Randomized experiments on a network often involve interference between connected units, namely, a situation in which an individual’s treatment can affect the response of another individual. Current approaches to deal with interference, in theory and in practice, often make restrictive assumptions on its structure—for instance, assuming that interference is local—even when using otherwise nonparametric inference strategies. This reliance on explicit restrictions on the interference mechanism suggests a shared intuition that inference is impossible without any assumptions on the interference structure. In this paper, we begin by formalizing this intuition in the context of a classical nonparametric approach to inference, referred to as design-based inference of causal effects. Next, we show how, always in the context of design-based inference, even parametric structural assumptions that allow the existence of unbiased estimators cannot guarantee a decreasing variance even in the large sample limit. This lack of concentration in large samples is often observed empirically, in randomized experiments in which interference of some form is expected to be present. This result has direct consequences for the design and analysis of large experiments—for instance, in online social platforms—where the belief is that large sample sizes automatically guarantee small variance. More broadly, our results suggest that although strategies for causal inference in the presence of interference borrow their formalism and main concepts from the traditional causal inference literature, much of the intuition from the no-interference case do not easily transfer to the interference setting.

中文翻译：

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任意和网络干扰下基于设计的因果推理和 A/B 测试的局限性

网络上的随机实验通常涉及连接单元之间的干扰，即个体的治疗会影响另一个个体的反应的情况。当前在理论上和实践中处理干扰的方法通常对其结构做出限制性假设——例如，假设干扰是局部的——即使在使用其他非参数推理策略时也是如此。这种对干扰机制的明确限制的依赖表明了一种共同的直觉，即在没有对干扰结构的任何假设的情况下，推理是不可能的。在本文中，我们首先在经典的非参数推理方法的背景下形式化这种直觉，称为因果效应的基于设计的推理。接下来，我们将展示如何，总是在基于设计的推理的背景下，即使是允许存在无偏估计量的参数结构假设，即使在大样本限制下也不能保证方差减少。在预期存在某种形式干扰的随机实验中，经常凭经验观察到这种大样本中浓度的缺乏。这一结果对大型实验的设计和分析具有直接影响——例如，在在线社交平台中——人们认为大样本量会自动保证小方差。更广泛地说，我们的结果表明，尽管在存在干扰的情况下进行因果推理的策略借用了传统因果推理文献中的形式主义和主要概念，但无干扰情况下的大部分直觉并不容易转移到干扰设置中。