  Sequences of events including infectious disease outbreaks, social network
activities, and crimes are ubiquitous and the data on such events carry
essential information about the underlying diffusion processes between
communities (e.g., regions, online user groups). Modeling diffusion processes
and predicting future events are crucial in many applications including
epidemic control, viral marketing, and predictive policing. Hawkes processes
offer a central tool for modeling the diffusion processes, in which the
influence from the past events is described by the triggering kernel. However,
the triggering kernel parameters, which govern how each community is influenced
by the past events, are assumed to be static over time. In the real world, the
diffusion processes depend not only on the influences from the past, but also
the current (time-evolving) states of the communities, e.g., people's awareness
of the disease and people's current interests. In this paper, we propose a
novel Hawkes process model that is able to capture the underlying dynamics of
community states behind the diffusion processes and predict the occurrences of
events based on the dynamics. Specifically, we model the latent dynamic
function that encodes these hidden dynamics by a mixture of neural networks.
Then we design the triggering kernel using the latent dynamic function and its
integral. The proposed method, termed DHP (Dynamic Hawkes Processes), offers a
flexible way to learn complex representations of the time-evolving communities'
states, while at the same time it allows to computing the exact likelihood,
which makes parameter learning tractable. Extensive experiments on four
real-world event datasets show that DHP outperforms five widely adopted methods
for event prediction.
