  We are now witnessing the increasing availability of event stream data, i.e.,
a sequence of events with each event typically being denoted by the time it
occurs and its mark information (e.g., event type). A fundamental problem is to
model and predict such kind of marked temporal dynamics, i.e., when the next
event will take place and what its mark will be. Existing methods either
predict only the mark or the time of the next event, or predict both of them,
yet separately. Indeed, in marked temporal dynamics, the time and the mark of
the next event are highly dependent on each other, requiring a method that
could simultaneously predict both of them. To tackle this problem, in this
paper, we propose to model marked temporal dynamics by using a mark-specific
intensity function to explicitly capture the dependency between the mark and
the time of the next event. Extensive experiments on two datasets demonstrate
that the proposed method outperforms state-of-the-art methods at predicting
marked temporal dynamics.
