Estimating causal effects under interference is pertinent to many real-world settings. However, the true interference network may be unknown to the practitioner, precluding many existing techniques that leverage this information. A recent line of work with low-order potential outcomes models uses staggered rollout designs to obtain unbiased estimators that require no network information. However, their use of polynomial extrapolation can lead to prohibitively high variance. To address this, we propose a two-stage experimental design that restricts treatment rollout to a sub-population. We analyze the bias and variance of an interpolation-style estimator under this experimental design. Through numerical simulations, we explore the trade-off between the error attributable to the subsampling of our experimental design and the extrapolation of the estimator. Under low-order interactions models with degree greater than 1, the proposed design greatly reduces the error of the polynomial interpolation estimator, such that it outperforms baseline estimators, especially when the treatment probability is small.

翻译：在干扰存在的情况下估计因果效应与许多现实场景相关。然而，真实的干扰网络对实践者而言可能是未知的，这排除了许多利用该信息的现有技术。最近一系列基于低阶潜在结果模型的研究采用交错滚动设计来获得无需网络信息的无偏估计量。但其使用的多项式外推方法可能导致方差过高。为解决此问题，我们提出一种两阶段实验设计，将处理分配限制在子群体中。我们分析了该实验设计下插值型估计量的偏差与方差。通过数值模拟，我们探究了由实验设计子采样与估计量外推共同导致的误差权衡。在阶数大于1的低阶交互模型下，所提出的设计显著降低了多项式插值估计量的误差，使其在基准估计量中表现更优，尤其是在处理概率较小时。