Bias-Aware External-Model-Assisted Inference in High-Dimensional Regression
Abstract
In high-dimensional semi-supervised linear regression, prediction-powered inference (PPI) corrects an external predictor with a rectifier estimated from the labeled data. In a linear model, however, this rectifier cancels the predictor: PPI and PPI++ reduce to ordinary least squares and can inflate variance when the predictor is close to the oracle. We propose the Debiased External-model-Assisted Lasso (DEAL), which routes the external estimator and the unlabeled covariates into the variance of a debiased estimator, with a bias-aware, cross-fitted shrinkage step that adapts across target-only, near-oracle, and biased-but-informative regimes. We prove coordinate-wise asymptotic normality with an adaptive variance, extend validity to the projection parameter under misspecification and nonlinear labelers, and show that, at a common unlabeled budget, DEAL intervals are shorter than those of debiased Lasso, PPI, and PPI++; a shift-aware variant preserves coverage under covariate shift. In simulations, DEAL intervals are 0.49-0.87 of the debiased-Lasso length, and across six real-data applications spanning astronomy, chemistry, proteomics, and oncology, the last using a large-language-model oracle, they tighten in every case, with median length ratios of 0.23-0.53.
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BibTeX
@misc{zhang2026biasaware,
title = {{Bias-Aware External-Model-Assisted Inference in High-Dimensional Regression}},
author = {Hongzhe Zhang and Hanxuan Ye and Hongzhe Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.15602},
eprint = {2606.15602},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.15602},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bias-Aware External-Model-Assisted Inference in High-Dimensional Regression
AU - Hongzhe Zhang
AU - Hanxuan Ye
AU - Hongzhe Li
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2606.15602
UR - https://arxiv.org/abs/2606.15602
AB - In high-dimensional semi-supervised linear regression, prediction-powered inference (PPI) corrects an external predictor with a rectifier estimated from the labeled data. In a linear model, however, this rectifier cancels the predictor: PPI and PPI++ reduce to ordinary least squares and can inflate variance when the predictor is close to the oracle. We propose the Debiased External-model-Assisted Lasso (DEAL), which routes the external estimator and the unlabeled covariates into the variance of a debiased estimator, with a bias-aware, cross-fitted shrinkage step that adapts across target-only, near-oracle, and biased-but-informative regimes. We prove coordinate-wise asymptotic normality with an adaptive variance, extend validity to the projection parameter under misspecification and nonlinear labelers, and show that, at a common unlabeled budget, DEAL intervals are shorter than those of debiased Lasso, PPI, and PPI++; a shift-aware variant preserves coverage under covariate shift. In simulations, DEAL intervals are 0.49-0.87 of the debiased-Lasso length, and across six real-data applications spanning astronomy, chemistry, proteomics, and oncology, the last using a large-language-model oracle, they tighten in every case, with median length ratios of 0.23-0.53.
ER -