Prediction-Powered Adaptive Shrinkage Estimation

TL;DR

The paper introduces Prediction-Powered Adaptive Shrinkage (PAS), a novel method that combines machine learning predictions with empirical Bayes shrinkage to improve multiple mean estimations in large-scale settings.

Contribution

PAS uniquely debiases ML predictions and adaptively shrinks estimates across tasks, with an asymptotically optimal tuning strategy, advancing PPI for large-scale statistical inference.

Findings

PAS outperforms traditional methods in synthetic datasets.

PAS demonstrates superior performance on real-world data.

The method adapts to the reliability of ML predictions.

Abstract

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