Multi-Source Prediction-Powered Inference

2026-06-19

AI Summary

This study addresses the challenge of improving statistical inference efficiency and accuracy through the fusion of multi-source pseudo-label data. It proposes the first inference framework capable of accommodating both homogeneous and heterogeneous data distributions, including covariate shift and domain shift. The method estimates optimal weighting coefficients by minimizing the asymptotic confidence region volume, enabling effective inference driven by multiple prediction sources. Theoretical analysis establishes its asymptotic optimality. Leveraging asymptotic normality and explicit modeling of distributional shifts, the approach significantly reduces confidence region volume while preserving valid inference, as demonstrated on both simulated and real-world bone mineral density datasets. It consistently outperforms baseline methods that rely solely on target data or a single pseudo-label source.

Abstract

Prediction-powered inference integrates a small gold-standard dataset with large pseudo-labeled data, whose labels are generated by machine learning methods, to enhance statistical inference. In modern applications, multiple data sources and diverse machine learning methods often give rise to multiple pseudo-labeled datasets, each encoding potentially different aspects of the underlying information. However, how to optimally combine multiple data sources and machine learning methods for statistical inference remains unclear. To address this problem, we propose a multi-source prediction-powered inference method by aggregating multiple pseudo-labeled datasets together, where the aggregation weights are estimated by minimizing the asymptotic volume of the resulting confidence region. We study both homogeneous settings, where the source and target distributions coincide, and heterogeneous settings, where distributional discrepancies arise between source and target distributions, including covariate shift and domain shift. Theoretically, we establish the asymptotic normality of the proposed estimator and show that the resulting confidence-region volume is asymptotically equivalent to the oracle optimal volume within the proposed weighting class. We further characterize when our method yields smaller confidence regions compared with both classical target-only inference and single-source prediction-powered inference. Simulation studies and a real-data application on dual-energy X-ray absorptiometry measured high body fat prevalence show that MPPI can reduce confidence-region volume while maintaining inferential validity in the settings considered.

Problem

• prediction-powered inference
• multi-source data
• pseudo-labeled data
• statistical inference
• confidence region

Innovation

• prediction-powered inference
• multi-source aggregation
• confidence region optimization
• asymptotic normality
• domain shift