  Learning causal structure among event types on multi-type event sequences is
an important but challenging task. Existing methods, such as the Multivariate
Hawkes processes, mostly assumed that each sequence is independent and
identically distributed. However, in many real-world applications, it is
commonplace to encounter a topological network behind the event sequences such
that an event is excited or inhibited not only by its history but also by its
topological neighbors. Consequently, the failure in describing the topological
dependency among the event sequences leads to the error detection of the causal
structure. By considering the Hawkes processes from the view of temporal
convolution, we propose a Topological Hawkes process (THP) to draw a connection
between the graph convolution in the topology domain and the temporal
convolution in time domains. We further propose a causal structure learning
method on THP in a likelihood framework. The proposed method is featured with
the graph convolution-based likelihood function of THP and a sparse
optimization scheme with an Expectation-Maximization of the likelihood
function. Theoretical analysis and experiments on both synthetic and real-world
data demonstrate the effectiveness of the proposed method
