一种面向多维网络的动态随机块模型
A Dynamic Stochastic Block Model for Multidimensional Networks
AI总结：
针对多维网络动态建模难题，提出带层间块因果关系的动态随机块模型，通过贝叶斯先验和Gibbs采样实现推断，模拟效果优于基线方法，还可统一用于国际贸易的社区检测与引力方程建模。
摘要：
关系数据的可得性能够为经济运行机制研究提供新洞见。然而，对包含多种类型关系的网络数据中的动态特性建模仍是一项具有挑战性的问题。随机块模型为网络分析提供了一种简约且灵活的方法。我们提出了一种适用于多维网络的新型随机块模型，该模型中各层专属的隐马尔可夫链过程驱动社区结构的变化。节点在给定层中的块成员身份变化可能受其自身在其他层中过往成员身份的影响。这一设定可支持聚类重叠、聚类解耦，或是层间更复杂的关系，包括单向或双向的非线性Granger块因果关系场景。我们通过在贝叶斯框架下假设多重拉普拉斯先验分布，解决了饱和设定带来的过参数化问题。我们采用数据增强和Gibbs采样方法提升推断问题的可处理性。通过模拟实验我们发现，标准线性模型和成对方法在大多数场景下都无法检测到块因果关系，而我们的模型能够还原真实的Granger因果结构。在国际贸易的应用研究中，我们的模型提供了一个统一框架，可同时涵盖社区检测和引力方程建模。我们在大样本国家数据中发现了贸易协定与贸易流量之间存在块Granger因果关系，以及两层网络均存在核心-边缘结构的新证据。
英文摘要：
The availability of relational data can offer new insights into the functioning of the economy. Nevertheless, modeling the dynamics in network data with multiple types of relationships is still a challenging issue. Stochastic block models provide a parsimonious and flexible approach to network analysis. We propose a new stochastic block model for multidimensional networks, where layer-specific hidden Markov-chain processes drive the changes in community formation. The changes in the block membership of a node in a given layer may be influenced by its own past membership in other layers. This allows for clustering overlap, clustering decoupling, or more complex relationships between layers, including settings of unidirectional, or bidirectional, non-linear Granger block causality. We address the overparameterization issue of a saturated specification by assuming a Multi-Laplacian prior distribution within a Bayesian framework. Data augmentation and Gibbs sampling are used to make the inference problem more tractable. Through simulations, we show that standard linear models and the pairwise approach are unable to detect block causality in most scenarios. In contrast, our model can recover the true Granger causality structure. As an application to international trade, we show that our model offers a unified framework, encompassing community detection and Gravity equation modeling. We found new evidence of block Granger causality of trade agreements and flows and core-periphery structure in both layers on a large sample of countries.
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