  We investigate spatio-temporal event analysis using point processes.
Inferring the dynamics of event sequences spatiotemporally has many practical
applications including crime prediction, social media analysis, and traffic
forecasting. In particular, we focus on spatio-temporal Hawkes processes that
are commonly used due to their capability to capture excitations between event
occurrences. We introduce a novel inference framework based on randomized
transformations and gradient descent to learn the process. We replace the
spatial kernel calculations by randomized Fourier feature-based
transformations. The introduced randomization by this representation provides
flexibility while modeling the spatial excitation between events. Moreover, the
system described by the process is expressed within closed-form in terms of
scalable matrix operations. During the optimization, we use maximum likelihood
estimation approach and gradient descent while properly handling positivity and
orthonormality constraints. The experiment results show the improvements
achieved by the introduced method in terms of fitting capability in synthetic
and real datasets with respect to the conventional inference methods in the
spatio-temporal Hawkes process literature. We also analyze the triggering
interactions between event types and how their dynamics change in space and
time through the interpretation of learned parameters.
