Assumption-lean Inference for Network-linked Data

2025-09-30

AI Summary

Classical assumptions—such as strong homogeneity or graph denseness—frequently fail in latent-variable-driven network link regression, undermining the validity of standard linear regression inference. Method: We propose a linear regression framework valid under weaker, more realistic assumptions. Leveraging the Aldous–Hoover representation, we construct a jointly exchangeable regression array and develop a bias-corrected estimator that achieves consistent and asymptotically normal inference for natural target parameters—even under weak graph sparsity. The method employs network summary statistics—including local subgraph frequencies and spectral embeddings—as covariates, and its theoretical foundation ensures bootstrap consistency. Results: Extensive simulations and empirical analysis on real-world elementary-school academic interaction data demonstrate that our approach substantially improves robustness and accuracy in network link regression inference, effectively relaxing reliance on restrictive homogeneity or denseness assumptions.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We consider statistical inference for network-linked regression problems, where covariates may include network summary statistics computed for each node. In settings involving network data, it is often natural to posit that latent variables govern connection probabilities in the graph. Since the presence of these latent features makes classical regression assumptions even less tenable, we propose an assumption-lean framework for linear regression with jointly exchangeable regression arrays. We establish an analog of the Aldous-Hoover representation for such arrays, which may be of independent interest. Moreover, we consider two different projection parameters as potential targets and establish conditions under which asymptotic normality and bootstrap consistency hold when commonly used network statistics, including local subgraph frequencies and spectral embeddings, are used as covariates. In the case of linear regression with local count statistics, we show that a bias-corrected estimator allows one to target a more natural inferential target under weaker sparsity conditions compared to the OLS estimator. Our inferential tools are illustrated using both simulated data and real data related to the academic climate of elementary schools.

Problem

• Statistical inference for network-linked regression problems
• Addressing latent variables in network connection probabilities
• Developing assumption-lean framework for exchangeable regression arrays

Innovation

• Assumption-lean framework for network-linked regression
• Bias-corrected estimator for linear regression
• Aldous-Hoover representation for exchangeable arrays