From structural biology to epidemiology, predictions from machine learning (ML) models increasingly complement costly gold-standard data to enable faster, more affordable, and scalable scientific inquiry. In response, prediction-based (PB) inference has emerged to accommodate statistical analysis using a large volume of predictions together with a small amount of gold-standard data. The goals of PB inference are two-fold: (i) to mitigate bias from errors in predictions and (ii) to improve efficiency relative to traditional inference using only the gold-standard data. Motwani and Witten (2023) recently revisited two key PB inference approaches and found that only one method, Prediction-powered Inference (PPI) proposed by Angelopoulos et al. (2023), achieves (i). In this paper, we find that PPI does not achieve (ii). We revisit the double sampling literature and show that, with a simple modification, PPI can be adjusted to provide theoretically justified improvements in efficiency. We also contextualize PB inference with economics and statistics literature dating back to the 1960s to highlight the utility of classical methods in this contemporary problem. Our extensive theoretical analyses, along with an analysis of UK Biobank data, indicate that our proposal effectively mitigates bias and improves efficiency, making it preferable for use in practice.
View on arXiv@article{gronsbell2025_2411.19908,
title={ Another look at inference after prediction },
author={ Jessica Gronsbell and Jianhui Gao and Yaqi Shi and Zachary R. McCaw and David Cheng },
journal={arXiv preprint arXiv:2411.19908},
year={ 2025 }
}