# Prediction-Powered E-Values

arXiv: https://arxiv.org/abs/2502.04294 · HTML: https://mlsanity.com/paper/2502.04294/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 38 references that are in the map.
- First posted on arXiv 6 Feb 2025.

## Builds on (most cited first, 24 of 24)

- [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)
- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [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)
- [Causal-learn: Causal Discovery in Python](https://mlsanity.com/paper/2307.16405/) (2023)
- [Hypothesis testing with e-values](https://mlsanity.com/paper/2410.23614/) (2024)
- [Cross-Prediction-Powered Inference](https://mlsanity.com/paper/2309.16598/) (2023)
- [AutoEval Done Right: Using Synthetic Data for Model Evaluation](https://mlsanity.com/paper/2403.07008/) (2024)
- [Tracking the risk of a deployed model and detecting harmful distribution shifts](https://mlsanity.com/paper/2110.06177/) (2021)
- [Anytime-valid off-policy inference for contextual bandits](https://mlsanity.com/paper/2210.10768/) (2022)
- [E-detectors: a nonparametric framework for sequential change detection](https://mlsanity.com/paper/2203.03532/) (2022)
- [Time-uniform central limit theory and asymptotic confidence sequences](https://mlsanity.com/paper/2103.06476/) (2021)
- [Prediction-Powered Ranking of Large Language Models](https://mlsanity.com/paper/2402.17826/) (2024)
- [Protected Test-Time Adaptation via Online Entropy Matching: A Betting Approach](https://mlsanity.com/paper/2408.07511/) (2024)
- [Sequential Predictive Two-Sample and Independence Testing](https://mlsanity.com/paper/2305.00143/) (2023)
- [Post-selection inference for e-value based confidence intervals](https://mlsanity.com/paper/2203.12572/) (2022)
- [Beyond Neyman-Pearson: e-values enable hypothesis testing with a data-driven alpha](https://mlsanity.com/paper/2205.00901/) (2022)
- [Model-X Sequential Testing for Conditional Independence via Testing by Betting](https://mlsanity.com/paper/2210.00354/) (2022)
- [Anytime Valid Tests of Conditional Independence Under Model-X](https://mlsanity.com/paper/2209.12637/) (2022)
- [Reducing sequential change detection to sequential estimation](https://mlsanity.com/paper/2309.09111/) (2023)
- [Local Prediction-Powered Inference](https://mlsanity.com/paper/2409.18321/) (2024)
- [Sequential change detection via backward confidence sequences](https://mlsanity.com/paper/2302.02544/) (2023)

## Built on by (most cited first, 16 of 16)

- [Noisy but Valid: Robust Statistical Evaluation of LLMs with Imperfect Judges](https://mlsanity.com/paper/2601.20913/) (2026)
- [Adaptive Prediction-Powered AutoEval with Reliability and Efficiency Guarantees](https://mlsanity.com/paper/2505.18659/) (2025)
- [Who Drifted: the System or the Judge? Anytime-Valid Attribution in LLM Evaluation Pipelines](https://mlsanity.com/paper/2606.15474/) (2026)
- [Anytime-valid, Bayes-assisted, Prediction-Powered Inference](https://mlsanity.com/paper/2505.18000/) (2025)
- [Revisiting Active Sequential Prediction-Powered Mean Estimation](https://mlsanity.com/paper/2604.18569/) (2026)
- [Do We Really Even Need Data? A Modern Look at Drawing Inference with Predicted Data](https://mlsanity.com/paper/2512.05456/) (2025)
- [Prediction-Powered Risk Monitoring of Deployed Models for Detecting Harmful Distribution Shifts](https://mlsanity.com/paper/2602.02229/) (2026)
- [Extending Prediction-Powered Inference through Conformal Prediction](https://mlsanity.com/paper/2510.16166/) (2025)
- [Differentially Private E-Values](https://mlsanity.com/paper/2510.18654/) (2025)
- [Improving Backward Conformal Prediction via Non-Conformity Score Transformation](https://mlsanity.com/paper/2602.01733/) (2026)
- [Semi-Supervised Hypothesis Testing by Betting on Predictions](https://mlsanity.com/paper/2605.28533/) (2026)
- [Industrializing Prediction-Powered Inference: The GLIDE Library for Reliable GenAI and Agentic Systems Evaluation](https://mlsanity.com/paper/2605.31278/) (2026)
- [Asymptotically Log-Optimal Bayes-Assisted Confidence Sequences for Bounded Means](https://mlsanity.com/paper/2605.07964/) (2026)
- [Metadata Predictability Is Not Evidence Dependence: An Intervention-Based Audit for Weak-Label Benchmarks](https://mlsanity.com/paper/2605.23701/) (2026)
- [When Can Old Evaluations Certify a New Model? Label-Efficient Release Decisions under Evaluator Drift](https://mlsanity.com/paper/2609.32267/) (2026)
- [How to Run Statistics over LLM Judges and Trust the Results: Calibrated Inference for Small-Sample AI Evaluation with evalstats](https://mlsanity.com/paper/2609.35815/) (2026)

## Abstract (arXiv)

Quality statistical inference requires a sufficient amount of data, which can be missing or hard to obtain. To this end, prediction-powered inference has risen as a promising methodology, but existing approaches are largely limited to Z-estimation problems such as inference of means and quantiles. In this paper, we apply ideas of prediction-powered inference to e-values. By doing so, we inherit all the usual benefits of e-values -- such as anytime-validity, post-hoc validity and versatile sequential inference -- as well as greatly expand the set of inferences achievable in a prediction-powered manner. In particular, we show that every inference procedure that can be framed in terms of e-values has a prediction-powered counterpart, given by our method. We showcase the effectiveness of our framework across a wide range of inference tasks, from simple hypothesis testing and confidence intervals to more involved procedures for change-point detection and causal discovery, which were out of reach of previous techniques. Our approach is modular and easily integrable into existing algorithms, making it a compelling choice for practical applications.