Design and analysis of bipartite experiments under a linear exposure-response model

A bipartite experiment consists of one set of units being assigned treatments and another set of units for whichwe measure outcomes. The two sets of units are connected by a bipartite graph, governing how the treatedunits can affect the outcome units. In this paper, we consider estimation of the average total treatment effectin the bipartite experimental framework under a linear exposure-response model. We introduce the ExposureReweighted Linear (ERL) estimator, and show that the estimator is unbiased, consistent and asymptoticallynormal, provided that the bipartite graph is sufficiently sparse. To facilitate inference, we introduce an unbiasedand consistent estimator of the variance of theERLpoint estimator. In addition, we introduce a cluster-baseddesign,Exposure-Design, that uses heuristics to increase the precision of theERLestimator by realizinga desirable exposure distribution. Finally, we demonstrate the application of the described methodology tomarketplace experiments using a publicly available Amazon user-item review dataset.

• Algorithms and Theory