This work proposes a unified framework for efficient estimation under latent space modeling of heterogeneous networks. We consider a class of latent space models that decompose latent vectors into shared and network-specific components across networks. We develop a novel procedure that first identifies the shared latent vectors and further refines estimates through efficient score equations to achieve statistical efficiency. Oracle error rates for estimating the shared and heterogeneous latent vectors are established simultaneously. The analysis framework offers remarkable flexibility, accommodating various types of edge weights under exponential family distributions.

翻译：本研究提出了一种在异构网络潜在空间建模下进行高效估计的统一框架。我们考虑一类将潜在向量分解为跨网络共享分量与网络特定分量的潜在空间模型。我们开发了一种新颖的估计流程：首先识别共享潜在向量，继而通过高效得分方程进一步优化估计量以达到统计有效性。我们同时建立了估计共享与异质潜在向量的理论误差界。该分析框架具有显著的灵活性，能够兼容指数族分布下的各类边权重类型。