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Modeling temporal event sequences on the vertices of a network is an important problem with widespread applications; examples include modeling influences in social networks, preventing crimes by modeling their space–time occurrences, and forecasting earthquakes. Existing solutions for this problem use a parametric approach, whose applicability is limited to event sequences following some well‐known distributions, which is not true for many real life event datasets. To overcome this limitation, in this work, we propose a composite recurrent neural network model for learning events occurring in the vertices of a network over time. Our proposed model combines two long short‐term memory units to capture base intensity and conditional intensity of an event sequence. We also introduce a second‐order statistic loss that penalizes higher divergence between the generated and the target sequence's distribution of hop count distance of consecutive events. Given a sequence of vertices of a network in which an event has occurred, the proposed model predicts the vertex where the next event would most likely occur. Experimental results on synthetic and real‐world datasets validate the superiority of our proposed model in comparison to various baseline methods.

 

Recent research has shown an association between monthly law enforcement drug seizure events and accidental drug overdose deaths using cross-sectional data in a single state, whereby increased seizures correlated with more deaths. In this study, we conduct statistical analysis of street-level data on law enforcement drug seizures, along with street-level data on fatal and non-fatal overdose events, to determine possible micro-level causal associations between opioid-related drug seizures and overdoses. For this purpose, we introduce a novel, modified two-process Knox test that controls for self-excitation to measure clustering of overdoses nearby in space and time following law enforcement seizures. We observe a small, but statistically significant ( p  < 0.001), effect of 17.7 excess non-fatal overdoses per 1000 law enforcement seizures within three weeks and 250 m of a seizure. We discuss the potential causal mechanism for this association along with policy implications.