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We present a fast, accurate estimation method for multivariate Hawkes self-exciting point processes widely used in seismology, criminology, finance and other areas. There are two major ingredients. The first is an analytic derivation of exact maximum likelihood estimates of the nonparametric triggering density. We develop this for the multivariate case and add regularization to improve stability and robustness. The second is a moment-based method for the background rate and triggering matrix estimation, which is extended here for the spatiotemporal case. Our method combines them together in an efficient way, and we prove the consistency of this new approach. Extensive numerical experiments, with synthetic data and real-world social network data, show that our method improves the accuracy, scalability and computational efficiency of prevailing estimation approaches. Moreover, it greatly boosts the performance of Hawkes process-based models on social network reconstruction and helps to understand the spatiotemporal triggering dynamics over social media. 

Multivariate spatial point process models can describe heterotopic data over space. However, highly multivariate intensities are computationally challenging due to the curse of dimensionality. To bridge this gap, we introduce a declustering based hidden variable model that leads to an efficient inference procedure via a variational autoencoder (VAE). We also prove that this model is a generalization of the VAE-based model for collaborative filtering. This leads to an interesting application of spatial point process models to recommender systems. Experimental results show the method’s utility on both synthetic data and real-world data sets. 

We present a framework for spatio-temporal (ST) data modeling, analysis, and forecasting, with a focus on data that is sparse in space and time. Our multi-scaled framework couples two components: a self-exciting point process that models the macroscale statistical behaviors of the ST data and a graph structured recurrent neural network (GSRNN) to discover the microscale patterns of the ST data on the inferred graph. This novel deep neural network (DNN) incorporates the real time interactions of the graph nodes to enable more accurate real time forecasting. The effectiveness of our method is demonstrated on both crime and traffic forecasting.