Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, October 13, 2020, 12:15 pm

Duration: 30 minutes

Location: Zoom: conference room

Speaker: Christopher Harshaw (Yale University)

Balancing covariates in randomized experiments using the Gram–Schmidt walk

In randomized experiments, such as a medical trials, we randomly assign the treatment, such as a drug or a placebo, that each experimental subject receives. Randomization can help us accurately estimate the difference in treatment effects with high probability. We also know that we want the two groups to be similar: ideally the two groups would be similar in every statistic we can measure beforehand. Recent advances in algorithmic discrepancy theory allow us to divide subjects into groups with similar statistics. By exploiting the recent Gram-Schmidt Walk algorithm of Bansal, Dadush, Garg, and Lovett, we can obtain random assignments of low discrepancy. These allow us to obtain more accurate estimates of treatment effects when the information we measure about the subjects is predictive, while also bounding the worst-case behavior when it is not.

We will explain the experimental design problem we address, how we use and analyze the Gram-Schmidt walk algorithm, and remaining open problems. This is joint work with Fredrik Sävje, Daniel Spielman, and Peng Zhang.

Paper: https://arxiv.org/abs/1911.03071
Code: https://github.com/crharshaw/GSWDesign.jl

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