Modeling and monitoring dynamic, directional, sparse, attributed networks via a dynamic Hurdle regression model with latent variables

Network data is commonly available across various domains, sparking a surge in research dedicated to modeling and monitoring network systems. In the realm of network analysis with node attributes, the majority of existing studies utilize generalized linear models (GLMs) to establish connections between network topology and node attributes. However, these studies often overlook the incongruity between directional edges and directionless attributes within the context of directional networks, as well as the inadequacy of using only observable attributes to explain the network topology. In this paper, we introduce a novel Hurdle regression model with latent variables (HRML), which assigns four latent variables to each node to govern the directionality of interactions. By integrating observable attributes, our proposed model adeptly manages directional, sparse, and attributed networks. We further develop the HRML into its dynamic version (D-HRML) within the state space model framework to capture the temporal dynamics of network streams. An extended Kalman filter (EKF) is employed for optimal parameter estimation. Ultimately, we devise a monitoring scheme based on the generalized likelihood ratio test (GLRT) to detect abrupt changes across diverse scenarios. Extensive simulations demonstrate that our proposed method outperforms several competitive approaches, particularly in detecting shifts in interaction propensities. A case study utilizing the Enron E-mail corpus further substantiates the high efficiency of our methodology.