# Cross-Prediction-Powered Inference arXiv: https://arxiv.org/abs/2309.16598 ยท HTML: https://mlsanity.com/paper/2309.16598/ ## Key facts - Cited by 58 papers in the map (data through 14 Oct 2026). - Builds on 14 of its 63 references that are in the map. - First posted on arXiv 28 Sep 2023. ## Builds on (most cited first, 14 of 14) - [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016) - [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021) - [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023) - [A Generalizable and Accessible Approach to Machine Learning with Global Satellite Imagery](https://mlsanity.com/paper/2010.08168/) (2020) - [Cross-validation: what does it estimate and how well does it do it?](https://mlsanity.com/paper/2104.00673/) (2021) - [ChatGPT Chemistry Assistant for Text Mining and Prediction of MOF Synthesis](https://mlsanity.com/paper/2306.11296/) (2023) - [Semi-supervised Inference: General Theory and Estimation of Means](https://mlsanity.com/paper/1606.07268/) (2016) - [Cross-validation Confidence Intervals for Test Error](https://mlsanity.com/paper/2007.12671/) (2020) - [A Deep Learning Approach for Population Estimation from Satellite Imagery](https://mlsanity.com/paper/1708.09086/) (2017) - [Semi-supervised Inference for Explained Variance in High-dimensional Linear Regression and Its Applications](https://mlsanity.com/paper/1806.06179/) (2018) - [Semi-Supervised Quantile Estimation: Robust and Efficient Inference in High Dimensional Settings](https://mlsanity.com/paper/2201.10208/) (2022) - [A Simple and General Debiased Machine Learning Theorem with Finite Sample Guarantees](https://mlsanity.com/paper/2105.15197/) (2021) - [High-dimensional semi-supervised learning: in search for optimal inference of the mean](https://mlsanity.com/paper/1902.00772/) (2019) - [Tailored inference for finite populations: conditional validity and transfer across distributions](https://mlsanity.com/paper/2104.04565/) (2021) ## Built on by (most cited first, 30 of 58) - [PPI++: Efficient Prediction-Powered Inference](https://mlsanity.com/paper/2311.01453/) (2023) - [Active Statistical Inference](https://mlsanity.com/paper/2403.03208/) (2024) - [How to Correctly Report LLM-as-a-Judge Evaluations](https://mlsanity.com/paper/2511.21140/) (2025) - [Prediction-Powered Ranking of Large Language Models](https://mlsanity.com/paper/2402.17826/) (2024) - [Stratified Prediction-Powered Inference for Hybrid Language Model Evaluation](https://mlsanity.com/paper/2406.04291/) (2024) - [Noisy but Valid: Robust Statistical Evaluation of LLMs with Imperfect Judges](https://mlsanity.com/paper/2601.20913/) (2026) - [Cost-Optimal Active AI Model Evaluation](https://mlsanity.com/paper/2506.07949/) (2025) - [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 Framework for Efficient Model Evaluation through Stratification, Sampling, and Estimation](https://mlsanity.com/paper/2406.07320/) (2024) - [Semi-Supervised Risk Control via Prediction-Powered Inference](https://mlsanity.com/paper/2412.11174/) (2024) - [Smoke and Mirrors in Causal Downstream Tasks](https://mlsanity.com/paper/2405.17151/) (2024) - [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) - [Best Arm Identification with LLM Judges and Limited Human](https://mlsanity.com/paper/2601.21471/) (2026) - [Demystifying Prediction Powered Inference](https://mlsanity.com/paper/2601.20819/) (2026) - [AI-Powered Bayesian Inference](https://mlsanity.com/paper/2502.19231/) (2025) - [No Free Lunch: Non-Asymptotic Analysis of Prediction-Powered Inference](https://mlsanity.com/paper/2505.20178/) (2025) - [Probably Approximately Correct Labels](https://mlsanity.com/paper/2506.10908/) (2025) - [Regression for the Mean: Auto-Evaluation and Inference with Few Labels through Post-hoc Regression](https://mlsanity.com/paper/2411.12665/) (2024) - [Another look at statistical inference with machine learning-imputed data](https://mlsanity.com/paper/2411.19908/) (2024) - [FAB-PPI: Frequentist, Assisted by Bayes, Prediction-Powered Inference](https://mlsanity.com/paper/2502.02363/) (2025) - [Constructing Confidence Intervals for Average Treatment Effects from Multiple Datasets](https://mlsanity.com/paper/2412.11511/) (2024) - [How to Bridge the Sim-to-Real Gap in Digital Twin-Aided Telecommunication Networks](https://mlsanity.com/paper/2507.07067/) (2025) - [Robust Sampling for Active Statistical Inference](https://mlsanity.com/paper/2511.08991/) (2025) - [Semi-Supervised U-statistics](https://mlsanity.com/paper/2402.18921/) (2024) - [Generalization Bounds and Stopping Rules for Learning with Self-Selected Data](https://mlsanity.com/paper/2505.07367/) (2025) - [Imputation-Powered Inference](https://mlsanity.com/paper/2509.13778/) (2025) - [Prediction-Powered Semi-Supervised Learning with Online Power Tuning](https://mlsanity.com/paper/2510.22586/) (2025) - [Deep Learning for Economists](https://mlsanity.com/paper/2407.15339/) (2024) ## Abstract (arXiv) While reliable data-driven decision-making hinges on high-quality labeled data, the acquisition of quality labels often involves laborious human annotations or slow and expensive scientific measurements. Machine learning is becoming an appealing alternative as sophisticated predictive techniques are being used to quickly and cheaply produce large amounts of predicted labels; e.g., predicted protein structures are used to supplement experimentally derived structures, predictions of socioeconomic indicators from satellite imagery are used to supplement accurate survey data, and so on. Since predictions are imperfect and potentially biased, this practice brings into question the validity of downstream inferences. We introduce cross-prediction: a method for valid inference powered by machine learning. With a small labeled dataset and a large unlabeled dataset, cross-prediction imputes the missing labels via machine learning and applies a form of debiasing to remedy the prediction inaccuracies. The resulting inferences achieve the desired error probability and are more powerful than those that only leverage the labeled data. Closely related is the recent proposal of prediction-powered inference, which assumes that a good pre-trained model is already available. We show that cross-prediction is consistently more powerful than an adaptation of prediction-powered inference in which a fraction of the labeled data is split off and used to train the model. Finally, we observe that cross-prediction gives more stable conclusions than its competitors; its confidence intervals typically have significantly lower variability.