Robust High-Dimensional Covariate-Assisted Network Modeling

TL;DR

This paper introduces a robust high-dimensional covariate-assisted network model that effectively captures the dependence between network structures and covariates, even with mismatches and high dimensionality, using scalable variational inference.

Contribution

The paper proposes a novel latent space model with sparse and low-rank covariate transformations, along with shrinkage priors and scalable algorithms for large-scale network analysis.

Findings

Model accurately captures network-covariate dependence.

Scalable variational algorithms enable analysis of large networks.

Simulation and real data confirm effectiveness.

Abstract

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 adequately handle cases involving high-dimensional covariates, where some covariates could be uninformative or misleading, or the possible mismatch between network and covariate information. To address this issue, we introduce a novel robust high-dimensional covariate-assisted latent space model. This framework links latent vectors representing network structures with simultaneously sparse and low-rank transformations of the high-dimensional covariates, capturing the mutual dependence between network structures and covariates. To robustly integrate this dependence, we use a shrinkage prior on the discrepancy between latent network vectors and low-rank covariate approximation vectors, allowing for potential mismatches between network and covariate information. For scalable inference, we develop two variational inference algorithms, enabling efficient analysis of large-scale sparse networks. We establish the posterior concentration rate within a suitable parameter space and demonstrate how the proposed model facilitates adaptive information aggregation between networks and high-dimensional covariates. Extensive simulation studies and real-world data analyses confirm the effectiveness of our approach.