We propose a generalization of the synthetic controls and synthetic interventions methodology to incorporate network interference. We consider the estimation of unit-specific potential outcomes from panel data in the presence of spillover across units and unobserved confounding. Key to our approach is a novel latent factor model that takes into account network interference and generalizes the factor models typically used in panel data settings. We propose an estimator, Network Synthetic Interventions (NSI), and show that it consistently estimates the mean outcomes for a unit under an arbitrary set of counterfactual treatments for the network. We further establish that the estimator is asymptotically normal. We furnish two validity tests for whether the NSI estimator reliably generalizes to produce accurate counterfactual estimates. We provide a novel graph-based experiment design that guarantees the NSI estimator produces accurate counterfactual estimates, and also analyze the sample complexity of the proposed design. We conclude with simulations that corroborate our theoretical findings.

翻译：我们提出了一种综合控制与合成干预方法的推广，以融入网络干扰。本文考虑在存在跨单元溢出效应和未观测混杂因素的情况下，从面板数据中估计单元特异性潜在结果。我们方法的核心是一个新颖的潜在因子模型，该模型考虑了网络干扰，并推广了面板数据设置中常用的因子模型。我们提出了一种估计量——网络合成干预（NSI），并证明该估计量能够一致地估计网络在任意反事实处理集下单元的平均结果。我们进一步证明了该估计量具有渐近正态性。我们提供了两种有效性检验，用于判断NSI估计量是否可靠地泛化以产生准确的反事实估计。我们提出了一种新颖的基于图的实验设计，该设计确保NSI估计量产生准确的反事实估计，并分析了所提出设计的样本复杂度。最后，通过仿真实验验证了我们的理论发现。