Balancing Covariates In Randomized Experiments: The Gram--Schmidt Walk Design

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" summary

Claims a fundamental balance–robustness trade-off in randomized experiments and gives a constructive design, the Gram–Schmidt walk, that interpolates between independent randomization and perfect covariate balance via a parameter ε. Produces finite-sample operator‑norm bounds on assignment covariance and on covariate sign discrepancy, yields a ridge‑style “regression by design” MSE bound, and shows in simulations it outperforms re‑randomization and matching. Provides an algorithm (roughly O(N^2 D) time), non‑asymptotic concentration results, and Julia/R implementations.

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" chapters (16)

1. 0:00Intro
2. 1:00Balancing Covariates in Randomized Experiments How should we randomize treatment assignments in experiments?
3. 2:53Covariate Balancing - A Historical Debate
4. 4:24Covariate Balancing - Existing Designs
5. 5:11Covariate Balancing - My Opinion
6. 11:44Covariate Balance
7. 13:28The Balance-Robustness Tradeoff
8. 13:57Distributional Discrepancy Problem
9. 15:09Relevant Values of oz and a
10. 18:21Main Result (GSW-Design)
11. 19:22Comparison to Other Designs Matched Pair Design: In general, any matching will incur the following balance term
12. 23:19Implications for Mean Squared Error Theorem: Suppose that distribution (design) satisfies problem 1. Then, Ridge regression
13. 24:05Gram-Schmidt Walk Design (GSW-Design)
14. 26:47The Gram-Schmidt Walk (algorithm) Gram-Schmidt Walk Algorithm
15. 28:28GSW-Design: Main Results (1 of 2)
16. 30:48Conclusion + Open Problems

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