  Learning heterogeneous treatment effects (HTEs) is an important problem
across many fields. Most existing methods consider the setting with a single
treatment arm and a single outcome metric. However, in many real world domains,
experiments are run consistently - for example, in internet companies, A/B
tests are run every day to measure the impacts of potential changes across many
different metrics of interest. We show that even if an analyst cares only about
the HTEs in one experiment for one metric, precision can be improved greatly by
analyzing all of the data together to take advantage of cross-experiment and
cross-outcome metric correlations. We formalize this idea in a tensor
factorization framework and propose a simple and scalable model which we refer
to as the low rank or LR-learner. Experiments in both synthetic and real data
suggest that the LR-learner can be much more precise than independent HTE
estimation.
