  Spatio-temporal point processes (STPPs) are potent mathematical tools for
modeling and predicting events with both temporal and spatial features. Despite
their versatility, most existing methods for learning STPPs either assume a
restricted form of the spatio-temporal distribution, or suffer from inaccurate
approximations of the intractable integral in the likelihood training
objective. These issues typically arise from the normalization term of the
probability density function. Moreover, current techniques fail to provide
uncertainty quantification for model predictions, such as confidence intervals
for the predicted event's arrival time and confidence regions for the event's
location, which is crucial given the considerable randomness of the data. To
tackle these challenges, we introduce SMASH: a Score MAtching-based
pSeudolikeliHood estimator for learning marked STPPs with uncertainty
quantification. Specifically, our framework adopts a normalization-free
objective by estimating the pseudolikelihood of marked STPPs through
score-matching and offers uncertainty quantification for the predicted event
time, location and mark by computing confidence regions over the generated
samples. The superior performance of our proposed framework is demonstrated
through extensive experiments in both event prediction and uncertainty
quantification.
