Neural Point Process for Learning Spatiotemporal Event Dynamics

Abstract

Learning the dynamics of spatiotemporal events is a fundamental problem. Neural point processes enhance the expressivity of point process models with deep neural networks. However, most existing methods only consider temporal dynamics without spatial modeling. We propose Deep Spatiotemporal Point Process (DeepSTPP), a deep dynamics model that integrates spatiotemporal point processes. Our method is flexible, efficient, and can accurately forecast irregularly sampled events over space and time. The key construction of our approach is the nonparametric space-time intensity function, governed by a latent process. The intensity function enjoys closed form integration for the density. The latent process captures the uncertainty of the event sequence. We use amortized variational inference to infer the latent process with deep networks. Using synthetic datasets, we validate our model can accurately learn the true intensity function. On real-world benchmark datasets, our model demonstrates superior performance over state-of-the-art baselines.

1.. Introduction

Accurate modeling of spatiotemporal event dynamics is fundamentally important for disaster response (Veen and Schoenberg, 2008), logistic optimization (Safikhani et al., 2018) and social media analysis (Liang et al., 2019) . Compared to other sequence data such as texts or time series, spatiotemporal events occur irregularly with uneven time and space intervals. Discrete-time deep dynamics models such as recurrent neural networks (RNNs) (Hochreiter and Schmidhuber, 1997; Chung et al., 2014 ) assume events to be evenly sampled. Interpolating an irregular sampled sequence into a regular sequence can introduce significant biases (Rehfeld et al., 2011) . Furthermore, event sequences contain strong spatiotemporal dependencies. The rate of an event depends on the preceding events, as well as the events geographically correlated to it. Spatiotemporal point processes (STPP) (Daley and Vere-Jones, 2007; Reinhart et al., 2018 ) provides the statistical framework for modeling continuous-time event dynamics. As shown in Figure 1 , given the history of events sequence, STPP estimates the intensity function that is evolv-



© 2022 Z. Zhou, X. Yang, R. Rossi, H. Zhao & R. Yu.

