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Conformalized Quantile Regression

arXiv 1905.03222 ↗First posted 8 May 2019stat.ME stat.MLcited by 629

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Abstract (arXiv)

Conformal prediction is a technique for constructing prediction intervals that attain valid coverage in finite samples, without making distributional assumptions. Despite this appeal, existing conformal methods can be unnecessarily conservative because they form intervals of constant or weakly varying length across the input space. In this paper we propose a new method that is fully adaptive to heteroscedasticity. It combines conformal prediction with classical quantile regression, inheriting the advantages of both. We establish a theoretical guarantee of valid coverage, supplemented by extensive experiments on popular regression datasets. We compare the efficiency of conformalized quantile regression to other conformal methods, showing that our method tends to produce shorter intervals.

Key facts. Cited by 629 papers in the map (data through 14 Oct 2026). First posted on arXiv 8 May 2019.

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Citing papers per year: 2021: 34; 2022: 62; 2023: 80; 2024: 114; 2025: 147; 2026: 192.

629 papers.

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  1. 2021A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantificationcited by 792
  2. 2024Chronos: Learning the Language of Time Seriescited by 759
  3. 2021Adaptive Conformal Inference Under Distribution Shiftcited by 375
  4. 2022Conformal Risk Controlcited by 299
  5. 2021Distribution-Free, Risk-Controlling Prediction Setscited by 288
  6. 2021Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Controlcited by 271
  7. 2023Conformal Language Modelingcited by 170
  8. 2022Adaptive Conformal Predictions for Time Seriescited by 161
  9. 2021Testing for Outliers with Conformal p-valuescited by 134
  10. 2022Conformal Inference for Online Prediction with Arbitrary Distribution Shiftscited by 128
  11. 2021Learning Optimal Conformal Classifierscited by 112
  12. 2023Class-Conditional Conformal Prediction with Many Classescited by 109
38 more
  1. 2022Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imagingcited by 107
  2. 2021Distribution-free uncertainty quantification for classification under label shiftcited by 101
  3. 2023Conformal PID Control for Time Series Predictioncited by 88
  4. 2023Uncertainty Quantification over Graph with Conformalized Graph Neural Networkscited by 79
  5. 2023Improved Online Conformal Prediction via Strongly Adaptive Online Learningcited by 78
  6. 2021Conformal Prediction using Conditional Histogramscited by 77
  7. 2022Sequential Predictive Conformal Inference for Time Seriescited by 75
  8. 2021Fair Conformal Predictors for Applications in Medical Imagingcited by 74
  9. 2021Classifier Calibration: A survey on how to assess and improve predicted class probabilitiescited by 73
  10. 2022Selection by Prediction with Conformal p-valuescited by 69
  11. 2022Batch Multivalid Conformal Predictioncited by 67
  12. 2022Practical Adversarial Multivalid Conformal Predictioncited by 65
  13. 2022Training Uncertainty-Aware Classifiers with Conformalized Deep Learningcited by 64
  14. 2022Trustworthy clinical AI solutions: a unified review of uncertainty quantification in deep learning models for medical image analysiscited by 63
  15. 2022Improving Expert Predictions with Conformal Predictioncited by 54
  16. 2024Conformal Alignment: Knowing When to Trust Foundation Models with Guaranteescited by 54
  17. 2021Few-shot Conformal Prediction with Auxiliary Taskscited by 53
  18. 2021Conformalized Survival Analysiscited by 53
  19. 2023Conformal Prediction for Deep Classifier via Label Rankingcited by 53
  20. 2021Calibrated Multiple-Output Quantile Regression with Representation Learningcited by 50
  21. 2023How to Trust Your Diffusion Model: A Convex Optimization Approach to Conformal Risk Controlcited by 50
  22. 2021Improving Conditional Coverage via Orthogonal Quantile Regressioncited by 48
  23. 2022Probabilistic Conformal Prediction Using Conditional Random Samplescited by 47
  24. 2025Decision Theoretic Foundations for Conformal Prediction: Optimal Uncertainty Quantification for Risk-Averse Agentscited by 40
  25. 2022Achieving Risk Control in Online Learning Settingscited by 39
  26. 2024Length Optimization in Conformal Predictioncited by 39
  27. 2022Improving Trustworthiness of AI Disease Severity Rating in Medical Imaging with Ordinal Conformal Prediction Setscited by 38
  28. 2022Predictive Inference with Feature Conformal Predictioncited by 34
  29. 2021Calibrated and Sharp Uncertainties in Deep Learning via Density Estimationcited by 33
  30. 2023Conformal Prediction Regions for Time Series using Linear Complementarity Programmingcited by 33
  31. 2023Conformal prediction under ambiguous ground truthcited by 31
  32. 2021Valid prediction intervals for regression problemscited by 29
  33. 2022Copula Conformal Prediction for Multi-step Time Series Forecastingcited by 29
  34. 2022Conformal Prediction Sets with Limited False Positivescited by 28
  35. 2022Distribution Free Prediction Sets for Node Classificationcited by 28
  36. 2023Principal Uncertainty Quantification with Spatial Correlation for Image Restoration Problemscited by 28
  37. 2024Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networkscited by 28
  38. 2022Ensemble Conformalized Quantile Regression for Probabilistic Time Series Forecastingcited by 27

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