AI 中文总结
该研究针对含多类交互的网络数据集，提出基于图极限的多网络直方图联合估计器，利用层间共享潜在变量降低估计误差，经模拟和印度村庄网络应用验证了方法有效性。
AI 中文摘要
现代应用中的网络数据集常涉及共享个体集合上发生的多种交互类型，联合建模可增强对这些交互生成机制的刻画，因为共享顶点能让各层辅助解释其他层的结构。我们采用称为缩放图函数集（scaled set of graphons）的图极限对多路复用观测值建模，并开发了一种基于块模型近似的非参数联合估计器，即多网络直方图（multi-network histogram）。该非参数框架可捕捉各层不同的稀疏性与连接结构，通过所有层共享的潜在变量考虑异质性。我们确立了多网络直方图的理论性质，给出加权平均积分平方误差的上界并推导最小化该误差的最优带宽。通过利用各层间的信息，这种联合建模实现了误差降低和更小的最优带宽，即使在更稀疏的层也能实现高分辨率估计。其有效性通过模拟研究和对印度村庄社会经济网络的应用得到验证。
英文摘要
Network datasets in modern applications often involve multiple types of interactions occurring over a shared set of individuals. Characterizing the generating mechanisms of these interactions can be enhanced by joint modelling, as shared vertices allow layers to help explain the structure of other layers. We model multiplex observations using graph limits, called a scaled set of graphons, and develop a nonparametric joint estimator based on blockmodel approximations, termed the multi-network histogram. This nonparametric framework captures each layer's varying sparsity and connection structure, accounting for heterogeneity via shared latent variables across all layers. We establish the theoretical properties of the multi-network histogram, providing an upper bound for the weighted mean integrated squared error and deriving the optimal bandwidth that minimizes this error. By leveraging information across layers, this joint modelling achieves a reduction in error and a smaller optimal bandwidth, which enables high-resolution estimation even in sparser layers. Its usefulness is demonstrated through simulation studies and an application to socioeconomic networks in an Indian village.
CommentsTotal 60 pages, 7 figures
