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This work studies the problem of inferring whether an agent is directlyinfluenced by another agent over an adaptive diffusion network. Agent iinfluences agent j if they are connected (according to the network topology),and if agent j uses the data from agent i to update its online statistic. Thesolution of this inference task is challenging for two main reasons. First,only the output of the diffusion learning algorithm is available to theexternal observer that must perform the inference based on these indirectmeasurements. Second, only output measurements from a fraction of the networkagents is available, with the total number of agents itself being also unknown.The main focus of this article is ascertaining under these demanding conditionswhether consistent tomography is possible, namely, whether it is possible toreconstruct the interaction profile of the observable portion of the network,with negligible error as the network size increases. We establish a criticalachievability result, namely, that for symmetric combination policies and forany given fraction of observable agents, the interacting and non-interactingagent pairs split into two separate clusters as the network size increases.This remarkable property then enables the application of clustering algorithmsto identify the interacting agents influencing the observations. We provide aset of numerical experiments that verify the results for finite network sizesand time horizons. The numerical experiments show that the results hold forasymmetric combination policies as well, which is particularly relevant in thecontext of causation.

Consistent Tomography under Partial Observations over Adaptive Networks