Structural Analysis of the Stochastic Influence Model for Identifiability and Reduced-Order Estimation

The influence model (IM) is a reduced-order stochastic network model that captures the spatiotemporal dynamics in a network of interactive Markov chains. Identifiability and reduced-order estimation of the IM from observation data are crucial for IM applications. Despite the tractability of IM analysis with its reduced-order representation, the identifiability and estimation of IM are challenging due to the tight coupling of both network and local level interactions. The limited identifiability studies in the literature only apply to homogeneous IMs and existing methods for IM estimation incur high-computational cost. In this article, we solve the identifiability problem by providing succinct if-and-only-if conditions for both the homogeneous and heterogeneous IMs. This is obtained through a structural analysis that establishes a novel connection between the high-order and low-order representations of the IMs. The identifiability analysis further leads to reduced-order parameter estimation algorithms of the homogeneous and heterogeneous IMs with reduced computation.