  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 model's 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.
