Modeling non-stationary dynamics of spatio-temporal sequences with self-organizing point process models

Abstract

We investigate the challenging problem of modeling the non-stationary dynam-ics of spatio-temporal sequences for prediction applications. Spatio-temporal se-quence modeling has critical real-life applications such as natural disaster, social, and criminal event prediction. Even though this problem has been thoroughly studied, many approaches do not address the non-stationarity and sparsity of the spatio-temporal sequences, which are frequently observed in real-life sequences. Here, we introduce a novel prediction algorithm that is capable of modeling non-stationarity in both time and space. Moreover, our algorithm can model both densely and sparsely populated sequences. We partition the spatial region with a decision tree, where each node of the tree corresponds to a subregion. We model the event occurrences in di˙erent subregions in space with individual but inter-acting point processes. Our algorithm can jointly optimize the partitioning tree and the interacting point processes through a gradient-based optimization. We compare our approach with statistical models, probabilistic approaches, and deep learning based approaches, and show that our model achieves the best forecasting performance on real-life datasets such as earthquake and criminal event records.