On the Identifiability of the Influence Model for Stochastic Spatiotemporal Spread Processes

The influence model is a discrete-time stochastic model that succinctly captures the interactions of a network of interacting Markov chains. The model produces a reduced-order representation of stochastic networks, 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 article provides sufficient and necessary conditions for the identifiability of the influence model, and also develops estimators for model structures 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. We develop an expectation-maximization (EM) algorithm-based estimator for POIMs.