  Many real-world objects can be modeled as a stream of events on the nodes of
a graph. In this paper, we propose a class of graphical event models named
temporal point process graphical models for representing the temporal
dependencies among different components of a multivariate point process. In our
model, the intensity of an event stream can depend on the historical events in
a nonlinear way. We provide a procedure that allows us to estimate the
parameters in the model with a convex loss function in the high-dimensional
setting. For the approximation error introduced during the implementation, we
also establish the error bound for our estimators. We demonstrate the
performance of our method with extensive simulations and a spike train data
set.
