# Distribution-Free, Risk-Controlling Prediction Sets

arXiv: https://arxiv.org/abs/2101.02703 · HTML: https://mlsanity.com/paper/2101.02703/

## Key facts

- Cited by 288 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 63 references that are in the map.
- First posted on arXiv 7 Jan 2021.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [PraNet: Parallel Reverse Attention Network for Polyp Segmentation](https://mlsanity.com/paper/2006.11392/) (2020)
- [Unlabeled Data Improves Adversarial Robustness](https://mlsanity.com/paper/1905.13736/) (2019)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [TResNet: High Performance GPU-Dedicated Architecture](https://mlsanity.com/paper/2003.13630/) (2020)
- [Nested conformal prediction and quantile out-of-bag ensemble methods](https://mlsanity.com/paper/1910.10562/) (2019)
- [A Conformal Prediction Approach to Explore Functional Data](https://mlsanity.com/paper/1302.6452/) (2013)
- [Robust Validation: Confident Predictions Even When Distributions Shift](https://mlsanity.com/paper/2008.04267/) (2020)
- [Flexible distribution-free conditional predictive bands using density estimators](https://mlsanity.com/paper/1910.05575/) (2019)
- [PAC Confidence Sets for Deep Neural Networks via Calibrated Prediction](https://mlsanity.com/paper/2001.00106/) (2019)
- [Prediction and outlier detection in classification problems](https://mlsanity.com/paper/1905.04396/) (2019)
- [Cautious Deep Learning](https://mlsanity.com/paper/1805.09460/) (2018)
- [Conformal prediction with localization](https://mlsanity.com/paper/1908.08558/) (2019)
- [Conformal calibrators](https://mlsanity.com/paper/1902.06579/) (2019)
- [PAC Confidence Predictions for Deep Neural Network Classifiers](https://mlsanity.com/paper/2011.00716/) (2020)

## Built on by (most cited first, 30 of 288)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Confident Adaptive Language Modeling](https://mlsanity.com/paper/2207.07061/) (2022)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [Conformal Language Modeling](https://mlsanity.com/paper/2306.10193/) (2023)
- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [Learning Optimal Conformal Classifiers](https://mlsanity.com/paper/2110.09192/) (2021)
- [Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imaging](https://mlsanity.com/paper/2202.05265/) (2022)
- [Trust or Escalate: LLM Judges with Provable Guarantees for Human Agreement](https://mlsanity.com/paper/2407.18370/) (2024)
- [Conformal PID Control for Time Series Prediction](https://mlsanity.com/paper/2307.16895/) (2023)
- [Uncertainty Quantification over Graph with Conformalized Graph Neural Networks](https://mlsanity.com/paper/2305.14535/) (2023)
- [Improved Online Conformal Prediction via Strongly Adaptive Online Learning](https://mlsanity.com/paper/2302.07869/) (2023)
- [Consistent Accelerated Inference via Confident Adaptive Transformers](https://mlsanity.com/paper/2104.08803/) (2021)
- [Fair Conformal Predictors for Applications in Medical Imaging](https://mlsanity.com/paper/2109.04392/) (2021)
- [Selection by Prediction with Conformal p-values](https://mlsanity.com/paper/2210.01408/) (2022)
- [Tomayto, Tomahto. Beyond Token-level Answer Equivalence for Question Answering Evaluation](https://mlsanity.com/paper/2202.07654/) (2022)
- [Training Uncertainty-Aware Classifiers with Conformalized Deep Learning](https://mlsanity.com/paper/2205.05878/) (2022)
- [Mitigating LLM Hallucinations via Conformal Abstention](https://mlsanity.com/paper/2405.01563/) (2024)
- [Improving Expert Predictions with Conformal Prediction](https://mlsanity.com/paper/2201.12006/) (2022)
- [Few-shot Conformal Prediction with Auxiliary Tasks](https://mlsanity.com/paper/2102.08898/) (2021)
- [Conformal Prediction for Deep Classifier via Label Ranking](https://mlsanity.com/paper/2310.06430/) (2023)
- [Conformal Prediction for Natural Language Processing: A Survey](https://mlsanity.com/paper/2405.01976/) (2024)
- [Calibrated Multiple-Output Quantile Regression with Representation Learning](https://mlsanity.com/paper/2110.00816/) (2021)
- [How to Trust Your Diffusion Model: A Convex Optimization Approach to Conformal Risk Control](https://mlsanity.com/paper/2302.03791/) (2023)
- [Improving Conditional Coverage via Orthogonal Quantile Regression](https://mlsanity.com/paper/2106.00394/) (2021)
- [Federated Conformal Predictors for Distributed Uncertainty Quantification](https://mlsanity.com/paper/2305.17564/) (2023)
- [PAC Prediction Sets Under Covariate Shift](https://mlsanity.com/paper/2106.09848/) (2021)
- [Tracking the risk of a deployed model and detecting harmful distribution shifts](https://mlsanity.com/paper/2110.06177/) (2021)
- [Achieving Risk Control in Online Learning Settings](https://mlsanity.com/paper/2205.09095/) (2022)
- [Robust Calibration with Multi-domain Temperature Scaling](https://mlsanity.com/paper/2206.02757/) (2022)

## Abstract (arXiv)

While improving prediction accuracy has been the focus of machine learning in recent years, this alone does not suffice for reliable decision-making. Deploying learning systems in consequential settings also requires calibrating and communicating the uncertainty of predictions. To convey instance-wise uncertainty for prediction tasks, we show how to generate set-valued predictions from a black-box predictor that control the expected loss on future test points at a user-specified level. Our approach provides explicit finite-sample guarantees for any dataset by using a holdout set to calibrate the size of the prediction sets. This framework enables simple, distribution-free, rigorous error control for many tasks, and we demonstrate it in five large-scale machine learning problems: (1) classification problems where some mistakes are more costly than others; (2) multi-label classification, where each observation has multiple associated labels; (3) classification problems where the labels have a hierarchical structure; (4) image segmentation, where we wish to predict a set of pixels containing an object of interest; and (5) protein structure prediction. Lastly, we discuss extensions to uncertainty quantification for ranking, metric learning and distributionally robust learning.