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

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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.