Ensemble-based filtering for uncovering an influence network from Hawkes processes driven by count data

许多网络，如通信，社交媒体，隐蔽和犯罪网络具有事件驱动的动态，其中事件的强度率根据网络中事件的历史数量而变化。特别地，由网络的节点生成的事件可以根据它们的因果关系来增加或减少其他节点的强度。这种网络结构被称为因果网络或影响网络，其链接表示节点之间的方向性影响。该研究为从计数数据的时间序列中推断影响网络提供了一个序列数据同化工具的前景。研究结果揭示了网络中某个节点所发生的事件会影响其他节点的强度变化率的复杂交互作用，例如，在犯罪热点区域，某些区域的犯罪发生会通过犯罪分子对犯罪事件的复杂反应而增加其他区域的犯罪率。空间位置上发生的犯罪之间的联系可以表示为一个复杂的网络，其中每一个联系都根据犯罪事件从一个位置到另一个位置的影响力来加权。影响力网络的结构将为积极主动的警务战略提供依据。研究成果也可以用于其他类似的应用环境（例如社会科学中的意见网络，地震网络，恐怖分子网络或医疗保健网络），其中复杂的影响结构是感兴趣的。

Many networks such as communication, social media, covert and criminal networks have event-driven dynamics where the intensity rate of the events is changed according to the historical number of events in the network. In particular, events generated by a node of the network may increase or decrease the intensity of other nodes depending on their causal relationship. Such a network structure is called a causal or influence network of which the links represent the directional influence between nodes. The proposed research offers the prospect of a sequential data assimilation tool for inference of influence network from a time-series of count data. The outcome will provide an insight into the complex interaction in which events generated by a node in the network could change the intensity rate of other nodes.For example, in the context of crime hot spots, crime occurrences in some spatial locations could increase the crime rate in others through complex reactions of criminals in each area over crime events. Linkages between crime occurrences in spatial locations can be represented as a complex network where each link is weighted by the strength of the influence of crime events from one location to another. The structure of the influence network will inform rationale strategies for proactive policing. The research outcome can also be used in other similar application contexts (e.g. opinion networks in social science, earthquake networks, terrorist networks, or healthcare networks) where complex influence structure is of interest.