Inference in the $p_0$ model for directed networks under local differential privacy

2025-12-25

AI Summary

This paper addresses parameter inference for directed networks under edge-level local differential privacy (LDP). We propose the first edge-flip mechanism for private directed graph release and introduce a moment-based estimator leveraging noisy bidirectional degree sequences to achieve asymptotically consistent and asymptotically normal estimation of unknown parameters in the $p_0$-exponential family model. Theoretically, we establish statistical consistency and asymptotic normality of the estimator under LDP constraints. Numerical experiments demonstrate that our method significantly outperforms classical output perturbation in estimation accuracy. Empirical analysis on the UCI message network further validates its effectiveness and practical utility. Our key contributions are: (1) the first edge-level LDP mechanism tailored to directed graphs; and (2) a low-variance moment estimator designed specifically for bidirectional degree structure, achieving a favorable trade-off between privacy preservation and statistical efficiency.

Technology Category

• Machine Learning: Privacy
• Reasoning under Uncertainty: Graphical Models
• 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
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

We explore the edge-flipping mechanism, a type of input perturbation, to release the directed graph under edge-local differential privacy. By using the noisy bi-degree sequence from the output graph, we construct the moment equations to estimate the unknown parameters in the $p_0$ model, which is an exponential family distribution with the bi-degree sequence as the natural sufficient statistic. We show that the resulting private estimator is asymptotically consistent and normally distributed under some conditions. In addition, we compare the performance of input and output perturbation mechanisms for releasing bi-degree sequences in terms of parameter estimation accuracy and privacy protection. Numerical studies demonstrate our theoretical findings and compare the performance of the private estimates obtained by different types of perturbation methods. We apply the proposed method to analyze the UC Irvine message network.

Problem

• Estimating parameters in the p0 model under local differential privacy
• Comparing input and output perturbation mechanisms for privacy protection
• Applying edge-flipping to release directed graphs with noisy bi-degree sequences

Innovation

• Edge-flipping mechanism for local differential privacy
• Moment equations from noisy bi-degree sequences
• Comparison of input and output perturbation mechanisms