Robust High-Dimensional Covariate-Assisted Network Modeling

2025-05-05

AI Summary

Traditional covariate-assisted network models suffer from sensitivity to uninformative or misleading high-dimensional covariates and struggle with information mismatch between networks and covariates. To address these issues, we propose a robust high-dimensional covariate-assisted latent space model that couples covariates with network latent representations via a sparse low-rank transformation and incorporates shrinkage Bayesian priors for mismatch tolerance. This work is the first to unify sparsity, low-rank structure, and robust priors within a covariate-assisted network modeling framework, enabling adaptive information aggregation. We develop an efficient algorithm based on variational inference and sparse low-rank decomposition, and establish theoretical guarantees on posterior convergence rates. Experiments demonstrate substantial improvements over state-of-the-art methods in link prediction and node clustering tasks, with scalability to large-scale sparse networks.

Technology Category

Reasoning under Uncertainty: Relational Probabilistic ModelsMachine Learning: Probabilistic Circuits and Graphical ModelsCognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsWeb Mining and Content Analysis: Models for Web evolutionSocial Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

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.

Problem

• Handling high-dimensional covariates in network modeling
• Addressing mismatch between network and covariate information
• Developing robust sparse and low-rank covariate transformations

Innovation

• Robust high-dimensional covariate-assisted latent space model
• Sparse and low-rank transformations for covariate integration
• Variational inference algorithms for scalable network analysis