# Semi-Supervised Risk Control via Prediction-Powered Inference

arXiv: https://arxiv.org/abs/2412.11174 · HTML: https://mlsanity.com/paper/2412.11174/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 67 references that are in the map.
- First posted on arXiv 15 Dec 2024.

## Builds on (most cited first, 30 of 43)

- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Using Self-Supervised Learning Can Improve Model Robustness and Uncertainty](https://mlsanity.com/paper/1906.12340/) (2019)
- [A Survey of Deep Learning Techniques for Autonomous Driving](https://mlsanity.com/paper/1910.07738/) (2019)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Interpretable machine learning: definitions, methods, and applications](https://mlsanity.com/paper/1901.04592/) (2019)
- [In Defense of Pseudo-Labeling: An Uncertainty-Aware Pseudo-label Selection Framework for Semi-Supervised Learning](https://mlsanity.com/paper/2101.06329/) (2021)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [A Survey on Deep Semi-supervised Learning](https://mlsanity.com/paper/2103.00550/) (2021)
- [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)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [PPI++: Efficient Prediction-Powered Inference](https://mlsanity.com/paper/2311.01453/) (2023)
- [Class-Conditional Conformal Prediction with Many Classes](https://mlsanity.com/paper/2306.09335/) (2023)
- [Batch Multivalid Conformal Prediction](https://mlsanity.com/paper/2209.15145/) (2022)
- [Veridical Data Science](https://mlsanity.com/paper/1901.08152/) (2019)
- [PAC Confidence Sets for Deep Neural Networks via Calibrated Prediction](https://mlsanity.com/paper/2001.00106/) (2019)
- [Cross-Prediction-Powered Inference](https://mlsanity.com/paper/2309.16598/) (2023)
- [Few-shot Conformal Prediction with Auxiliary Tasks](https://mlsanity.com/paper/2102.08898/) (2021)
- [PAC Prediction Sets Under Covariate Shift](https://mlsanity.com/paper/2106.09848/) (2021)
- [Fast yet Safe: Early-Exiting with Risk Control](https://mlsanity.com/paper/2405.20915/) (2024)
- [Efficient and Adaptive Linear Regression in Semi-Supervised Settings](https://mlsanity.com/paper/1701.04889/) (2017)
- [Efficiently Controlling Multiple Risks with Pareto Testing](https://mlsanity.com/paper/2210.07913/) (2022)
- [HappyMap: A Generalized Multi-calibration Method](https://mlsanity.com/paper/2303.04379/) (2023)
- [Doubly Robust Self-Training](https://mlsanity.com/paper/2306.00265/) (2023)
- [Few-Shot Calibration of Set Predictors via Meta-Learned Cross-Validation-Based Conformal Prediction](https://mlsanity.com/paper/2210.03067/) (2022)
- [Improving Adaptive Conformal Prediction Using Self-Supervised Learning](https://mlsanity.com/paper/2302.12238/) (2023)

## Built on by (most cited first, 13 of 13)

- [Adaptive Prediction-Powered AutoEval with Reliability and Efficiency Guarantees](https://mlsanity.com/paper/2505.18659/) (2025)
- [Synthetic-Powered Predictive Inference](https://mlsanity.com/paper/2505.13432/) (2025)
- [A Joint Finite-Sample Certificate for Adaptive Selective Conformal Risk Control](https://mlsanity.com/paper/2606.08517/) (2026)
- [Ensuring Reliability via Hyperparameter Selection: Review and Advances](https://mlsanity.com/paper/2502.04206/) (2025)
- [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)
- [Synthetic Counterfactual Labels for Efficient Conformal Counterfactual Inference](https://mlsanity.com/paper/2509.04112/) (2025)
- [Uncertainty Quantification and Data Efficiency in AI: An Information-Theoretic Perspective](https://mlsanity.com/paper/2512.05267/) (2025)
- [Semi-Supervised Conformal Prediction With Unlabeled Nonconformity Score](https://mlsanity.com/paper/2505.21147/) (2025)
- [Reliable Wireless Indoor Localization via Cross-Validated Prediction-Powered Calibration](https://mlsanity.com/paper/2507.20268/) (2025)
- [MEC: Machine-Learning-Assisted Generalized Entropy Calibration for Semi-Supervised Mean Estimation](https://mlsanity.com/paper/2604.05446/) (2026)
- [Semi-Supervised Hypothesis Testing by Betting on Predictions](https://mlsanity.com/paper/2605.28533/) (2026)
- [Stable Localized Conformal Prediction via Transduction](https://mlsanity.com/paper/2605.01452/) (2026)

## Abstract (arXiv)

The risk-controlling prediction sets (RCPS) framework is a general tool for transforming the output of any machine learning model to design a predictive rule with rigorous error rate control. The key idea behind this framework is to use labeled hold-out calibration data to tune a hyper-parameter that affects the error rate of the resulting prediction rule. However, the limitation of such a calibration scheme is that with limited hold-out data, the tuned hyper-parameter becomes noisy and leads to a prediction rule with an error rate that is often unnecessarily conservative. To overcome this sample-size barrier, we introduce a semi-supervised calibration procedure that leverages unlabeled data to rigorously tune the hyper-parameter without compromising statistical validity. Our procedure builds upon the prediction-powered inference framework, carefully tailoring it to risk-controlling tasks. We demonstrate the benefits and validity of our proposal through two real-data experiments: few-shot image classification and early time series classification.