Dynamic Networks with Node Heterogeneity and Homophily

2026-08-07

AI Summary

This study addresses the coexistence of node heterogeneity and link homophily in dynamic networks by proposing a unified joint modeling framework that simultaneously captures both observed and latent attribute-driven homophily effects alongside node-specific heterogeneity. To tackle the challenges posed by high-dimensional parameter estimation, the authors introduce a normalized squared loss function that ensures estimation stability and computational efficiency. Theoretical analysis establishes favorable statistical properties of the proposed estimator, while extensive experiments on both simulated and real-world network data demonstrate that the method significantly outperforms existing approaches in predicting future network structures, exhibiting strong effectiveness and robustness.

Abstract

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.

Problem

• dynamic networks
• node heterogeneity
• homophily
• statistical inference
• high-dimensional estimation

Innovation

• dynamic networks
• node heterogeneity
• homophily
• normalized squared loss
• high-dimensional inference