Unveiling Dynamic Relations from Corrupted Data Streams

金融市场、神经系统、电网和天气系统等系统是由相互作用的过程组成的网络所控制的。在这样的系统中，过程及其相互作用的复杂性使得基于第一性原理的数学建模无效。在这些情况下，可以直接从测量数据中获得过程之间关系的模型。然而，从数据创建交互系统模型的方法应该考虑到数据损坏的常见方式。在现实世界的系统中，传感器读数可能会损坏，时钟可能会不同步，消息可能会在无线网络传输中丢失。因此，真实世界的数据可能是有噪声的，记录的顺序可能是混乱的，部分数据可能丢失。该项目建立了一个新的框架，用于识别组成网络系统的组件之间的相互依赖关系，并对来自系统组件的测量数据进行了现实的建模假设。该项目将提供数据损坏对交互拓扑重建影响程度的可证明保证和分析结果。基于分析的见解，将设计出对数据损坏不太敏感的传感器系统和网络的策略。这项工作将对生物学、物理科学、工程学和经济学中的网络模型产生重要影响。所开发的方法将特别适用于识别面对数据损坏的关系，包括在低成本和能源受限的传感系统中常见的不完美的时间和信息丢失。该项目还将包括开发研究生课程，并为本科生提供设计和部署传感器网络的实践经验。相互作用的线性系统之间的动态关系可以通过带有与边相关的传递函数的有向图来建模。在过去的十年中，已经设计了一套丰富的方法来识别图形结构以及传递函数。然而，在确定交互拓扑的领域中，缺乏解释和量化由于几种常见类型的数据损坏（如传感器噪声、时间戳不准确或数据包丢失）而引入的错误程度的方法。利用估计理论和图论的技术，本项目将描述损坏的数据流可能对网络识别和估计算法造成的退化。特别是，如果应用现有算法而不考虑数据损坏，它将显示损坏的数据如何导致对虚假关系的预测。此外，该工作将描述当多个数据流损坏时，这些虚假关系如何通过网络传播。为了纠正这种情况，这项工作将展示高保真传感器的战略位置如何能够定位损坏数据的影响。对于工程系统，如电网和物联网网络，这项工作将导致设计能够抵御数据损坏的网络的方法。这些方法的理论分析将伴随着模拟，以及在测试台上进行分布式传感和计算的实验。

Systems such as financial markets, neural systems, the power grid, and weather systems are governed by networks of interacting processes. In such systems, the complexity of processes and their interactions makes mathematical modeling from first-principles ineffective. In these cases, models of the relationships between the processes can be obtained directly from measured data. However, methods to create models of interacting systems from data should account for common ways that data become corrupted. In real-world systems, sensor readings can be corrupted, clocks can get out of sync, and messages can get lost in transmission over a wireless network. Thus real-world data can be noisy, it can be recorded out of order, and parts of data can be missing. This project builds a novel framework for identifying interdependencies between components that comprise a networked system with realistic modeling assumptions on the measured data from system components. The project will provide provable guarantees and analysis results on the extent of the impact of data corruption on the reconstruction of the interaction topology. Based on the analytical insights, strategies will be devised for designing sensor systems and networks that are less sensitive to data corruption. The work will have important ramifications for network models arising in biology, physical sciences, engineering, and economics. Methods developed will be particularly relevant for identifying relationships in the face of data-corruption, including imperfect timing and lost information that are common in low cost and energy constrained sensing systems. The project will also include development of graduate level course and hands-on experience for undergraduates in designing and deploying sensor network.The dynamic relationships between interacting linear systems can be modeled via a directed graph with transfer functions associated with the edges. Over the last decade, a rich collection of methods that identify graphical structures as well as the transfer functions have been devised. However, in the area of determining interaction topologies, there is a paucity of methods that account for, and quantify, the extent of the errors introduced due to several common types of data corruption, such as sensor noise, time-stamp inaccuracy, or packet loss. Utilizing techniques from estimation theory and graph theory, this project will characterize the degradation that corrupted data streams can cause on network identification and estimation algorithms. In particular, it will show how corrupt data can lead to the prediction of spurious relationships if existing algorithms are applied without accounting for data corruption. Furthermore, the work will characterize how these spurious relationships can spread through a network when multiple data streams are corrupted. To remedy the situation, the work will show how strategic placement of high-fidelity sensors can localize the influence of corrupted data. For engineered systems such as power grids and Internet-of-Things networks, the work will lead to methods for designing networks which are resilient to data corruption. The theoretical analysis of the methods will be accompanied by simulations, as well as experiments on a test-bed performing distributed sensing and computation.