论文标题
具有差异私有双度序列的加权定向网络
Weighted directed networks with a differentially private bi-degree sequence
论文作者
论文摘要
$ P_0 $模型是针对有针对性网络的指数随机图模型，其双度序列是完全足够的统计量。它捕获了学位异质性的网络功能。已经建立了私人$ P_0 $模型中参数的差异私有估计器的一致性和渐近正态性。但是，$ P_0 $模型仅关注二进制边缘。在许多现实的网络中，可以加权边缘，采用一组有限的离散值。在本文中，我们进一步表明，基于加权$ P_0 $模型中差异私有双度序列的参数的力矩估计器是一致且渐近正常的。数值研究证明了我们的理论发现。
The $p_0$ model is an exponential random graph model for directed networks with the bi-degree sequence as the exclusively sufficient statistic. It captures the network feature of degree heterogeneity. The consistency and asymptotic normality of a differentially private estimator of the parameter in the private $p_0$ model has been established. However, the $p_0$ model only focuses on binary edges. In many realistic networks, edges could be weighted, taking a set of finite discrete values. In this paper, we further show that the moment estimators of the parameters based on the differentially private bi-degree sequence in the weighted $p_0$ model are consistent and asymptotically normal. Numerical studies demonstrate our theoretical findings.
