论文标题
随机图群集随机化
Randomized Graph Cluster Randomization
论文作者
论文摘要
全球平均治疗效果（GATE）是网络干扰下因果推断研究的主要兴趣。通过正确指定的干扰暴露模型，GATE的Horvitz-Thompson（HT）和Hájek估计器分别是公正和一致的，但已知在许多设计和许多感兴趣的环境下都表现出极大的差异。通过固定的干扰图聚类，与节点级随机分配相比，图形簇随机化（GCR）设计已大大降低了方差，但即使如此，差异仍然通常很大。在这项工作中，我们提出了GCR设计的随机版本，描述了随机图群集随机化（RGCR），该图是使用随机聚类而不是单个固定群集。通过考虑许多不同集群分配的合奏，此设计避免了GCR的关键问题，在给定的集群中，给定节点有时会“幸运”或“不幸”。我们提出了两种随机图分解算法，可与RGCR，随机3-NET和1-HOP-MAX一起使用，该算法是根据多路剪切问题的先前工作改编而成的。当整合自己的随机性时，这些算法提供了可以有效估计的网络暴露概率。在干扰图的度量结构上的假设下，我们在门的HT估计器的方差上开发了上限。如果在GCR设计下，最知名的HT估计器上限在公制结构的参数中是指数的，那么我们给出了RGCR下的可比方差上限，而相反，在相同的参数中是多项式的。我们提供了比较RGCR和GCR设计的广泛模拟，观察到在各种设置中，HT和Hájek估计器的平方误差的大幅减少。
The global average treatment effect (GATE) is a primary quantity of interest in the study of causal inference under network interference. With a correctly specified exposure model of the interference, the Horvitz-Thompson (HT) and Hájek estimators of the GATE are unbiased and consistent, respectively, yet known to exhibit extreme variance under many designs and in many settings of interest. With a fixed clustering of the interference graph, graph cluster randomization (GCR) designs have been shown to greatly reduce variance compared to node-level random assignment, but even so the variance is still often prohibitively large. In this work we propose a randomized version of the GCR design, descriptively named randomized graph cluster randomization (RGCR), which uses a random clustering rather than a single fixed clustering. By considering an ensemble of many different cluster assignments, this design avoids a key problem with GCR where a given node is sometimes "lucky" or "unlucky" in a given clustering. We propose two randomized graph decomposition algorithms for use with RGCR, randomized 3-net and 1-hop-max, adapted from prior work on multiway graph cut problems. When integrating over their own randomness, these algorithms furnish network exposure probabilities that can be estimated efficiently. We develop upper bounds on the variance of the HT estimator of the GATE under assumptions on the metric structure of the interference graph. Where the best known variance upper bound for the HT estimator under a GCR design is exponential in the parameters of the metric structure, we give a comparable variance upper bound under RGCR that is instead polynomial in the same parameters. We provide extensive simulations comparing RGCR and GCR designs, observing substantial reductions in the mean squared error for both HT and Hájek estimators of the GATE in a variety of settings.
