the corresponding Hawkes processes and simulate event sequences.
Learning this graphon-based Hawkes process model helps to 1) infer the
underlying relations shared by different Hawkes processes; and 2) simulate
event sequences with different event types but similar dynamics. We learn the
proposed model by minimizing the hierarchical optimal transport distance
between the generated event sequences and the observed ones, leading to a novel
reward-augmented maximum likelihood estimation method. We analyze the
properties of our model in-depth and demonstrate its rationality and
effectiveness in both theory and experiments.
