Bias-Aware External-Model-Assisted Inference in High-Dimensional Regression

2026-06-14

AI Summary

This work addresses the degradation of existing prediction-augmented inference methods in high-dimensional semi-supervised linear regression, where reliance on an external predictor close to the true model leads to inflated variance and overly wide confidence intervals. To overcome this limitation, the authors propose Debiased External-model-Assisted Lasso (DEAL), which explicitly models the bias of the external estimator and adaptively integrates unlabeled covariates with the external predictor through a bias-aware cross-fitting shrinkage mechanism. DEAL ensures valid inference and robust coverage for the projected parameter even under model misspecification, nonlinear label generation, or covariate shift. Empirical results demonstrate that, under identical unlabeled data budgets, DEAL yields substantially shorter confidence intervals—reducing their length to 0.49–0.87 times that of competing methods in simulations and achieving median ratios of 0.23–0.53 across six real-world applications, including those leveraging large language model priors.

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.

Problem

• high-dimensional regression
• semi-supervised inference
• external model
• prediction-powered inference
• covariate shift

Innovation

• debiased inference
• semi-supervised regression
• external model assistance
• adaptive shrinkage
• high-dimensional statistics