mlsanityData to 7 Oct 2026

Improving Conditional Coverage via Orthogonal Quantile Regression

arXiv 2106.00394 ↗First posted 1 Jun 2021cs.LGcited by 48

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Abstract (arXiv)

We develop a method to generate prediction intervals that have a user-specified coverage level across all regions of feature-space, a property called conditional coverage. A typical approach to this task is to estimate the conditional quantiles with quantile regression -- it is well-known that this leads to correct coverage in the large-sample limit, although it may not be accurate in finite samples. We find in experiments that traditional quantile regression can have poor conditional coverage. To remedy this, we modify the loss function to promote independence between the size of the intervals and the indicator of a miscoverage event. For the true conditional quantiles, these two quantities are independent (orthogonal), so the modified loss function continues to be valid. Moreover, we empirically show that the modified loss function leads to improved conditional coverage, as evaluated by several metrics. We also introduce two new metrics that check conditional coverage by looking at the strength of the dependence between the interval size and the indicator of miscoverage.

Key facts. Cited by 48 papers in the map (data through 7 Oct 2026). Builds on 18 of its 55 references that are in the map. First posted on arXiv 1 Jun 2021.

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18 of 55 references.

References · 18

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2019Conformalized Quantile Regressioncited by 620
  3. 2020Uncertainty Sets for Image Classifiers using Conformal Predictioncited by 365
  4. 2021Distribution-Free, Risk-Controlling Prediction Setscited by 278
  5. 2015Generative Moment Matching Networkscited by 252
  6. 2018Empirical Risk Minimization under Fairness Constraintscited by 226
  7. 2019Distributional conformal predictioncited by 104
  8. 2019Nested conformal prediction and quantile out-of-bag ensemble methodscited by 88
  9. 2020Beyond Pinball Loss: Quantile Methods for Calibrated Uncertainty Quantificationcited by 77
  10. 2019A comparison of some conformal quantile regression methodscited by 76
  11. 2020CD-split and HPD-split: efficient conformal regions in high dimensionscited by 74
  12. 2019Flexible distribution-free conditional predictive bands using density estimatorscited by 64
6 more
  1. 2019Adaptive, Distribution-Free Prediction Intervals for Deep Networkscited by 56
  2. 2019With Malice Towards None: Assessing Uncertainty via Equalized Coveragecited by 43
  3. 2020Achieving Equalized Odds by Resampling Sensitive Attributescited by 42
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  5. 2013The Randomized Dependence Coefficientcited by 24
  6. 2021Distribution-Free Conditional Median Inferencecited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 7; 2023: 13; 2024: 9; 2025: 10; 2026: 6.

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  1. 2021A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantificationcited by 777
  2. 2022Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imagingcited by 107
  3. 2024Online conformal prediction with decaying step sizescited by 53
  4. 2024Conformal Prediction for Natural Language Processing: A Surveycited by 52
  5. 2021Calibrated Multiple-Output Quantile Regression with Representation Learningcited by 49
  6. 2021Sample-Efficient Safety Assurances using Conformal Predictioncited by 41
  7. 2023High-Dimensional Prediction for Sequential Decision Makingcited by 41
  8. 2024Length Optimization in Conformal Predictioncited by 39
  9. 2022Achieving Risk Control in Online Learning Settingscited by 38
  10. 2023A Large-Scale Study of Probabilistic Calibration in Neural Network Regressioncited by 26
  11. 2022Efficient and Differentiable Conformal Prediction with General Function Classescited by 25
  12. 2024Conformal Prediction with Learned Featurescited by 23
36 more
  1. 2022Split Localized Conformal Predictioncited by 20
  2. 2023Integrating Uncertainty Awareness into Conformalized Quantile Regressioncited by 17
  3. 2023Equal Opportunity of Coverage in Fair Regressioncited by 16
  4. 2025Wasserstein-regularized Conformal Prediction under General Distribution Shiftcited by 14
  5. 2023Calibration in Machine Learning Uncertainty Quantification: beyond consistency to target adaptivitycited by 13
  6. 2022Towards Instance-Wise Calibration: Local Amortized Diagnostics and Reshaping of Conditional Densities (LADaR)cited by 9
  7. 2025Epistemic Uncertainty in Conformal Scores: A Unified Approachcited by 9
  8. 2023Conformalized Unconditional Quantile Regressioncited by 8
  9. 2023Adaptive Conformal Regression with Jackknife+ Rescaled Scorescited by 8
  10. 2024Relaxed Quantile Regression: Prediction Intervals for Asymmetric Noisecited by 8
  11. 2024Conformalized Interval Arithmetic with Symmetric Calibrationcited by 8
  12. 2025Conditional Coverage Diagnostics for Conformal Predictioncited by 8
  13. 2023Conformalized Multimodal Uncertainty Regression and Reasoningcited by 6
  14. 2023Validation of uncertainty quantification metrics: a primer based on the consistency and adaptivity conceptscited by 5
  15. 2023Likelihood Annealing: Fast Calibrated Uncertainty for Regressioncited by 3
  16. 2023Distribution-Free Model-Agnostic Regression Calibration via Nonparametric Methodscited by 3
  17. 2024Uncertainty Quantification on Graph Learning: A Surveycited by 3
  18. 2025Conformal Prediction in Hierarchical Classification with Constrained Representation Complexitycited by 3
  19. 2025Colorful Pinball: Density-Weighted Quantile Regression for Conditional Guarantee of Conformal Predictioncited by 3
  20. 2023Design-based conformal predictioncited by 2
  21. 2025Probabilistic Conformal Coverage Guarantees in Small-Data Settingscited by 2
  22. 2022Ensemble Multi-Quantiles: Adaptively Flexible Distribution Prediction for Uncertainty Quantificationcited by 1
  23. 2022Improving Uncertainty Quantification of Variance Networks by Tree-Structured Learningcited by 1
  24. 2023QuantProb: Generalizing Probabilities along with Predictions for a Pre-trained Classifiercited by 1
  25. 2025One Model to Forecast Them All and in Entity Distributions Bind Themcited by 1
  26. 2025Scalable and adaptive prediction bands with kernel sum-of-squarescited by 1
  27. 2025Provably Minimum-Length Conformal Prediction Sets for Ordinal Classificationcited by 1
  28. 2026On Optimal Data Splitting for Split Conformal Predictioncited by 1
  29. 2024Enhancing reliability in prediction intervals using point forecasters: Heteroscedastic Quantile Regression and Width-Adaptive Conformal Inferencecited by 0
  30. 2024Adjusting Regression Models for Conditional Uncertainty Calibrationcited by 0
  31. 2025Enforcing Calibration in Multi-Output Probabilistic Regression with Pre-rank Regularizationcited by 0
  32. 2026Questioning the Coverage-Length Metric in Conformal Prediction: When Shorter Intervals Are Not Bettercited by 0
  33. 2026Safe Urban Traffic Control via Uncertainty-Aware Conformal Prediction and World-Model Reinforcement Learningcited by 0
  34. 2026Trustworthy Predictive Distributions for Tail Events with Semiparametric Diagnostic Transport Mapscited by 0
  35. 2026Generative Score Inference for Multimodal Datacited by 0
  36. 2026Robust Conditional Conformal Prediction via Branched Normalizing Flowcited by 0