  Self- and mutually-exciting point processes are popular models in machine
learning and statistics for dependent discrete event data. To date, most
existing models assume stationary kernels (including the classical Hawkes
processes) and simple parametric models. Modern applications with complex event
data require more general point process models that can incorporate contextual
information of the events, called marks, besides the temporal and location
information. Moreover, such applications often require non-stationary models to
capture more complex spatio-temporal dependence. To tackle these challenges, a
key question is to devise a versatile influence kernel in the point process
model. In this paper, we introduce a novel and general neural network-based
non-stationary influence kernel with high expressiveness for handling complex
discrete events data while providing theoretical performance guarantees. We
demonstrate the superior performance of our proposed method compared with the
state-of-the-art on synthetic and real data.
