Adaptive Principal Component Regression with Applications to Panel Data

TL;DR

This paper introduces adaptive principal component regression with finite sample guarantees for online data collection, applying it to panel data for experiment design and adaptive intervention policies, with theoretical and empirical validation.

Contribution

It provides the first uniform finite sample guarantees for regularized PCR in adaptive data collection, extending analysis tools to the online error-in-variables setting.

Findings

Theoretical performance guarantees for adaptive PCR in panel data.

Framework for adaptive experiment design in econometrics.

Empirical results show improved performance over baseline methods.

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 (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.