Design and Analysis of Bipartite Experiments Under a Linear Exposure-response Model

Cluster Randomized Designs for One-Sided Bipartite Experiments

“…The exposure mapping approach [20,25], formalized by Aronow and Samii [4], defines a notion of when a unit is "completely treated" or "completely controlled," then uses the inverse propensity score (IPS, also known as Horvitz-Thompson) estimator to construct an unbiased estimate of the average treatment effect. By contrast, an alternate approach is to propose a model for the effect of interference on the potential outcomes, and then rely on this model to estimate the average treatment effect using data from all units (even the ones experiencing a great deal of interference) [17,15,29,19]. Since the quality of the estimate depends on the accuracy of the modeling assumptions, several methods have been developed to estimate the magnitude and form of interference [2,33,3,6,35,34].…”

“…Our work assumes this same regime, in which the graphs are sufficiently dense that an IPS estimator will be too high-variance to be practical, so we accept an estimator with some bias. We assume a linear model of the potential outcome on the measured exposure, as done in [17,19]. To avoid strong dependence on the linear assumption, we use the difference-in-means estimator which does not rely on the model of interference, and we choose our experimental design to be minimax optimal over the class of linear potential outcomes models.…”

“…In the specific case of bipartite graphs, other works propose modifications to unit-level randomization by choosing which side of the graph to randomize [22,24,8]. The authors of [29,19] look directly at clustered designs on bipartite graphs, but they study a two-sided experimental framework in which one side of the graph is randomized while the other is measured. Perhaps closest to our work is that of Rolnick et al [30], which suggests a balanced partitioning of geographical regions using a clustering objective that is similar to ours.…”

“…which is commonly used in the interference literature [17,19], although other models are discussed in Section 4. Following the tradition of the finite population model, first defined by Neyman [27], we treat the coefficients α i , β i and γ i as fixed but unknown so that the only randomness in the observation model is due to the choice of treatment assignment Z.…”

“…Cluster-randomized designs have also been considered in the setting of two-sided bipartite experiments, in which treatment is assigned to the experimental units but outcomes are measured on the interference units. When the potential outcome of an interference unit is a linear function of the dose d s , Pouget-Abadie et al [29] and Harshaw et al [19] recommend assigning treatments Z in a way that maximizes the empirical variance of the realized doses. In the one-sided bipartite setting it is important to enforce balancedness of the clusters to control the variance of τ DIM , so an extension of their objective to this setting would be to maximize Tr(Var(d)) over a balanced cluster-randomized assignment.…”