For the differential privacy under the sub-Gamma noise, we derive the asymptotic properties of a class of network models with binary values with a general link function. In this paper, we release the degree sequences of the binary networks under a general noisy mechanism with the discrete Laplace mechanism as a special case. We establish the asymptotic result including both consistency and asymptotically normality of the parameter estimator when the number of parameters goes to infinity in a class of network models. Simulations and a real data example are provided to illustrate asymptotic results.

翻译：针对次Gamma噪声下的差分隐私，我们推导了一类具有二元值且使用一般链接函数的网络模型的渐近性质。本文中，在一般噪声机制下（以离散拉普拉斯机制为特例）发布了二元网络的度序列。当参数个数趋于无穷时，我们在该类网络模型中建立了参数估计量的渐近结果，包括一致性和渐近正态性。通过模拟实验和实际数据案例验证了渐近结果。