A fundamental problem in network experiments is selecting an appropriate experimental design in order to precisely estimate a given causal effect of interest. In fact, optimal rates of estimation remain unknown for essentially all causal effects in network experiments. In this work, we propose a general approach for constructing experiment designs under network interference with the goal of precisely estimating a pre-specified causal effect. A central aspect of our approach is the notion of a conflict graph, which captures the fundamental unobservability associated with the casual effect and the underlying network. We refer to our experimental design as the Conflict Graph Design. In order to estimate effects, we propose a modified Horvitz--Thompson estimator. We show that its variance under the Conflict Graph Design is bounded as $O(\lambda(H) / n )$, where $\lambda(H)$ is the largest eigenvalue of the adjacency matrix of the conflict graph. These rates depend on both the underlying network and the particular causal effect under investigation. Not only does this yield the best known rates of estimation for several well-studied causal effects (e.g. the global and direct effects) but it also provides new methods for effects which have received less attention from the perspective of experiment design (e.g. spill-over effects). Our results corroborate two implicitly understood points in the literature: (1) that in order to increase precision, experiment designs should be tailored to specific causal effects of interest and (2) that "more local" effects are easier to estimate than "more global" effects. In addition to point estimation, we construct conservative variance estimators which facilitate the construction of asymptotically valid confidence intervals for the casual effect of interest.

翻译：网络实验中的一个基本问题在于选择合适的实验设计，以精确估计感兴趣的特定因果效应。事实上，对于网络实验中几乎所有因果效应，其最优估计速率至今仍未明确。本研究提出一种在网络干扰下构建实验设计的通用方法，旨在精确估计预先设定的因果效应。该方法的核心理念是冲突图概念，它捕捉了与因果效应及底层网络相关的基本不可观测性。我们将此实验设计称为冲突图设计。为估计效应，我们提出一种改进的霍维茨-汤普森估计量。我们证明其在冲突图设计下的方差上界为$O(\lambda(H) / n )$，其中$\lambda(H)$是冲突图邻接矩阵的最大特征值。这些速率既取决于底层网络结构，也取决于所研究的特定因果效应。这不仅为若干经典因果效应（如全局效应与直接效应）提供了目前已知的最佳估计速率，还为实验设计视角下关注较少的效应（如溢出效应）提供了新的研究方法。我们的结果印证了文献中两个隐含共识：（1）为提高估计精度，实验设计应针对特定目标因果效应进行定制；（2）“更局部”的效应比“更全局”的效应更容易估计。除点估计外，我们还构建了保守的方差估计量，可为目标因果效应构建渐近有效的置信区间。