Robust Estimation under Spurious Correlation via Statistical Counterfactual Augmentation
Abstract
Spurious correlations between nuisance features and outcomes present a fundamental challenge for statistical learning and inference. Counterfactual Data Augmentation (CDA), the practice of resampling nuisance features while preserving features of interest, has emerged as a popular strategy to mitigate such correlations, yet its statistical properties, and its reliance on an untestable validity assumption, remain largely unexplored. We provide a statistical treatment of CDA, termed Statistical CDA (SCDA), with two components. First, casting SCDA as a simulated-moment M-estimator, we establish consistency, asymptotic normality with a sandwich covariance and a finite-augmentation-draw variance correction, oracle efficiency for the target parameter, and the equivalence of iterative and one-shot procedures via stochastic approximation, yielding valid large-sample inference where previously none was available. Second, because the augmentation's validity cannot be tested from the observed data when features are entangled (a fact we prove), we develop a sensitivity analysis that bounds the residual nuisance--outcome dependence by a parameter Γ, giving sharp identified intervals for the target with valid confidence intervals and a breakdown frontier; the point-identified theory is the Γ=0 special case. Simulations confirm the efficiency gains under validity and the robustness bounds under possible invalidity, placing a widely used augmentation method on a transparent inferential footing.
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BibTeX
@misc{zhou2026robust,
title = {{Robust Estimation under Spurious Correlation via Statistical Counterfactual Augmentation}},
author = {Yi-Hui Zhou and George Sun},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22649},
eprint = {2610.22649},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22649},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Robust Estimation under Spurious Correlation via Statistical Counterfactual Augmentation
AU - Yi-Hui Zhou
AU - George Sun
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22649
UR - https://arxiv.org/abs/2610.22649
AB - Spurious correlations between nuisance features and outcomes present a fundamental challenge for statistical learning and inference. Counterfactual Data Augmentation (CDA), the practice of resampling nuisance features while preserving features of interest, has emerged as a popular strategy to mitigate such correlations, yet its statistical properties, and its reliance on an untestable validity assumption, remain largely unexplored. We provide a statistical treatment of CDA, termed Statistical CDA (SCDA), with two components. First, casting SCDA as a simulated-moment M-estimator, we establish consistency, asymptotic normality with a sandwich covariance and a finite-augmentation-draw variance correction, oracle efficiency for the target parameter, and the equivalence of iterative and one-shot procedures via stochastic approximation, yielding valid large-sample inference where previously none was available. Second, because the augmentation's validity cannot be tested from the observed data when features are entangled (a fact we prove), we develop a sensitivity analysis that bounds the residual nuisance--outcome dependence by a parameter Γ, giving sharp identified intervals for the target with valid confidence intervals and a breakdown frontier; the point-identified theory is the Γ=0 special case. Simulations confirm the efficiency gains under validity and the robustness bounds under possible invalidity, placing a widely used augmentation method on a transparent inferential footing.
ER -