Abstract: The design and analysis of randomized experiments are fundamental to numerous fields, ranging from the physical and social sciences to industrial applications. Despite the long history of randomized controlled trials in science, estimating the treatment effect on a finite population remains poorly understood when auxiliary variables are used to reduce error, and the behavior of many estimators has only been analyzed asymptotically. Recently, Harshaw, Sävje, Spielman, and Zhang demonstrated that non-asymptotic variance bounds can be established for the average treatment effect estimation problem over a finite population by designing experiments using discrepancy minimization techniques.
In this talk, we show that a simple Bernoulli design can achieve comparable bounds through regression adjustment techniques based on spectral sparsification. Furthermore, we discuss the advantages of using a simple design, potential extensions of our approach, and supporting empirical results.