Prediction-Powered Adaptive Shrinkage Estimation

2025-02-20

AI Summary

In large-scale parallel mean estimation, machine learning (ML) predictions suffer from high noise, and existing methods underutilize cross-task information. Method: We propose Prediction-Powered Empirical Bayes (PPEB), the first framework to tightly integrate prediction-powered inference (PPI) with empirical Bayes shrinkage. PPEB leverages ML predictions as shared reference points to enable principled cross-task information borrowing and introduces an asymptotically optimal shrinkage-parameter tuning strategy based on unbiased risk estimation, jointly achieving task-level debiasing and adaptive shrinkage. Contribution/Results: Theoretically, PPEB achieves asymptotic optimality under mild conditions. Empirically, it significantly outperforms classical and state-of-the-art baselines on both synthetic and real-world datasets. Crucially, PPEB automatically adapts to the reliability of underlying ML predictors, yielding improved estimation accuracy and stability in large-scale settings.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: ML for personalized search and recommendations
• Web Mining and Content Analysis: Large pretrained models with web data

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 tasks, 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.

Problem

• Enhances statistical estimates with ML predictions
• Improves estimation of multiple means
• Adapts to reliability of ML predictions

Innovation

• Combines ML predictions with gold-standard data
• Uses empirical Bayes shrinkage for multiple means
• Minimizes unbiased risk for optimal shrinkage