The stochastic block model (SBM) is a widely used framework for community detection in networks, where the network structure is typically represented by an adjacency matrix. However, conventional SBMs are not directly applicable to an adjacency matrix that consists of non-negative zero-inflated continuous edge weights. To model the international trading network, where edge weights represent trading values between countries, we propose an innovative SBM based on a restricted Tweedie distribution. Additionally, we incorporate nodal information, such as the geographical distance between countries, and account for its dynamic effect on edge weights. Notably, we show that given a sufficiently large number of nodes, estimating this covariate effect becomes independent of community labels of each node when computing the maximum likelihood estimator of parameters in our model. This result enables the development of an efficient two-step algorithm that separates the estimation of covariate effects from other parameters. We demonstrate the effectiveness of our proposed method through extensive simulation studies and an application to real-world international trading data.

提出了一种基于受限 Tweedie 分布的创新的随机分块模型，用于模拟国际贸易网络中的非负零膨胀连续边权重，并结合节点信息和其对边权重的动态影响，实现了有效的两步算法来估计协变效应和其他参数，并通过广泛的模拟研究和真实的国际贸易数据的应用证明了该方法的有效性。

受限Tweedie随机块模型