Network interference, where the outcome of an individual is affected by the treatment assignment of those in their social network, is pervasive in real-world settings. However, it poses a challenge to estimating causal effects. We consider the task of estimating the total treatment effect (TTE), or the difference between the average outcomes of the population when everyone is treated versus when no one is, under network interference. Under a Bernoulli randomized design, we provide an unbiased estimator for the TTE when network interference effects are constrained to low order interactions among neighbors of an individual. We make no assumptions on the graph other than bounded degree, allowing for well-connected networks that may not be easily clustered. We derive a bound on the variance of our estimator and show in simulated experiments that it performs well compared with standard estimators for the TTE. We also derive a minimax lower bound on the mean squared error of our estimator which suggests that the difficulty of estimation can be characterized by the degree of interactions in the potential outcomes model. We also prove that our estimator is asymptotically normal under boundedness conditions on the network degree and potential outcomes model. Central to our contribution is a new framework for balancing model flexibility and statistical complexity as captured by this low order interactions structure.

翻译：网络干扰（个体结果受其社交网络中他人处理分配影响的现象）在现实场景中普遍存在，但其给因果效应估计带来了挑战。我们研究在网络干扰条件下估计总处理效应（TTE）的问题，即群体中所有人接受处理与无人接受处理时平均结果的差异。在伯努利随机化设计下，当网络干扰效应局限于个体邻居间的低阶交互作用时，我们为TTE提供了无偏估计量。我们不对图结构施加除有界度以外的任何假设，从而允许存在难以聚类的稠密连接网络。我们推导了估计量方差的界，并通过模拟实验证明其相比于标准TTE估计量具有更优性能。我们进一步导出了估计量均方误差的极小极大下界，表明估计难度可由潜在结果模型中的交互阶数来刻画。同时证明在网络度与潜在结果模型满足有界性条件时，该估计量具有渐近正态性。我们核心贡献在于建立了一个平衡模型灵活性与统计复杂性的新框架，该框架通过低阶交互结构来表征这种平衡关系。