论文标题
样本约束治疗效果估计
Sample Constrained Treatment Effect Estimation
论文作者
论文摘要
治疗效应估计是因果推断中的一个基本问题。我们专注于设计有效的随机对照试验，以准确估计某些治疗对$ n $个人人群的影响。特别是，我们研究了样本受限的治疗效果估计，在该估计中，我们必须选择$ s \ ll n $个体的子集进行实验。该子集必须进一步分为治疗组和对照组。已精心研究了用于将整个人群分配为治疗组或选择单个代表性子集的算法。我们环境中的主要挑战是共同选择代表性子集和该集合的分区。 在线性效应模型下，我们专注于个人和平均治疗效应估计。我们通过确定与随机数值线性代数中使用的差异最小化和基于杠杆评分的采样的连接，从而提供了有效的实验设计和相应的估计器。当$ s $等于人口规模时，我们的理论结果可以平稳过渡到已知的保证。我们还经验证明了算法的性能。
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.
