ATD: Algorithms for Anomaly Detection Using Graphical Models

我们的物理和虚拟环境的连接性的增加导致来自利用互联性进行传播和交流的代理人的风险增加。PI将开发一种数学方法和算法，以在相互联系和动态变化的环境中检测腐败代理人/元素。潜在的应用包括检测政府和金融网络中的腐败代理人，以及检测电网、化工厂和其他物理基础设施中的异常情况，以及检测选举篡改。该项目的共同主题是研究状态由图定义的系统，其中异常检测基于图属性和图算法。PI将研究图上的损坏检测，其中节点表示可以检查其邻居状态的实体。如果存在损坏的节点，哪些图和哪些算法可以有效地恢复损坏的节点？在不同的方向上，PI将利用马尔可夫随机场作为模型，代表个体之间的相互作用，目标是从动态角度检测异常。PI将进一步研究投票异常的新概念，其中PI将利用噪声稳定性和等密度理论中的数学工具来定义和检测不可能的投票配置。

The increased connectivity of our physical and virtual environments results in elevated risks from agents who utilize interconnectedness in order to spread and communicate. The PI will develop a mathematical methodology and algorithms to detect corrupt agents / elements in interconnected and dynamically changing environments. Potential applications include the detection of corrupt agents in governmental and financial networks as well as detection of anomalies in electrical networks, chemical plants and other physical infrastructure and detection of election tampering. The common theme of the project is studying systems whose states are defined by graphs and where the detection of an anomaly is based on graph properties and graph algorithms. The PI will study corruption detection on a graph where nodes represent entities that can examine the status of their neighbors. Which graphs and which algorithms are efficient at recovering corrupt nodes if such exist? In a different direction, the PI will utilize Markov Random Fields as models representing the interaction between individuals with the goal of detecting anomalies from a dynamic perspective. The PI will further study new notions of anomalies in voting, where the PI will utilize the mathematical tools from the theories of noise stability and isoperimetry to define and detect unlikely voting configurations.