  Bipartite Experiments are randomized experiments where the treatment is
applied to a set of units (randomization units) that is different from the
units of analysis, and randomization units and analysis units are connected
through a bipartite graph. The scale of experimentation at large online
platforms necessitates both accurate inference in the presence of a large
bipartite interference graph, as well as a highly scalable implementation. In
this paper, we describe new methods for inference that enable practical,
scalable analysis of bipartite experiments: (1) We propose CA-ERL, a
covariate-adjusted variant of the exposure-reweighted-linear (ERL) estimator
[9], which empirically yields 60-90% variance reduction. (2) We introduce a
randomization-based method for inference and prove asymptotic validity of a
Wald-type confidence interval under graph sparsity assumptions. (3) We present
a linear-time algorithm for randomization inference of the CA-ERL estimator,
which can be easily implemented in query engines like Presto or Spark. We
evaluate our methods both on a real experiment at Meta that randomized
treatment on Facebook Groups and analyzed user-level metrics, as well as
simulations on synthetic data. The real-world data shows that our CA-ERL
estimator reduces the confidence interval (CI) width by 60-90% (compared to
ERL) in a practical setting. The simulations using synthetic data show that our
randomization inference procedure achieves correct coverage across instances,
while the ERL estimator has incorrectly small CI widths for instances with
large true effect sizes and is overly conservative when the bipartite graph is
dense.
