Causal inference for network data is an area of active interest in the social sciences. Unfortunately, the complicated dependence structure of network data presents an obstacle to many causal inference procedures. We consider the task of mediation analysis for network data, and present a model in which mediation occurs in a latent embedding space. Under this model, node-level interventions have causal effects on nodal outcomes, and these effects can be partitioned into a direct effect independent of the network, and an indirect effect induced by homophily. To estimate network-mediated effects, we embed nodes into a low-dimensional space and fit two regression models: (1) an outcome model describing how nodal outcomes vary with treatment, controls, and position in latent space; and (2) a mediator model describing how latent positions vary with treatment and controls. We prove that the estimated coefficients are asymptotically normal about the true coefficients under a sub-gamma generalization of the random dot product graph, a widely-used latent space model. We show that these coefficients can be used in product-of-coefficients estimators for causal inference. Our method is easy to implement, scales to networks with millions of edges, and can be extended to accommodate a variety of structured data.

翻译：网络数据的因果推断是社会科学中一个活跃的研究领域。然而，网络数据复杂的依赖结构给许多因果推断程序带来了障碍。我们考虑了网络数据的中介分析任务，并提出了一个模型，其中中介效应发生在潜在嵌入空间中。在该模型下，节点层面的干预对节点结果产生因果效应，这些效应可以分解为独立于网络的直接效应和由同质性引起的间接效应。为了估计网络介导的效应，我们将节点嵌入到一个低维空间中，并拟合两个回归模型：(1) 结果模型，描述节点结果如何随处理、控制变量和潜在空间位置变化；(2) 中介模型，描述潜在位置如何随处理和控制变量变化。我们证明，在随机点积图（一种广泛使用的潜在空间模型）的次伽马推广下，估计系数关于真实系数是渐近正态的。我们展示了这些系数可用于因果推断的系数乘积估计量。我们的方法易于实现，可扩展到具有数百万条边的网络，并可以扩展到适应各种结构化数据。