Privacy utility trade offs for parameter estimation in degree heterogeneous higher order networks

2026-02-03

AI Summary

This study addresses the problem of accurately estimating parameters of the β-model in sensitive relational networks under both local and central differential privacy constraints, leveraging node degree information. Focusing on higher-order hypergraphs with heterogeneous node degrees, it provides the first finite-sample characterization of the privacy–utility trade-off, establishing minimax lower bounds that explicitly depend on the privacy parameter and network size. A simple yet efficient estimator is constructed that matches these lower bounds up to constant and logarithmic factors. The theoretical analysis integrates differential privacy mechanisms, minimax theory, and higher-order hypergraph modeling, demonstrating that the proposed estimator achieves optimal performance under both privacy regimes. Empirical validation on synthetic and real-world communication networks confirms its effectiveness.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Privacy
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Security and Privacy: Large-scale security measurements

Abstract

In sensitive applications involving relational datasets, protecting information about individual links from adversarial queries is of paramount importance. In many such settings, the available data are summarized solely through the degrees of the nodes in the network. We adopt the $\beta$ model, which is the prototypical statistical model adopted for this form of aggregated relational information, and study the problem of minimax-optimal parameter estimation under both local and central differential privacy constraints. We establish finite sample minimax lower bounds that characterize the precise dependence of the estimation risk on the network size and the privacy parameters, and we propose simple estimators that achieve these bounds up to constants and logarithmic factors under both local and central differential privacy frameworks. Our results provide the first comprehensive finite sample characterization of privacy utility trade offs for parameter estimation in $\beta$ models, addressing the classical graph case and extending the analysis to higher order hypergraph models. We further demonstrate the effectiveness of our methods through experiments on synthetic data and a real world communication network.

Problem

• privacy-utility trade-off
• parameter estimation
• degree heterogeneous networks
• differential privacy
• higher-order networks

Innovation

• differential privacy
• minimax estimation
• β model
• hypergraph
• privacy-utility trade-off