Sample Constrained Treatment Effect Estimation

Raghavendra Addanki, David Arbour, Tung Mai, Cameron N Musco, Anup Rao

Keywords: average treatment effect estimation, individual treatment effect estimation, experimental design, randomized numerical linear algebra, discrepancy minimization, causal inference

TL;DR: We study sample (or budget) constrained treatment effect estimation and provide efficient experimental designs and estimators.

Abstract:

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 \textit{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.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2210.06594/code)