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

Given a large pool of unlabelled data and a smaller amount of labels, predictionpowered 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 predictionpowered 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. * Equal contribution. Order decided by coin toss. 39th Conference on Neural Information Processing Systems (NeurIPS 2025).