Sample Constrained Treatment Effect EstimationTreatment effect estimation is a fundamental problem in causal inference. We
focus on designing efficient randomized controlled trials, to accurately
estimate the effect of some treatment on a population of $n$ individuals. In
particular, we study sample-constrained treatment effect estimation, where we
must select a subset of $s \ll n$ individuals from the population to experiment
on. This subset must be further partitioned into treatment and control groups.
Algorithms for partitioning the entire population into treatment and control
groups, or for choosing a single representative subset, have been well-studied.
The key challenge in our setting is jointly choosing a representative subset
and a partition for that set.
We focus on both individual and average treatment effect estimation, under a
linear effects model. We give provably efficient experimental designs and
corresponding estimators, by identifying connections to discrepancy
minimization and leverage-score-based sampling used in randomized numerical
linear algebra. Our theoretical results obtain a smooth transition to known
guarantees when $s$ equals the population size. We also empirically demonstrate
the performance of our algorithms.
arxiv.org