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

arXiv: https://arxiv.org/abs/2505.18000 · HTML: https://mlsanity.com/paper/2505.18000/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 51 references that are in the map.
- First posted on arXiv 23 May 2025.

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Time-uniform, nonparametric, nonasymptotic confidence sequences](https://mlsanity.com/paper/1810.08240/) (2018)
- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [Estimating means of bounded random variables by betting](https://mlsanity.com/paper/2010.09686/) (2020)
- [Game-theoretic statistics and safe anytime-valid inference](https://mlsanity.com/paper/2210.01948/) (2022)
- [PPI++: Efficient Prediction-Powered Inference](https://mlsanity.com/paper/2311.01453/) (2023)
- [Mixture Martingales Revisited with Applications to Sequential Tests and Confidence Intervals](https://mlsanity.com/paper/1811.11419/) (2018)
- [Hypothesis testing with e-values](https://mlsanity.com/paper/2410.23614/) (2024)
- [Active Statistical Inference](https://mlsanity.com/paper/2403.03208/) (2024)
- [Semi-supervised Inference: General Theory and Estimation of Means](https://mlsanity.com/paper/1606.07268/) (2016)
- [Time-uniform central limit theory and asymptotic confidence sequences](https://mlsanity.com/paper/2103.06476/) (2021)
- [A unified recipe for deriving (time-uniform) PAC-Bayes bounds](https://mlsanity.com/paper/2302.03421/) (2023)
- [PAC-Bayes Generalisation Bounds for Heavy-Tailed Losses through Supermartingales](https://mlsanity.com/paper/2210.00928/) (2022)
- [Sequential Nonparametric Testing with the Law of the Iterated Logarithm](https://mlsanity.com/paper/1506.03486/) (2015)
- [Prediction-Powered E-Values](https://mlsanity.com/paper/2502.04294/) (2025)
- [Near-Optimal Non-Parametric Sequential Tests and Confidence Sequences with Possibly Dependent Observations](https://mlsanity.com/paper/2212.14411/) (2022)
- [FAB-PPI: Frequentist, Assisted by Bayes, Prediction-Powered Inference](https://mlsanity.com/paper/2502.02363/) (2025)
- [Anytime-Valid Inference for Double/Debiased Machine Learning of Causal Parameters](https://mlsanity.com/paper/2408.09598/) (2024)
- [The extended Ville's inequality for nonintegrable nonnegative supermartingales](https://mlsanity.com/paper/2304.01163/) (2023)

## Built on by (most cited first, 7 of 7)

- [Who Drifted: the System or the Judge? Anytime-Valid Attribution in LLM Evaluation Pipelines](https://mlsanity.com/paper/2606.15474/) (2026)
- [Testing For Distribution Shifts with Conditional Conformal Test Martingales](https://mlsanity.com/paper/2602.13848/) (2026)
- [Prediction-Powered Risk Monitoring of Deployed Models for Detecting Harmful Distribution Shifts](https://mlsanity.com/paper/2602.02229/) (2026)
- [Differentially Private E-Values](https://mlsanity.com/paper/2510.18654/) (2025)
- [Active Multiple-Prediction-Powered Inference](https://mlsanity.com/paper/2605.08429/) (2026)
- [Semi-Supervised Hypothesis Testing by Betting on Predictions](https://mlsanity.com/paper/2605.28533/) (2026)
- [Asymptotically Log-Optimal Bayes-Assisted Confidence Sequences for Bounded Means](https://mlsanity.com/paper/2605.07964/) (2026)

## Abstract (arXiv)

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.