Structural Analysis of the Stochastic Influence Model for Identifiability and Reduced-Order Estimation
研究了随机影响模型的可辨识性条件，提出了针对同质和异质模型的降阶参数估计算法，降低了计算成本，适用于网络交互马尔可夫链的时空动态分析。
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.