# Calibeating Prediction-Powered Inference

arXiv: https://arxiv.org/abs/2604.21260 · HTML: https://mlsanity.com/paper/2604.21260/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 185 references that are in the map.
- First posted on arXiv 23 Apr 2026.

## Builds on (most cited first, 30 of 37)

- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [PPI++: Efficient Prediction-Powered Inference](https://mlsanity.com/paper/2311.01453/) (2023)
- [Calibration in Deep Learning: A Survey of the State-of-the-Art](https://mlsanity.com/paper/2308.01222/) (2023)
- [Active Statistical Inference](https://mlsanity.com/paper/2403.03208/) (2024)
- [Predictions as Surrogates: Revisiting Surrogate Outcomes in the Age of AI](https://mlsanity.com/paper/2501.09731/) (2025)
- [Combining T-learning and DR-learning: a framework for oracle-efficient estimation of causal contrasts](https://mlsanity.com/paper/2402.01972/) (2024)
- [Causal Inference: A Missing Data Perspective](https://mlsanity.com/paper/1712.06170/) (2017)
- [Prediction-powered Generalization of Causal Inferences](https://mlsanity.com/paper/2406.02873/) (2024)
- [A Unified Framework for Semiparametrically Efficient Semi-Supervised Learning](https://mlsanity.com/paper/2502.17741/) (2025)
- [Doubly robust inference via calibration](https://mlsanity.com/paper/2411.02771/) (2024)
- [Stabilized Inverse Probability Weighting via Isotonic Calibration](https://mlsanity.com/paper/2411.06342/) (2024)
- [Demystifying Prediction Powered Inference](https://mlsanity.com/paper/2601.20819/) (2026)
- [Local Prediction-Powered Inference](https://mlsanity.com/paper/2409.18321/) (2024)
- [Semiparametric Double Reinforcement Learning with Applications to Long-Term Causal Inference](https://mlsanity.com/paper/2501.06926/) (2025)
- [Automatic Debiased Machine Learning for Smooth Functionals of Nonparametric M-Estimands](https://mlsanity.com/paper/2501.11868/) (2025)
- [Generalized Venn and Venn-Abers Calibration with Applications in Conformal Prediction](https://mlsanity.com/paper/2502.05676/) (2025)
- [Fine-Tune, Then Rectify](https://mlsanity.com/paper/2511.19486/) (2025)
- [PPI is the Difference Estimator: Recognizing the Survey Sampling Roots of Prediction-Powered Inference](https://mlsanity.com/paper/2603.19160/) (2026)
- [Orthogonal Causal Calibration](https://mlsanity.com/paper/2406.01933/) (2024)
- [Improving the Finite Sample Estimation of Average Treatment Effects using Double/Debiased Machine Learning with Propensity Score Calibration](https://mlsanity.com/paper/2409.04874/) (2024)
- [Adaptive Sequential Design for a Single Time-Series](https://mlsanity.com/paper/2102.00102/) (2021)
- [Towards a Unified Theory for Semiparametric Data Fusion with Individual-Level Data](https://mlsanity.com/paper/2409.09973/) (2024)
- [Data-adaptive smoothing for optimal-rate estimation of possibly non-regular parameters](https://mlsanity.com/paper/1706.07408/) (2017)
- [Propensity score models are better when post-calibrated](https://mlsanity.com/paper/2211.01221/) (2022)
- [Calibration Strategies for Robust Causal Estimation: Theoretical and Empirical Insights on Propensity Score-Based Estimators](https://mlsanity.com/paper/2503.17290/) (2025)
- [Constructing Confidence Intervals for Infinite-Dimensional Functional Parameters by Highly Adaptive Lasso](https://mlsanity.com/paper/2507.10511/) (2025)
- [Efficient Statistical Estimation for Sequential Adaptive Experiments with Implications for Adaptive Designs](https://mlsanity.com/paper/2508.09135/) (2025)
- [Bellman Calibration for V-Learning in Offline Reinforcement Learning](https://mlsanity.com/paper/2512.23694/) (2025)
- [Prediction-Powered Conditional Inference](https://mlsanity.com/paper/2603.05575/) (2026)
- [Robust Estimation and Inference in Hybrid Controlled Trials for Binary Outcomes: A Case Study on Non-Small Cell Lung Cancer](https://mlsanity.com/paper/2505.00217/) (2025)

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

- [Prediction-Powered Inference Across Many Tasks for AI Evaluation & Social Science Research](https://mlsanity.com/paper/2605.29249/) (2026)
- [Maximum Likelihood Estimation for Entity Ranking under Iterative Synthetic Data Augmentation](https://mlsanity.com/paper/2609.32987/) (2026)
- [Artificial intelligence surrogates for treatment effect estimation with before-and-after data](https://mlsanity.com/paper/2609.27180/) (2026)
- [ABC-Align: Prediction-Powered Alignment with Adaptive Bias Control](https://mlsanity.com/paper/2609.34374/) (2026)

## Abstract (arXiv)

We study semisupervised mean estimation with a small labeled sample, a large unlabeled sample, and a black-box prediction model whose output may be miscalibrated. A standard approach in this setting is augmented inverse-probability weighting (AIPW) [Robins et al., 1994], which protects against prediction-model misspecification but can be inefficient when the prediction score is poorly aligned with the outcome scale. We introduce Calibrated Prediction-Powered Inference, which post-hoc calibrates the prediction score on the labeled sample before using it for semisupervised estimation. This simple step requires no retraining and can improve the original score both as a predictor of the outcome and as a regression adjustment for semisupervised inference. We study both linear and isotonic calibration. For isotonic calibration, we establish first-order optimality guarantees: isotonic post-processing can improve predictive accuracy and estimator efficiency relative to the original score and simpler post-processing rules, while no further post-processing of the fitted isotonic score yields additional first-order gains. For linear calibration, we show first-order equivalence to PPI++. We also clarify the relationship among existing estimators, showing that the original PPI estimator is a special case of AIPW and can be inefficient when the prediction model is accurate, while PPI++ is AIPW with empirical efficiency maximization [Rubin et al., 2008]. In simulations and real-data experiments, our calibrated estimators often outperform PPI and are competitive with, or outperform, AIPW and PPI++. We provide an accompanying Python package, ppi_aipw, at https://larsvanderlaan.github.io/ppi-aipw/.