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（即个体的结果受其社交网络中他人的处理分配影响）在现实环境中普遍存在，但这对因果效应的估计构成了挑战。我们考虑在存在网络干扰的情况下，估计总处理效应（TTE）的问题，即所有人接受处理与无人接受处理时群体平均结果之差。在伯努利随机化设计下，当网络干扰效应被限制为个体邻居间的低阶交互作用时，我们为TTE提供了一个无偏估计量。除有界度外，我们不对图结构做任何假设，允许存在难以聚类的紧密连接网络。我们推导了估计量方差的界，并通过模拟实验表明，与标准TTE估计量相比，该估计量表现良好。同时推导了估计量均方误差的极小化最大下界，表明估计难度可通过潜在结果模型中的交互作用阶数来刻画。我们进一步证明，在网络度与潜在结果模型满足有界性条件下，该估计量具有渐近正态性。本研究的核心贡献在于建立了一个新框架，通过低阶交互作用结构在模型灵活性与统计复杂度之间实现平衡。