Anytime-valid, Bayes-assisted, Prediction-Powered Inference

Valentin Kilian (University of Oxford) · Stefano Cortinovis (University of Oxford) · Francois Caron (University of Oxford)

asymptotic validityconfidence interval proceduresconfidence sequence proceduresdesign choiceslabelled datamethod of mixturesprediction quality prediction-powered inference prior knowledgereal examplessequential settingstatistical efficiency synthetic examplesunlabelled dataville's inequality

Given a large pool of unlabelled data and a smaller amount of labels, prediction-powered inference (PPI) leverages machine learning predictions to increase the statistical efficiency of confidence interval procedures based solely on labelled data, while preserving fixed-time validity. In this paper, we extend the PPI framework to the sequential setting, where labelled and unlabelled datasets grow over time. Exploiting Ville's inequality and the method of mixtures, we propose prediction-powered confidence sequence procedures that are asymptotically valid uniformly over time and naturally accommodate prior knowledge on the quality of the predictions to further boost efficiency. We carefully illustrate the design choices behind our method and demonstrate its effectiveness in real and synthetic examples.