Dynamic network data analysis requires joint modelling individual snapshots and time dynamics. This paper proposes a new two-way heterogeneity model towards this goal. The new model equips each node of the network with two heterogeneity parameters, one to characterize the propensity of forming ties with other nodes and the other to differentiate the tendency of retaining existing ties over time. Though the negative log-likelihood function is non-convex, it is locally convex in a neighbourhood of the true value of the parameter vector. By using a novel method of moments estimator as the initial value, the consistent local maximum likelihood estimator (MLE) can be obtained by a gradient descent algorithm. To establish the upper bound for the estimation error of the MLE, we derive a new uniform deviation bound, which is of independent interest. The usefulness of the model and the associated theory are further supported by extensive simulation and the analysis of some real network data sets.

翻译：动态网络数据分析需要联合建模个体快照与时间动态。本文提出了一种新的双向异质性模型以实现这一目标。该模型为网络中的每个节点配备了两个异质性参数：一个用于表征与其他节点形成连接倾向，另一个用于区分随时间推移保留现有连接的倾向。尽管负对数似然函数是非凸的，但在参数向量真实值的邻域内它是局部凸的。通过使用新颖的矩估计量作为初始值，可通过梯度下降算法获得一致局部最大似然估计量。为了建立最大似然估计误差的上界，我们推导了一个新的均匀偏差界，该结果具有独立研究价值。模型及其相关理论的有效性通过大量仿真和真实网络数据集的分析得到了进一步验证。