# On Model Identification and Out-of-Sample Prediction of Principal Component Regression: Applications to Synthetic Controls

arXiv: https://arxiv.org/abs/2010.14449 · HTML: https://mlsanity.com/paper/2010.14449/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Oct 2020.

## Built on by (most cited first, 2 of 2)

- [A Causal Inference Framework for Data Rich Environments](https://mlsanity.com/paper/2504.01702/) (2025)
- [Incentive-Aware Synthetic Control: Accurate Counterfactual Estimation via Incentivized Exploration](https://mlsanity.com/paper/2312.16307/) (2023)

## Abstract (arXiv)

We analyze principal component regression (PCR) in a high-dimensional error-in-variables setting with fixed design. Under suitable conditions, we show that PCR consistently identifies the unique model with minimum ℓ2-norm. These results enable us to establish non-asymptotic out-of-sample prediction guarantees that improve upon the best known rates. In the course of our analysis, we introduce a natural linear algebraic condition between the in- and out-of-sample covariates, which allows us to avoid distributional assumptions for out-of-sample predictions. Our simulations illustrate the importance of this condition for generalization, even under covariate shifts. Accordingly, we construct a hypothesis test to check when this conditions holds in practice. As a byproduct, our results also lead to novel results for the synthetic controls literature, a leading approach for policy evaluation. To the best of our knowledge, our prediction guarantees for the fixed design setting have been elusive in both the high-dimensional error-in-variables and synthetic controls literatures.