  We present a novel Neural Embedding Spatio-Temporal (NEST) point process
model for spatio-temporal discrete event data and develop an efficient
imitation learning (a type of reinforcement learning) based approach for model
fitting. Despite the rapid development of one-dimensional temporal point
processes for discrete event data, the study of spatial-temporal aspects of
such data is relatively scarce. Our model captures complex spatio-temporal
dependence between discrete events by carefully design a mixture of
heterogeneous Gaussian diffusion kernels, whose parameters are parameterized by
neural networks. This new kernel is the key that our model can capture
intricate spatial dependence patterns and yet still lead to interpretable
results as we examine maps of Gaussian diffusion kernel parameters. The
imitation learning model fitting for the NEST is more robust than the maximum
likelihood estimate. It directly measures the divergence between the empirical
distributions between the training data and the model-generated data. Moreover,
our imitation learning-based approach enjoys computational efficiency due to
the explicit characterization of the reward function related to the likelihood
function; furthermore, the likelihood function under our model enjoys tractable
expression due to Gaussian kernel parameterization. Experiments based on real
data show our method's good performance relative to the state-of-the-art and
the good interpretability of NEST's result.
