Identifiability and Estimation of Partially Observed Influence Models

The influence model (IM) is a discrete-time stochastic model that captures the spatiotemporal dynamics of networked Markov chains. Partially-observed IM (POIM) is an IM in which the statuses for some sites are unobserved. Identifiability and estimation of POIMs from incomplete state information are critical for POIM applications. In this letter, we develop a new estimation algorithm for both homogeneous and heterogeneous POIMs. The method, called EM-JMPE, integrates expectation maximization (EM) and joint-margin probability estimation (JMPE) to achieve reduced computation. In addition, we study the identifiability of POIMs by exploring the reduced-size joint-margin matrix, based on which necessary conditions for both homogeneous and heterogeneous POIMs are provided. The simulation studies verify the developed results.