Sequences of events including infectious disease outbreaks, social network activities, and crimes are ubiquitous and the data on such events carry essential information about the underlying diffusion processes between communities (e.g., regions, online user groups). Modeling diffusion processes and predicting future events are crucial in many applications including epidemic control, viral marketing, and predictive policing. Hawkes processes offer a central tool for modeling the diffusion processes, in which the influence from the past events is described by the triggering kernel. However, the triggering kernel parameters, which govern how each community is influenced by the past events, are assumed to be static over time. In the real world, the diffusion processes depend not only on the influences from the past, but also the current (time-evolving) states of the communities, e.g., people's awareness of the disease and people's current interests. In this paper, we propose a novel Hawkes process model that is able to capture the underlying dynamics of community states behind the diffusion processes and predict the occurrences of events based on the dynamics. Specifically, we model the latent dynamic function that encodes these hidden dynamics by a mixture of neural networks. Then we design the triggering kernel using the latent dynamic function and its integral. The proposed method, termed DHP (Dynamic Hawkes Processes), offers a flexible way to learn complex representations of the time-evolving communities' states, while at the same time it allows to computing the exact likelihood, which makes parameter learning tractable. Extensive experiments on four real-world event datasets show that DHP outperforms five widely adopted methods for event prediction.
翻译:包括传染病爆发、社会网络活动和犯罪等事件序列的序列无处不在,关于此类事件的数据含有社区(如区域、在线用户群体)之间基本扩散过程的基本信息。模拟传播过程和预测未来事件在许多应用中至关重要,包括流行病控制、病毒营销和预测治安。霍克斯进程为模拟传播过程提供了一个核心工具,其中对过去事件的影响通过触发内核来描述。然而,决定每个社区如何受过去事件影响的触发内核参数假定是静止的。在现实世界中,扩散过程不仅取决于过去的影响,而且取决于社区当前(时间变化)的状况,例如,人们对疾病的认识和人们当前的利益。在本文件中,我们提出了一个新型的鹰进程模型,能够捕捉社区国家过去事件背后的弹性动态动态,并根据动态预测事件发生的情况。具体地说,我们用动态的动态函数来模拟动态时间动态函数,将这些隐藏的动态动态动态变量用于构建动态动态动态的动态动态动态动态模型,我们用动态的动态系统模型来显示其动态的动态动态系统。