Anish Agarwal, Keegan Harris, Justin Whitehouse, Zhiwei Steven Wu
arXiv 3 Jul 2023 · Machine Learning · 1 citations (OpenAlex)
arXiv:2307.01357 · PDF · DOI · OpenAlex · Extracted main text
Principal component regression (PCR) is a popular technique for fixed-design error-in-variables regression, a generalization of the linear regression setting in which the observed covariates are corrupted with random noise. We provide the first time-uniform finite sample guarantees for (regularized) PCR whenever data is collected adaptively. Since the proof techniques for analyzing PCR in the fixed design setting do not readily extend to the online setting, our results rely on adapting tools from modern martingale concentration to the error-in-variables setting. We demonstrate the usefulness of our bounds by applying them to the domain of panel data, a ubiquitous setting in econometrics and statistics. As our first application, we provide a framework for experiment design in panel data settings when interventions are assigned adaptively. Our framework may be thought of as a generalization of the synthetic control and synthetic interventions frameworks, where data is collected via an adaptive intervention assignment policy. Our second application is a procedure for learning such an intervention assignment policy in a setting where units arrive sequentially to be treated. In addition to providing theoretical performance guarantees (as measured by regret), we show that our method empirically outperforms a baseline which does not leverage error-in-variables regression.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Anish Agarwal, Devavrat Shah, and Dennis Shen (2006) Synthetic interventions self | 1.000 | 13 | 3 | 100% |
| 2 | Alberto Abadie and Javier Gardeazabal (2003) The economic costs of conflict: A case study of the basque country | 1.000 | 5 | 3 | 100% |
| 3 | Alberto Abadie, Alexis Diamond, and Jens Hainmueller (2010) Synthetic control methods for comparative case studies: Estimating the effect of california’s tobacco control program | 1.000 | 5 | 3 | 100% |
| 4 | Anish Agarwal, Devavrat Shah, and Dennis Shen (2010) On principal component regression in a high-dimensional error-in-variables setting self | 0.982 | 19 | 5 | 95% |
| 5 | Yasin Abbasi-Yadkori, Dávid Pál, and Csaba Szepesvári (2011) Improved algorithms for linear stochastic bandits | 0.909 | 8 | 5 | 75% |
| 6 | Victor H de la Peña, Michael J Klass, and Tze Leung Lai (2004) Self-normalized processes: exponential inequalities, moment bounds and iterated logarithm laws | 0.894 | 7 | 3 | 71% |
| 7 | Victor H de la Peña, Michael J Klass, and Tze Leung Lai (2007) Pseudo-maximization and self-normalized processes | 0.894 | 7 | 3 | 71% |
| 8 | Vivek Farias, Ciamac Moallemi, Tianyi Peng, and Andrew Zheng (2022) Synthetically controlled bandits | 0.737 | 3 | 2 | 100% |
| 9 | Steven R Howard, Aaditya Ramdas, Jon McAuliffe, and Jasjeet Sekhon (2020) Time-uniform chernoff bounds via nonnegative supermartingales | 0.721 | 8 | 3 | 38% |
| 10 | Steven R Howard, Aaditya Ramdas, Jon McAuliffe, and Jasjeet Sekhon (2021) Time-uniform, nonparametric, nonasymptotic confidence sequences | 0.693 | 9 | 3 | 33% |
Showing the top 10 of 94 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Incentive-Aware Synthetic Control: Accurate Counterfactual Estimation via Incentivized Exploration | 0.935 | 11 | 7 |
| 2 | Strategyproof Decision-Making in Panel Data Settings and Beyond | 0.811 | 4 | 2 |
| 3 | A Causal Inference Framework for Data Rich Environments | 0.405 | 1 | 1 |