ATD: Relational Point Process Models: Theory, Methods, and Applications

由一组实体之间带有时间戳的关系事件组成的数据(如社区中个人之间的交互、在线社交网络用户之间的消息或股票市场中的金融交易)已变得广泛可用，并且在流行病学、计算机科学和金融等不同学科中非常重要。关于这类问题的数学模型的文献很有限，主要集中在事件的发生可能会产生额外事件的情况。虽然这种类型的自我和相互兴奋过程在许多社会科学应用中是有意义的，但它们在许多其他环境中并不合适。该项目旨在为有时间戳的关系数据开发新的数学模型，允许更广泛的行为，以及从数据中学习这些模型并预测系统未来行为所需的计算和理论工具。该项目中开发的方法与国家地理空间情报局、国家安全局和联邦调查局、国土安全部和各种国家实验室等机构的任务直接相关。因此，该项目可能会对国防和自然安全(DNS)产生明显和直接的影响。除技术进步外，该项目还将有助于培养一支在数学和统计科学方面具有很强技能的劳动力队伍，熟悉域名系统应用，并认识到公共部门的职业机会。最后，该项目还将协助传播由ATD方案支持的所有私人投资机构所开展的工作，并通过为组织ATD年度讲习班提供后勤支持，促进更广泛的劳动力发展。该项目每年为一名研究生提供支持。带有时间戳的关系事件数据通常使用静态或离散时间网络模型进行分析，方法是聚合一段时间内的事件以生成网络快照。然而，尽管这种聚合在某些应用程序(如变点分析)中可能很有帮助，但它会丢弃大量信息，这些信息对于理解驱动数据生成的底层微过程可能是至关重要的。该项目将为连续时间关系点过程开发一个通用框架，可用于直接对带有时间戳的数据进行建模，从而避免了聚合的需要。除了提出一个可用于设计和评估关系点过程的通用框架外，该提案还开发了适用于流行病学、人员流动性、信息传播和金融等各种应用的这类通用模型的新实例。这些应用总体上都与国防和国家安全界高度相关，特别是国家地理空间情报局。我们的贡献包括排斥物质和马尔可夫更新过程的关系版本，以及依赖于其分支泊松集群结构并允许节点之间同时交互的关系霍克斯过程的新颖构造。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Data consisting of time-stamped relational events between a set of entities (such as interactions between individuals in a community, messages between users of an online social network, or financial transactions in a stock market) have become widely available and are of great importance in disciplines as diverse as epidemiology, computer science, and finance. The literature on mathematical models for this class of problems is limited, and mostly focuses on situations where the occurrence of an event is likely to create additional ones. While this type of self- and mutually-excitatory processes are of interest in many social sciences applications, they are not appropriate in numerous other settings. This project aims to develop novel mathematical models for time-stamped relational data that allow for a wider range of behaviors, along with the computational and theoretical tools necessary to learn those models from data, and to predict the future behavior of the systems. The methods developed in this project have direct relevance to the mission of agencies such as the National Geospatial-Intelligence Agency, the National Security Agency and the Federal Bureau of Investigation, the Department of Homeland Security, and various National Laboratories. Hence, the project is likely to have a clear and direct impact on defense and natural security (DNS). Besides technical advances, this project will also contribute to the development of a workforce with strong skills in mathematical and statistical sciences, familiarity with DNS applications and awareness of the career opportunities in the public sector. Finally, the project will also assist in the dissemination of the work performed by all PIs supported by the ATD program and contribute to broader workforce development by providing logistical support to the organization of an annual ATD workshop. This project will provide support for one graduate student per year.Time-stamped relational event data is often analyzed using static or discrete time network models by aggregating events over time to generate network snapshots. However, while this kind of aggregation can be helpful in some applications such as change-point analysis, it discards a significant amount of information that can be critical to understanding the underlying micro-processes that drive the generation of the data. This project will develop a general framework for continuous time relational point process that can be used to directly model the time-stamped data, thereby avoiding the need for aggregation. In addition to presenting a general framework that can be used to design and evaluate relational point processes, this proposal develops novel instantiations of this general class of models that are suitable for various applications related to epidemiology, human mobility, information diffusion, and finance. These applications are all highly relevant to the defense and national security community in general, and the National Geospatial-Intelligence Agency in particular. Our contributions include relational versions of repulsive Matern and Markov renewal process, as well as novel constructions of relational Hawkes processes that rely on its branching Poisson cluster construction and allow for simultaneous interactions between nodes.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.