Design and Analysis of Bipartite Experiments under a Linear Exposure-Response Model

Abstract

The bipartite experimental framework is a recently proposed causal setting, where a bipartite graph links two distinct types of units: units that receive treatment and units whose outcomes are of interest to the experimenter. Often motivated by market experiments, the bipartite experimental framework has been used for example to investigate the causal effects of supply-side changes on demand-side behavior. Similar to settings with interference and other violations of the stable unit treatment value assumption (SUTVA), additional assumptions on potential outcomes must be made for valid inference. In this paper, we consider the problem of estimating the average treatment effect in the bipartite experimental framework under a linear exposure-response model. We propose the Exposure Reweighted Linear (ERL) Estimator, an unbiased linear estimator of the average treatment effect in this setting. Furthermore, we present 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 proposed estimator and design on a publicly available Amazon user-item review graph.

Causal Estimation of User Learning in Personalized Systems

“…One strand of the literature addresses issues caused by interference, when individuals interact with one another through an equilibrium, a network, or a market platform Fradkin et al (2021); Eckles et al (2017). There is a large literature on cluster-randomized designs, see Hudgens and Halloran (2008) for a general cluster design, Harshaw et al (2021) for design in two-sided markets, and Leung (2022) for designs under a spatial model. Bajari et al (2021) and Johari et al (2022) introduce designs that randomize at an item-user level for two-sided markets, Munro et al (2021) analyzes an individual-level augmented randomized experiment that jointly randomizes prices and treatments, and Viviano (2020) studies two-wave experiments under network interference to estimate spillover effects.…”

A Design-based Riesz Representation Framework for Randomized Experiments

“…The conventional estimand in this setting is the so-called Global Average Treatment Effect, or the "all-or-nothing" effect, which is the difference in outcomes when all units are assigned to the extreme ends of the treatment variable interval: n −1 n i=1 [y i (1) − y i (0)]. This estimand has been investigated by Eckles, Karrer, and Ugander (2017), Chin (2019), Harshaw, Sävje, Eisenstat, Mirrokni, and Pouget-Abadie (2021) and Leung (2022b), among others. While the all-or-nothing effect is useful in some settings, and an estimand that our framework can accommodate, it is a crude summary of the ways the treatments affect the outcomes.…”

“…However, while second-order positivity violations are common, there situations where all variance functionals satisfy positivity, in which case unbiased variance estimation is possible. One such setting is studied by Harshaw, Sävje, Eisenstat, Mirrokni, and Pouget-Abadie (2021).…”

Causal Inference in the Presence of Interference in Sponsored Search Advertising

“…Moreover, a proper understanding of the interference issue in relation to causal inference directly impacts engineering of more purposeful interventions and design of more effective A/B testing for ad placement. Alternatively, randomized experiments via bipartite graphs offer a useful formalism to study two-sided market experiments under violation of iid assumption (Pouget-Abadie et al, 2018 , 2019 ; Bajari et al, 2021 ; Harshaw et al, 2021 ; Johari et al, 2022 ). This stands in contrast with interference that occurs on networks where all units are of the same type (e.g., ads in a block)—in bipartite experiments, there is a distinction between units that can be subject to an intervention and units whose responses are of interest to the experimenter.…”