ABSTRACT

Many systems arising in important application domains are complicated interconnections of many components. These systems are commonly referred to as networks of agents, and the observed behavior of one agent depends on the behavior of the many other agents, observed or not, in the network. Examples of such systems include not only biological or brain networks, gene regulatory networks, and pandemics spreading over populations, but also large critical physical infrastructures like the electric-power grid. For example, with brain networks, it is important to infer from electroencephalography (EEG) recordings which neural networks form in order to better understand the neural activity and thereby provide a means to better diagnose a number of brain injuries or diseases. The project will develop methods to determine the unknown and hidden connections among the parts (agents) of a system, often a necessary first step to understand the global behavior of the overall system. In complex systems, like EEG arrays, the number of measuring probes is small compared to the much larger number of unobserved but interconnected components. The methods to be developed will reliably infer the connections among the agents that are observed or measured, even in the presence of many latent, unobserved parts of the system. These methods will have broad applicability across many different practical domains. The project will support at least two PhD students and will engage a broad, diverse group of Master and undergraduate students at Carnegie Mellon University.

The problem of uncovering the interconnections among parts of a network dynamical system (NDS), known as structure identification, has received significant attention in the research community. But the success of current approaches is limited by various factors. For example, some methods require total observability, i.e., observing the activity of all the interconnected agents in the NDS. However, this is often unrealistic due to the large scale of many NDS or because it is impractical or impossible to track the behavior of all the agents (e.g., neuron activity in a brain network). A second limitation relates to assuming that the samples of the observed behavior of different agents are independent and identically distributed. Again, such an assumption is very limiting since, in many scenarios, there are significant dependencies in the observed behaviors across time and across agents. The research pursued will consider the total- and partial-observability contexts with possibly temporal and spatial (across-agent) dependencies. For every pair of agents, the approach engineers a high-dimensional feature vector that is then input to a classifier that clusters the features, with a high-dimensional manifold separating the connected pairs from the unconnected pairs. The work will provide theoretical guarantees regarding the separability of the features as well as the stability of the separating manifold to various regimens of connectivity, observability, and disturbances affecting the behaviors of the agents. The generalizability of the approach will also be studied, e.g., training with a lower-dimensional NDS and then inferring the structure of much larger-scale systems. The project will test the methods with synthetic and real-word datasets drawn from a number of practically relevant applications.

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.

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