ATD: Algorithms for Point Processes on Networks for Threat Detection

我们生活在一个充满网络的世界：联系和社交网络将我们与家人、朋友和同事联系起来;互联网等计算机网络使我们能够远程访问大量数据和信息;交通和物流网络比以往任何时候都更快地运送人员、水/食物和各种货物。当我们享受这些网络带来的便利时，我们也必须意识到威胁和危害，如果他们受到危害，例如，传染性病毒，网络攻击等，该项目的目标是开发基于新颖而严格的数学建模和数据分析概念的自动早期威胁检测的计算算法。特别是，这些网络上的人类和其他来源产生的活动被建模为所谓的交互式随机点过程。这些动态在跳跃随机微分方程的数学框架中进行研究和推断，并进一步扩展到集成平均场近似和深度学习技术，充分利用现有的大数据进行快速准确的威胁检测。该项目将深入探讨三个密切相关的计算问题：影响预测、最优传感器分配和源识别，所有这些都是大型、异构真实世界的网络。这个项目将利用两种新的方法来影响预测的基础上跳随机微分方程（JAPAN）公式化以及平均场近似和深度学习技术的集成。Jestival公式给出了时间点过程的简洁而精确的数学公式，该公式考虑了已知的网络结构和流行病传播机制;而由Jesus公式推导出的深度神经平均场方法将数值分析中的经典差分方法映射为结构化的多层残差网络，其中平均场近似的未知偏差可以有效地从观测的级联数据中学习，用于快速影响预测。这些预测算法将用于最佳传感器分配和流行病源识别问题的威胁检测和缓解。在这个项目中产生的结果，预计将作出重大贡献，我们的相互依存的活动的理解，大规模的异构网络和新的，有效的威胁检测算法的发展。该项目的成果包括新颖的计算技术、严格的数学理论和分析以及用于威胁检测应用的高效数值算法。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

We live in a world full of networks: contact and social networks connect us to our family, friends and colleagues; computer networks such as Internet allow us to access huge amount of data and information remotely; traffic and logistical networks deliver people, water/food, and all kinds of goods faster than ever before. While we enjoy the conveniences brought by these networks, we must also be aware of the threats and harms if they get jeopardized by, for example, infectious virus, cyber-attacks, etc. The goal of this project is to develop computational algorithms for automated early threat detection based on novel and rigorous mathematical modeling and data analysis concepts. In particular, the activities generated by human and other sources on these networks are modeled as the so-called interactive stochastic point processes. These dynamics are studied and inferred in a mathematical framework of jump stochastic differential equations, which is further extended to integrate mean-field approximation and deep learning techniques that fully leverage the existing big data for fast and accurate threat detection. This project will exploit three closely related computational problems in-depth: influence prediction, optimal sensor allocation, and source identification, all of which are fundamental in threat detection applications on large, heterogeneous, real-world networks.This project will exploit two novel approaches to influence prediction based on a jump stochastic differential equation (JSDE) formulation and an integration of mean field approximation and deep learning techniques. The JSDE formulation yields a concise and exact mathematical formulation of the temporal point process that takes into account the known network structure and mechanism of epidemic spread; and the deep neural mean field approach deduced from JSDE formulation maps the classical difference method in numerical analysis into a structured multi-layer residual network, where the unknown bias of mean field approximation can be effectively learned from observed cascade data for rapid influence prediction. These prediction algorithms will be used in the optimal sensor allocation and epidemic source identification problems for threat detection and mitigation. The results produced in this project are expected to make significant contributions to our understanding of interdependent activities on large-scale heterogeneous networks and the development of new, efficient algorithms for threat detection. The outcomes of the project include novel computational techniques, rigorous mathematical theory and analysis, and efficient numerical algorithms for threat detection applications.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.