FAB-PPI: Frequentist, Assisted by Bayes, Prediction-Powered Inference

TL;DR

FAB-PPI enhances prediction-powered inference by integrating prior knowledge on prediction quality, leading to more accurate estimates and adaptable confidence intervals while preserving frequentist guarantees.

Contribution

The paper introduces FAB-PPI, a novel method that combines Bayesian prior information with PPI to improve inference accuracy and adaptivity.

Findings

FAB-PPI outperforms traditional PPI in high-quality prediction scenarios.

FAB-PPI maintains frequentist guarantees even with Bayesian prior integration.

The method adaptively reverts to standard PPI in low prior probability regions.

Abstract

Prediction-powered inference (PPI) enables valid statistical inference by combining experimental data with machine learning predictions. When a sufficient number of high-quality predictions is available, PPI results in more accurate estimates and tighter confidence intervals than traditional methods. In this paper, we propose to inform the PPI framework with prior knowledge on the quality of the predictions. The resulting method, which we call frequentist, assisted by Bayes, PPI (FAB-PPI), improves over PPI when the observed prediction quality is likely under the prior, while maintaining its frequentist guarantees. Furthermore, when using heavy-tailed priors, FAB-PPI adaptively reverts to standard PPI in low prior probability regions. We demonstrate the benefits of FAB-PPI in real and synthetic examples.