# Revisiting Active Sequential Prediction-Powered Mean Estimation

arXiv: https://arxiv.org/abs/2604.18569 · HTML: https://mlsanity.com/paper/2604.18569/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 59 references that are in the map.
- First posted on arXiv 20 Apr 2026.

## Builds on (most cited first, 30 of 40)

- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [A Survey of Deep Active Learning](https://mlsanity.com/paper/2009.00236/) (2020)
- [Online Learning: A Modern Introduction Using Convex Optimization](https://mlsanity.com/paper/1912.13213/) (2019)
- [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)
- [Adversarial Active Learning for Deep Networks: a Margin Based Approach](https://mlsanity.com/paper/1802.09841/) (2018)
- [PPI++: Efficient Prediction-Powered Inference](https://mlsanity.com/paper/2311.01453/) (2023)
- [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)
- [Limits to scalable evaluation at the frontier: LLM as Judge won't beat twice the data](https://mlsanity.com/paper/2410.13341/) (2024)
- [Active Statistical Inference](https://mlsanity.com/paper/2403.03208/) (2024)
- [Can Unconfident LLM Annotations Be Used for Confident Conclusions?](https://mlsanity.com/paper/2408.15204/) (2024)
- [Using Imperfect Surrogates for Downstream Inference: Design-based Supervised Learning for Social Science Applications of Large Language Models](https://mlsanity.com/paper/2306.04746/) (2023)
- [Predictions as Surrogates: Revisiting Surrogate Outcomes in the Age of AI](https://mlsanity.com/paper/2501.09731/) (2025)
- [Prediction-Powered Ranking of Large Language Models](https://mlsanity.com/paper/2402.17826/) (2024)
- [Assumption-Lean and Data-Adaptive Post-Prediction Inference](https://mlsanity.com/paper/2311.14220/) (2023)
- [No-Regret Dynamics in the Fenchel Game: A Unified Framework for Algorithmic Convex Optimization](https://mlsanity.com/paper/2111.11309/) (2021)
- [Cost-Optimal Active AI Model Evaluation](https://mlsanity.com/paper/2506.07949/) (2025)
- [High-Dimensional Robust Mean Estimation via Gradient Descent](https://mlsanity.com/paper/2005.01378/) (2020)
- [Prediction-Powered E-Values](https://mlsanity.com/paper/2502.04294/) (2025)
- [Prediction De-Correlated Inference: A safe approach for post-prediction inference](https://mlsanity.com/paper/2312.06478/) (2023)
- [A Unified Framework for Semiparametrically Efficient Semi-Supervised Learning](https://mlsanity.com/paper/2502.17741/) (2025)
- [Multi-Armed Bandits With Machine Learning-Generated Surrogate Rewards](https://mlsanity.com/paper/2506.16658/) (2025)
- [Adaptive Prediction-Powered AutoEval with Reliability and Efficiency Guarantees](https://mlsanity.com/paper/2505.18659/) (2025)
- [Don't fear the unlabelled: safe semi-supervised learning via simple debiasing](https://mlsanity.com/paper/2203.07512/) (2022)
- [A Note on the Prediction-Powered Bootstrap](https://mlsanity.com/paper/2405.18379/) (2024)
- [Task-Agnostic Machine-Learning-Assisted Inference](https://mlsanity.com/paper/2405.20039/) (2024)
- [Efficient Randomized Experiments Using Foundation Models](https://mlsanity.com/paper/2502.04262/) (2025)
- [No Free Lunch: Non-Asymptotic Analysis of Prediction-Powered Inference](https://mlsanity.com/paper/2505.20178/) (2025)
- [Mechanism Design for Collaborative Normal Mean Estimation](https://mlsanity.com/paper/2306.06351/) (2023)

## Built on by (most cited first, 4 of 4)

- [Who Drifted: the System or the Judge? Anytime-Valid Attribution in LLM Evaluation Pipelines](https://mlsanity.com/paper/2606.15474/) (2026)
- [Efficient Sequential Evaluation of Large Language Models](https://mlsanity.com/paper/2607.17409/) (2026)
- [Prediction-Powered Active Testing](https://mlsanity.com/paper/2607.08347/) (2026)
- [ABC-Align: Prediction-Powered Alignment with Adaptive Bias Control](https://mlsanity.com/paper/2609.34374/) (2026)

## Abstract (arXiv)

In this work, we revisit the problem of active sequential prediction-powered mean estimation, where at each round one must decide the query probability of the ground-truth label upon observing the covariates of a sample. Furthermore, if the label is not queried, the prediction from a machine learning model is used instead. Prior work proposed an elegant scheme that determines the query probability by combining an uncertainty-based suggestion with a constant probability that encodes a soft constraint on the query probability. We explored different values of the mixing parameter and observed an intriguing empirical pattern: the smallest confidence width tends to occur when the weight on the constant probability is close to one, thereby reducing the influence of the uncertainty-based component. Motivated by this observation, we develop a non-asymptotic analysis of the estimator and establish a data-dependent bound on its confidence interval. Our analysis further suggests that when a no-regret learning approach is used to determine the query probability and control this bound, the query probability converges to the constraint of the max value of the query probability when it is chosen obliviously to the current covariates. We also conduct simulations that corroborate these theoretical findings.