  Transformer Hawkes process models have shown to be successful in modeling
event sequence data. However, most of the existing training methods rely on
maximizing the likelihood of event sequences, which involves calculating some
intractable integral. Moreover, the existing methods fail to provide
uncertainty quantification for model predictions, e.g., confidence intervals
for the predicted event's arrival time. To address these issues, we propose
SMURF-THP, a score-based method for learning Transformer Hawkes process and
quantifying prediction uncertainty. Specifically, SMURF-THP learns the score
function of events' arrival time based on a score-matching objective that
avoids the intractable computation. With such a learned score function, we can
sample arrival time of events from the predictive distribution. This naturally
allows for the quantification of uncertainty by computing confidence intervals
over the generated samples. We conduct extensive experiments in both event type
prediction and uncertainty quantification of arrival time. In all the
experiments, SMURF-THP outperforms existing likelihood-based methods in
confidence calibration while exhibiting comparable prediction accuracy.
