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A comparison of some conformal quantile regression methods

arXiv 1909.05433 ↗First posted 12 Sep 2019stat.ME math.ST stat.MLcited by 76

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Abstract (arXiv)

We compare two recently proposed methods that combine ideas from conformal inference and quantile regression to produce locally adaptive and marginally valid prediction intervals under sample exchangeability (Romano et al., 2019; Kivaranovic et al., 2019). First, we prove that these two approaches are asymptotically efficient in large samples, under some additional assumptions. Then we compare them empirically on simulated and real data. Our results demonstrate that the method in Romano et al. (2019) typically yields tighter prediction intervals in finite samples. Finally, we discuss how to tune these procedures by fixing the relative proportions of observations used for training and conformalization.

Key facts. Cited by 76 papers in the map (data through 7 Oct 2026). First posted on arXiv 12 Sep 2019.

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Citing papers per year: 2021: 7; 2022: 11; 2023: 13; 2024: 20; 2025: 11; 2026: 14.

76 papers.

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  1. 2021Testing for Outliers with Conformal p-valuescited by 133
  2. 2021Conformal Prediction using Conditional Histogramscited by 77
  3. 2021Conformalized Survival Analysiscited by 53
  4. 2021Calibrated Multiple-Output Quantile Regression with Representation Learningcited by 49
  5. 2021Improving Conditional Coverage via Orthogonal Quantile Regressioncited by 48
  6. 2022Predictive Inference with Feature Conformal Predictioncited by 33
  7. 2022A review of predictive uncertainty estimation with machine learningcited by 29
  8. 2021Valid prediction intervals for regression problemscited by 28
  9. 2022Ensemble Conformalized Quantile Regression for Probabilistic Time Series Forecastingcited by 27
  10. 2025Analyzing Uncertainty of LLM-as-a-Judge: Interval Evaluations with Conformal Predictioncited by 26
  11. 2023Conformal Contextual Robust Optimizationcited by 25
  12. 2024Boosted Conformal Prediction Intervalscited by 25
38 more
  1. 2024Conformal Prediction: A Data Perspectivecited by 25
  2. 2023Conformal Prediction with Missing Valuescited by 24
  3. 2023Adaptive conformal classification with noisy labelscited by 24
  4. 2024Probabilistic Conformal Prediction with Approximate Conditional Validitycited by 23
  5. 2023Confident Object Detection via Conformal Prediction and Conformal Risk Control: an Application to Railway Signalingcited by 22
  6. 2023Integrating Uncertainty Awareness into Conformalized Quantile Regressioncited by 17
  7. 2025Rectifying Conformity Scores for Better Conditional Coveragecited by 17
  8. 2022Conformal Off-policy Predictioncited by 14
  9. 2023Conformal inference is (almost) free for neural networks trained with early stoppingcited by 14
  10. 2024Looks Too Good To Be True: An Information-Theoretic Analysis of Hallucinations in Generative Restoration Modelscited by 12
  11. 2024Kernel-based Optimally Weighted Conformal Time-Series Predictioncited by 12
  12. 2022Conformal Methods for Quantifying Uncertainty in Spatiotemporal Data: A Surveycited by 11
  13. 2024Conformal Load Prediction with Transductive Graph Autoencoderscited by 11
  14. 2024Conformal Thresholded Intervals for Efficient Regressioncited by 11
  15. 2022Conformal Frequency Estimation using Discrete Sketched Data with Coverage for Distinct Queriescited by 10
  16. 2024Uncertainty quantification for probabilistic machine learning in earth observation using conformal predictioncited by 9
  17. 2024TorchCP: A Python Library for Conformal Predictioncited by 9
  18. 2025Epistemic Uncertainty in Conformal Scores: A Unified Approachcited by 9
  19. 2023On training locally adaptive CPcited by 8
  20. 2024Relaxed Quantile Regression: Prediction Intervals for Asymmetric Noisecited by 8
  21. 2024Conformalized Interval Arithmetic with Symmetric Calibrationcited by 8
  22. 2025Multivariate Conformal Selectioncited by 8
  23. 2024Distribution-Free Conformal Joint Prediction Regions for Neural Marked Temporal Point Processescited by 7
  24. 2026VLM Judges Can Rank but Cannot Score: Task-Dependent Uncertainty in Multimodal Evaluationcited by 7
  25. 2023Distribution-free risk assessment of regression-based machine learning algorithmscited by 6
  26. 2024Conformal Predictive Programming for Chance Constrained Optimizationcited by 6
  27. 2022Improved conformalized quantile regressioncited by 5
  28. 2022Nonparametric Quantile Regression: Non-Crossing Constraints and Conformal Predictioncited by 5
  29. 2022What's Behind the Mask: Estimating Uncertainty in Image-to-Image Problemscited by 5
  30. 2023Post-selection Inference for Conformal Prediction: Trading off Coverage for Precisioncited by 5
  31. 2023Variational Inference with Coverage Guarantees in Simulation-Based Inferencecited by 5
  32. 2024What If We Had Used a Different App? Reliable Counterfactual KPI Analysis in Wireless Systemscited by 5
  33. 2024Toward Conditional Distribution Calibration in Survival Predictioncited by 5
  34. 2021Deep Quantile Regression for Uncertainty Estimation in Unsupervised and Supervised Lesion Detectioncited by 4
  35. 2022Conformal Frequency Estimation with Sketched Datacited by 4
  36. 2023Conditional validity of heteroskedastic conformal regressioncited by 4
  37. 2024Adaptive Uncertainty Quantification for Generative AIcited by 4
  38. 2024Uncertainty quantification in metric spacescited by 3

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