# Adaptive Principal Component Regression with Applications to Panel Data

arXiv: https://arxiv.org/abs/2307.01357 · HTML: https://mlsanity.com/paper/2307.01357/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 89 references that are in the map.
- First posted on arXiv 3 Jul 2023.

## Builds on (most cited first, 25 of 25)

- [Introduction to Multi-Armed Bandits](https://mlsanity.com/paper/1904.07272/) (2019)
- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Time-uniform, nonparametric, nonasymptotic confidence sequences](https://mlsanity.com/paper/1810.08240/) (2018)
- [Confidence Intervals for Policy Evaluation in Adaptive Experiments](https://mlsanity.com/paper/1911.02768/) (2019)
- [Causal Matrix Completion](https://mlsanity.com/paper/2109.15154/) (2021)
- [Synthetic Difference in Differences](https://mlsanity.com/paper/1812.09970/) (2018)
- [Statistical Inference with M-Estimators on Adaptively Collected Data](https://mlsanity.com/paper/2104.14074/) (2021)
- [Accurate Inference for Adaptive Linear Models](https://mlsanity.com/paper/1712.06695/) (2017)
- [Why Adaptively Collected Data Have Negative Bias and How to Correct for It](https://mlsanity.com/paper/1708.01977/) (2017)
- [Strategic Instrumental Variable Regression: Recovering Causal Relationships From Strategic Responses](https://mlsanity.com/paper/2107.05762/) (2021)
- [On Robustness of Principal Component Regression](https://mlsanity.com/paper/1902.10920/) (2019)
- [Synthetic Interventions](https://mlsanity.com/paper/2006.07691/) (2020)
- [Robust Synthetic Control](https://mlsanity.com/paper/1711.06940/) (2017)
- [The Augmented Synthetic Control Method](https://mlsanity.com/paper/1811.04170/) (2018)
- [A unified recipe for deriving (time-uniform) PAC-Bayes bounds](https://mlsanity.com/paper/2302.03421/) (2023)
- [Fully Adaptive Composition in Differential Privacy](https://mlsanity.com/paper/2203.05481/) (2022)
- [Martingale Methods for Sequential Estimation of Convex Functionals and Divergences](https://mlsanity.com/paper/2103.09267/) (2021)
- [Causal Inference with Corrupted Data: Measurement Error, Missing Values, Discretization, and Differential Privacy](https://mlsanity.com/paper/2107.02780/) (2021)
- [Causal Imputation via Synthetic Interventions](https://mlsanity.com/paper/2011.03127/) (2020)
- [Synthetic Combinations: A Causal Inference Framework for Combinatorial Interventions](https://mlsanity.com/paper/2303.14226/) (2023)
- [Synthetically Controlled Bandits](https://mlsanity.com/paper/2202.07079/) (2022)
- [Synthetic Control As Online Linear Regression](https://mlsanity.com/paper/2202.08426/) (2022)
- [Strategyproof Decision-Making in Panel Data Settings and Beyond](https://mlsanity.com/paper/2211.14236/) (2022)
- [Brownian Noise Reduction: Maximizing Privacy Subject to Accuracy Constraints](https://mlsanity.com/paper/2206.07234/) (2022)

## Built on by (most cited first, 5 of 5)

- [A Causal Inference Framework for Data Rich Environments](https://mlsanity.com/paper/2504.01702/) (2025)
- [De-floored Principal Component Regression: When Rank Selection Alone Is Insufficient for Prediction](https://mlsanity.com/paper/2607.16638/) (2026)
- [Incentive-Aware Synthetic Control: Accurate Counterfactual Estimation via Incentivized Exploration](https://mlsanity.com/paper/2312.16307/) (2023)
- [Calibrated Principal Component Regression](https://mlsanity.com/paper/2510.19020/) (2025)
- [Beyond Second-Order Information: Paid Logistic Regression with Noisy Features](https://mlsanity.com/paper/2610.12919/) (2026)

## Abstract (arXiv)

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.