  Learning causal structure among event types from discrete-time event
sequences is a particularly important but challenging task. Existing methods,
such as the multivariate Hawkes processes based methods, mostly boil down to
learning the so-called Granger causality which assumes that the cause event
happens strictly prior to its effect event. Such an assumption is often
untenable beyond applications, especially when dealing with discrete-time event
sequences in low-resolution; and typical discrete Hawkes processes mainly
suffer from identifiability issues raised by the instantaneous effect, i.e.,
the causal relationship that occurred simultaneously due to the low-resolution
data will not be captured by Granger causality. In this work, we propose
Structure Hawkes Processes (SHPs) that leverage the instantaneous effect for
learning the causal structure among events type in discrete-time event
sequence. The proposed method is featured with the minorization-maximization of
the likelihood function and a sparse optimization scheme. Theoretical results
show that the instantaneous effect is a blessing rather than a curse, and the
causal structure is identifiable under the existence of the instantaneous
effect. Experiments on synthetic and real-world data verify the effectiveness
of the proposed method.
