Prediction-Powered Adaptive Shrinkage Estimation

• DOI: 10.48550/arxiv.2502.14166
• Publication Date: 2025-02-19
• Authors: Sida Li; Nikolaos Ignatiadis
• Keywords: Shrinkage

Prediction-Powered Inference (PPI) is a powerful framework for enhancing statistical estimates by combining limited gold-standard data with machine learning (ML) predictions. While prior work has demonstrated PPI's benefits individual tasks, modern applications require answering numerous parallel questions. We introduce Adaptive Shrinkage (PAS), method that bridges PPI empirical Bayes shrinkage to improve the estimation of multiple means. PAS debiases noisy ML predictions within each task and then borrows strength across tasks using those same as reference point shrinkage. The amount determined minimizing an unbiased estimate risk, we prove this tuning strategy asymptotically optimal. Experiments on both synthetic real-world datasets show adapts reliability outperforms traditional baselines in large-scale applications.