Adaptive Principal Component Regression with Applications to Panel Data

Anish Agarwal, Keegan Harris, Justin Whitehouse, Steven Wu

Keywords: adaptive data collection, principal component regression, error-in-variables regression, panel data, synthetic controls, synthetic interventions, causal inference

TL;DR: We derive adaptive bounds for online (regularized) principal component regression, and apply them to the problem of unit-specific counterfactual estimation under different interventions in panel data settings.

Abstract: 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 online (regularized) PCR whenever data is collected adaptively. Since the proof techniques for 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. As an application of our bounds, we provide a framework for counterfactual estimation of unit-specific treatment effects in panel data settings when interventions are assigned adaptively. Our framework may be thought of as a generalization of the synthetic interventions framework where data is collected via an adaptive intervention assignment policy.

Submission Number: 5031