Cluster-Robust Prediction-Powered Inference

2026-10-07

AI Summary

This study addresses the severe undercoverage of confidence intervals in prediction-powered inference (PPI) applied to clustered data, where within-group correlations are typically ignored. To overcome this limitation, we propose Cluster-Robust PPI++, a method tailored for partially labeled clustered settings. Leveraging asymptotic theory, it derives cluster-aware power-tuning rules and closed-form variance estimators, enabling efficient calibration without resampling. The core contribution lies in analytically resolving the challenge of clustered dependence while providing valid confidence intervals. In an empirical application involving television news data, the proposed approach improves coverage from below 60% to the nominal 95% level, demonstrating its reliability and practical effectiveness.

Abstract

Data collection is often costly or logistically demanding, limiting both the questions researchers can pursue and how precisely they can answer them. Prediction-powered inference (PPI) can reduce the amount of data needed for precise parameter estimation by combining labeled data with machine learning predictions. However, ignoring dependence within clusters can produce confidence intervals that cover the true parameter less often than their nominal rate. We introduce Cluster-Robust PPI++, which provides standard errors in closed form and asymptotically valid confidence intervals under arbitrary dependence within independent clusters, requiring no bootstrap or resampling. Our central contribution is to accommodate partially labeled clusters, a common empirical setting in which clusters contain both labeled and unlabeled units. As units are dependent within clusters, partially labeled clusters violate the independence assumption of PPI++. We also show how precision increases depend on the labeling design, and derive a cluster-aware power tuning rule that minimizes asymptotic variance. In an application to television news, standard PPI++ confidence intervals have coverage below 60%, whereas Cluster-Robust PPI++ can achieve nominal 95% coverage.

Problem

• Prediction-Powered Inference
• Cluster-Robust
• Partially Labeled Clusters
• Confidence Intervals
• Dependence

Innovation

• Prediction-Powered Inference
• Cluster-Robust
• Partially Labeled Clusters
• Closed-form Standard Errors
• Power Tuning