Sample Constrained Treatment Effect Estimation
This addresses the challenge of efficient randomized controlled trials in causal inference when only a limited sample can be experimented on, representing an incremental advancement by combining existing methods for subset selection and partitioning.
The paper tackles the problem of sample-constrained treatment effect estimation by jointly selecting a subset of individuals and partitioning them into treatment and control groups, achieving provably efficient designs and estimators with theoretical guarantees that transition smoothly to known results when the subset size equals the population.
Treatment 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.