The stable unit treatment value assumption states that the outcome of an individual is not affected by the treatment statuses of others, however in many real world applications, treatments can have an effect on many others beyond the immediately treated. Interference can generically be thought of as mediated through some network structure. In many empirically relevant situations however, complete network data (required to adjust for these spillover effects) are too costly or logistically infeasible to collect. Partially or indirectly observed network data (e.g., subsamples, aggregated relational data (ARD), egocentric sampling, or respondent-driven sampling) reduce the logistical and financial burden of collecting network data, but the statistical properties of treatment effect adjustments from these design strategies are only beginning to be explored. In this paper, we present a framework for the estimation and inference of treatment effect adjustments using partial network data through the lens of structural causal models. We also illustrate procedures to assign treatments using only partial network data, with the goal of either minimizing estimator variance or optimally seeding. We derive single network asymptotic results applicable to a variety of choices for an underlying graph model. We validate our approach using simulated experiments on observed graphs with applications to information diffusion in India and Malawi.

翻译：稳定单位处理值假设指出，个体的结果不受其他个体处理状态的影响，然而在许多实际应用中，处理不仅对直接处理对象产生影响，还可能对众多其他个体产生作用。干扰效应通常可视为通过某种网络结构介导产生。但在许多实证相关场景中，收集完整网络数据（用于调整这些溢出效应所需）成本过高或在操作上不可行。部分观测或间接观测的网络数据（例如子样本、聚合关系数据、自我中心抽样或受访者驱动抽样）降低了收集网络数据的操作与财务负担，但这些设计策略所得处理效应调整的统计特性才刚刚开始被探索。本文通过结构因果模型的视角，提出了一个利用部分网络数据进行处理效应调整估计与推断的框架。我们还阐述了仅使用部分网络数据分配处理的方法，其目标在于最小化估计量方差或实现最优种子选择。我们推导了适用于多种基础图模型选择的单网络渐近结果，并通过在观测图上的模拟实验验证了我们的方法，应用于印度和马拉维的信息传播案例。