The influence model is a discrete-time stochastic model that succinctly captures the interactions of a network of Markov chains. The model produces a reduced-order representation of the stochastic network, and can be used to describe and tractably analyze probabilistic spatiotemporal spread dynamics, and hence has found broad usage in network applications such as social networks, traffic management, and failure cascades in power systems. This paper provides sufficient and necessary conditions for the identifiability of the influence model, and also develops estimators for the model structure through exploiting the models special properties. In addition, we analyze conditions for the identifiability of the partially observed influence model (POIM), for which not all of the sites can be measured.
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