Imitation Learning of Neural Spatio-Temporal Point Processes
This work addresses a gap in spatio-temporal event modeling for applications like epidemiology or urban planning, though it appears incremental as it builds on existing point process and neural network techniques.
The authors tackled the problem of modeling spatio-temporal discrete event data, which is scarce compared to one-dimensional temporal point processes, by proposing a Neural Embedding Spatio-Temporal (NEST) point process model with a mixture of heterogeneous Gaussian diffusion kernels and an imitation learning-based fitting approach, achieving good performance and interpretability relative to state-of-the-art methods in experiments on real data.
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.