Robust High-Dimensional Covariate-Assisted Network Modeling

Modern network data analysis often involves analyzing network structures alongside covariate features to gain deeper insights into underlying patterns. However, traditional covariate-assisted statistical network models may not fully consider the cases of high-dimensional covariates, where some covariates could be uninformative or misleading, and the possible mismatching between the information of the networks and covariates. To address this gap, we introduce a novel robust high-dimensional covariate-assisted latent space model. This framework links latent vectors representing network structures with simultaneous sparse and low-rank transformations of the high-dimensional covariates, capturing their mutual dependence. To robustly integrate the dependence, we use a shrinkage prior to the discrepancy between latent network vectors and low-rank covariate approximation vectors, allowing the possibility of mismatching of information from covariates for some network nodes. To achieve computation efficiency, we developed a mean-field variational inference algorithm to approximate the posterior distribution. We establish the posterior concentration rate within a suitable parameter space and demonstrate how our model facilitates adaptive information aggregation between networks and covariates with the presence of high-dimensional covariates. Extensive simulations and real-world data analyses confirm the effectiveness of our approach.