Tomography Of Adaptive Multi-Agent Networks Under Limited Observation

This work studies the problem of inferring from streaming data whether an agent is directly influenced by another agent over an adaptive network of interacting agents. Agent i influences agent j if they are connected, and if agent j uses the information from agent i to update its inference. The solution of this inference task is challenging for at least two reasons. First, only the output of the learning algorithm is available to the external observer and not the raw data. Second, only observations from a fraction of the network agents is available, with the total number of agents itself being also unknown. This work establishes, under reasonable conditions, that consistent tomography is possible, namely, that it is possible to reconstruct the interaction profile of the observable portion of the network, with negligible error as the network size increases. We characterize the decaying behavior of the error with the network size, and provide a set of numerical experiments to illustrate the results.