Unveiling Dynamic Relations from Corrupted Data Streams

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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.