ATD: Collaborative Research: Theory and Algorithms for Real-Time Threat Detection from Massive Data Streams

国家安全利益要求提高对各种对手行动的认识。这种对信息的贪婪胃口导致了压倒性的时空数据流。新的数学是有效管理这些数据洪流的必要条件；本研究项目旨在为此开发新的理论和算法。该方法以以下威胁检测问题的抽象描述为指导：给定大量时空数据流，任务是维持一个缓慢发展的“常态”模型，任何偏离都将作为潜在威胁进一步调查。该项目将重点关注以下两个目标：(1)开发处理海量数据流的算法和最优编码；(2)为前沿学习算法开发快速证书和保证。为此，本研究旨在解决优化、框架理论和机器学习中的一些重大开放性问题：(a)从流数据中快速解决NP-hard无监督学习问题的凸松弛；(b)构造最优的线路填料，包括Zauner推测存在的填料；(c)寻找np困难学习问题的次线性后验逼近证明；(d)解释生成对抗网络表现出的行为良好的优化景观；(e)为黑箱分类开发快速的事后解释，使人们能够做出明智的决策。该奖项反映了美国国家科学基金会的法定使命，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。

National security interests demand a heightened awareness of the actions of various adversaries. This voracious appetite for information results in an overwhelming stream of spatiotemporal data. New mathematics is necessary to effectively manage this data deluge; this research project aims to develop new theory and algorithms for this cause. The approach is guided by the following abstract description of the threat detection problem: Given a massive stream of spatiotemporal data, the task is to maintain a slowly evolving model of "normalcy," any deviations from which are to be further investigated as potential threats. The project will focus on the following two objectives: (1) develop algorithms and optimal encodings to process massive data streams, and (2) develop fast certificates and guarantees for cutting-edge learning algorithms. To this end, the research aims to solve some of the big open problems in optimization, frame theory, and machine learning: (a) to quickly solve convex relaxations of NP-hard unsupervised learning problems from streaming data; (b) to construct optimal line packings, including the packings conjectured to exist by Zauner; (c) to find sub-linear a posteriori approximation certificates for NP-hard learning problems; (d) to explain the well-behaved optimization landscapes exhibited by generative adversarial networks; and (e) to develop fast, after-the-fact explanations for black-box classification, enabling well-informed human decision making.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.