In a bipartite experiment, units that are assigned treatments differ from the units for which we measure outcomes. The two groups of units are connected by a bipartite graph, governing how the treated units can affect the outcome units. Often motivated by experiments in marketplaces, the bipartite experimental framework has been used for example to investigate the causal effects of supply-side changes on demand-side behavior. In this paper, we consider the problem of estimating the average total treatment effect in the bipartite experimental framework under a linear exposure-response model. We introduce the Exposure Reweighted Linear (ERL) Estimator, an unbiased linear estimator of the average treatment effect in this setting. We show that the estimator is consistent and asymptotically normal, provided that the bipartite graph is sufficiently sparse. We derive a variance estimator which facilitates confidence intervals based on a normal approximation. In addition, we introduce Exposure-Design, a cluster-based design which aims to increase the precision of the ERL estimator by realizing desirable exposure distributions. Finally, we demonstrate the effectiveness of the described estimator and design with an application using a publicly available Amazon user-item review graph.

翻译：在双面实验中,指定处理的单位不同于我们测量结果的单位。两组单位通过双面图连接,说明处理的单位如何影响结果单位。通常在市场实验的推动下,使用双面试验框架来调查供方变化对需求方行为的因果关系。在本文中,我们考虑在线性暴露反应模型下估计双方实验框架中的平均总处理效应的问题。我们引入了曝光重量线性线性模拟器(ERL),这是在这个环境中对平均处理效果的不偏向线性线性估计器。我们显示,估计器是一致的,不时正常的,条件是双面图足够稀少。我们得出一个差异估计器,它有助于在正常近似的基础上建立信任间隔。此外,我们引入了以曝光量为基础的集群设计,目的是通过实现理想的暴露分布来提高ERL估计器的精确度。最后,我们展示了所描述的估算器的有效性,我们使用了可公开使用的图表,用一个可使用的地图来展示其有效性。