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<p>Network data typically contain sensitive relational information, where direct release or sharing may lead to non-negligible privacy violations without proper statistical safeguards. While differential privacy has emerged as a powerful framework for privacy-preserving network data analysis, theoretical understanding remains limited particularly for models incorporating both network structure and nodal attributes. This paper bridges this gap by investigating a directed <i>β</i>-model with covariates under differential privacy constraints. The proposed model accounts for both node-level heterogeneity (via 2<i>n</i>-dimensional degree parameters <Emphasis Type="BoldItalic">θ</Emphasis>) and covariate-driven homogeneity (via a <i>p</i>-dimensional parameter <Emphasis Type="BoldItalic">γ</Emphasis>). To protect privacy, the authors introduce a joint Laplace mechanism for releasing network statistics while satisfying differential privacy constraints. Leveraging moment-based estimation techniques, the authors estimate the parameters of both degree heterogeneity and homogeneity and derive the consistency and asymptotic normality of the differentially private estimators as the network size tends to infinity. The proposed theoretical findings are validated through numerical simulations and real-world case studies, demonstrating the validity of the obtained theoretical results.</p>

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Differential Privacy Statistical Inference for a Directed Network Model with Covariates

  • 期刊论文

  • 发表日期：

    2026年5月6日

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  • Jing Luo,
  • Hong Qin,
  • Zhimeng Xu

摘要

Network data typically contain sensitive relational information, where direct release or sharing may lead to non-negligible privacy violations without proper statistical safeguards. While differential privacy has emerged as a powerful framework for privacy-preserving network data analysis, theoretical understanding remains limited particularly for models incorporating both network structure and nodal attributes. This paper bridges this gap by investigating a directed β-model with covariates under differential privacy constraints. The proposed model accounts for both node-level heterogeneity (via 2n-dimensional degree parameters θ) and covariate-driven homogeneity (via a p-dimensional parameter γ). To protect privacy, the authors introduce a joint Laplace mechanism for releasing network statistics while satisfying differential privacy constraints. Leveraging moment-based estimation techniques, the authors estimate the parameters of both degree heterogeneity and homogeneity and derive the consistency and asymptotic normality of the differentially private estimators as the network size tends to infinity. The proposed theoretical findings are validated through numerical simulations and real-world case studies, demonstrating the validity of the obtained theoretical results.