Dynamic Networks with Node Heterogeneity and Homophily
The goal of this paper is to model node heterogeneity and link homophily for dynamic networks. The proposed framework brings new insights on how networks evolve over time. It also provides more sophisticated tools for the prediction of future networks with statistical guarantees. The new model accounts for the link homophily associated with both observed traits and latent traits. The joint modeling of node heterogeneity and both observed and latent homophily effects also poses the significant challenge in statistical inference, resulted from the large number of confounding parameters in the model. To overcome this, we propose a novel normalized squared loss, paving the way for efficient and stable estimation of parameters in a high-dimensional setting. We provide a rigorous theoretical analysis of the estimation method, and demonstrate its effectiveness through extensive simulations and the illustration with some real-world network data.