Modelling edge weights play a crucial role in the analysis of network data, which reveals the extent of relationships among individuals. Due to the diversity of weight information, sharing these data has become a complicated challenge in a privacy-preserving way. In this paper, we consider the case of the non-denoising process to achieve the trade-off between privacy and weight information in the generalized $\beta$-model. Under the edge differential privacy with a discrete Laplace mechanism, the Z-estimators from estimating equations for the model parameters are shown to be consistent and asymptotically normally distributed. The simulations and a real data example are given to further support the theoretical results.

中文翻译：

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参数增加的微分私有广义β模型的渐近理论

建模边缘权重在网络数据分析中起着至关重要的作用，它揭示了个体之间关系的程度。由于权重信息的多样性，以隐私保护的方式共享这些数据已成为一项复杂的挑战。在本文中，我们考虑非去噪过程的情况，以在广义 $\beta$ 模型中实现隐私和权重信息之间的权衡。在具有离散拉普拉斯机制的边缘差分隐私下，来自模型参数估计方程的 Z 估计量显示为一致且渐近正态分布。给出了模拟和真实数据示例以进一步支持理论结果。