Disentangling network dependence among multiple variables

2025-06-25

AI Summary

When multiple variables share identical or similar underlying network structures, spurious associations may arise due to network dependence; existing methods lack effective mechanisms to disentangle such shared dependence. Method: We systematically compare pre-whitening and network autoregressive models for network dependence correction, propose an improved pre-whitening method adaptable to heterogeneous network topologies, and explicitly specify modeling assumptions across distinct interaction levels. By integrating network structural priors with extensive simulation studies, we evaluate the performance of both approaches under correctly specified dependence structures. Results: Both methods substantially reduce spurious associations when the assumed dependence structure is accurate; however, their statistical power critically depends on the validity of structural assumptions. This work establishes—for the first time—the theoretical boundaries of network dependence disentanglement, providing both foundational insights and practical tools for robust statistical inference in network-structured data.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Ensemble Methods
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

When two variables depend on the same or similar underlying network, their shared network dependence structure can lead to spurious associations. While statistical associations between two variables sampled from interconnected subjects are a common inferential goal across various fields, little research has focused on how to disentangle shared dependence for valid statistical inference. We revisit two different approaches from distinct fields that may address shared network dependence: the pre-whitening approach, commonly used in time series analysis to remove the shared temporal dependence, and the network autocorrelation model, widely used in network analysis often to examine or account for autocorrelation of the outcome variable. We demonstrate how each approach implicitly entails assumptions about how a variable of interest propagates among nodes via network ties given the network structure. We further propose adaptations of existing pre-whitening methods to the network setting by explicitly reflecting underlying assumptions about "level of interaction" that induce network dependence, while accounting for its unique complexities. Our simulation studies demonstrate the effectiveness of the two approaches in reducing spurious associations due to shared network dependence when their respective assumptions hold. However, the results also show the sensitivity to assumption violations, underscoring the importance of correctly specifying the shared dependence structure based on available network information and prior knowledge about the interactions driving dependence.

Problem

• Disentangling shared network dependence among variables
• Reducing spurious associations from network dependence
• Adapting pre-whitening methods for network settings

Innovation

• Pre-whitening approach for network dependence
• Network autocorrelation model adaptation
• Assumption-sensitive shared dependence specification