mlsanityData to 7 Oct 2026

Relaxed Quantile Regression: Prediction Intervals for Asymmetric Noise

arXiv 2406.03258 ↗First posted 5 Jun 2024stat.ML cs.LGcited by 8

Not on the map. Why?

Abstract (arXiv)

Constructing valid prediction intervals rather than point estimates is a well-established approach for uncertainty quantification in the regression setting. Models equipped with this capacity output an interval of values in which the ground truth target will fall with some prespecified probability. This is an essential requirement in many real-world applications where simple point predictions' inability to convey the magnitude and frequency of errors renders them insufficient for high-stakes decisions. Quantile regression is a leading approach for obtaining such intervals via the empirical estimation of quantiles in the (non-parametric) distribution of outputs. This method is simple, computationally inexpensive, interpretable, assumption-free, and effective. However, it does require that the specific quantiles being learned are chosen a priori. This results in (a) intervals that are arbitrarily symmetric around the median which is sub-optimal for realistic skewed distributions, or (b) learning an excessive number of intervals. In this work, we propose Relaxed Quantile Regression (RQR), a direct alternative to quantile regression based interval construction that removes this arbitrary constraint whilst maintaining its strengths. We demonstrate that this added flexibility results in intervals with an improvement in desirable qualities (e.g. mean width) whilst retaining the essential coverage guarantees of quantile regression.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 40 of its 88 references that are in the map. First posted on arXiv 5 Jun 2024.

Builds on

40 of 88 references.

References · 40

  1. 2015Rethinking the Inception Architecture for Computer Visioncited by 5,451
  2. 2017On Calibration of Modern Neural Networkscited by 4,860
  3. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,416
  4. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,888
  5. 2017What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?cited by 2,335
  6. 2016Concrete Problems in AI Safetycited by 1,582
  7. 2019Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methodscited by 903
  8. 2021A Survey of Uncertainty in Deep Neural Networkscited by 675
  9. 2019Conformalized Quantile Regressioncited by 620
  10. 2020Bayesian Deep Learning and a Probabilistic Perspective of Generalizationcited by 480
  11. 2017Regularizing Neural Networks by Penalizing Confident Output Distributionscited by 461
  12. 2015Deep Kernel Learningcited by 440
28 more
  1. 2019Deep Ensembles: A Loss Landscape Perspectivecited by 438
  2. 2018Accurate Uncertainties for Deep Learning Using Calibrated Regressioncited by 417
  3. 2020BatchEnsemble: An Alternative Approach to Efficient Ensemble and Lifelong Learningcited by 368
  4. 2021Laplace Redux -- Effortless Bayesian Deep Learningcited by 359
  5. 2017Advances in Variational Inferencecited by 236
  6. 2019Practical Deep Learning with Bayesian Principlescited by 158
  7. 2020Uncertainty Quantification and Deep Ensemblescited by 138
  8. 2018High-Quality Prediction Intervals for Deep Learning: A Distribution-Free, Ensembled Approachcited by 117
  9. 2016Stochastic Variational Deep Kernel Learningcited by 92
  10. 2020Beyond Pinball Loss: Quantile Methods for Calibrated Uncertainty Quantificationcited by 77
  11. 2021Conformal Prediction using Conditional Histogramscited by 77
  12. 2019A comparison of some conformal quantile regression methodscited by 76
  13. 2020The Case for Bayesian Deep Learningcited by 68
  14. 2019Reliable training and estimation of variance networkscited by 63
  15. 2022Deep Ensembles Work, But Are They Necessary?cited by 63
  16. 2020Post-hoc Uncertainty Calibration for Domain Drift Scenarioscited by 61
  17. 2019Quality of Uncertainty Quantification for Bayesian Neural Network Inferencecited by 58
  18. 2021Improving Conditional Coverage via Orthogonal Quantile Regressioncited by 48
  19. 2022Uncertainty Quantification of Collaborative Detection for Self-Drivingcited by 46
  20. 2016DisturbLabel: Regularizing CNN on the Loss Layercited by 41
  21. 2019Robust Learning with the Hilbert-Schmidt Independence Criterioncited by 36
  22. 2021Valid prediction intervals for regression problemscited by 28
  23. 2023Joint Training of Deep Ensembles Fails Due to Learner Collusioncited by 23
  24. 2023Improving Adaptive Conformal Prediction Using Self-Supervised Learningcited by 17
  25. 2023Pathologies of Predictive Diversity in Deep Ensemblescited by 16
  26. 2022Deep Non-Crossing Quantiles through the Partial Derivativecited by 12
  27. 2022A Contextual Bandit Approach for Value-oriented Prediction Interval Forecastingcited by 2
  28. 2023Safety Evaluation of Robot Systems via Uncertainty Quantificationcited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 2; 2026: 4.

8 papers.

  1. 2024Utility-Directed Conformal Prediction: A Decision-Aware Framework for Actionable Uncertainty Quantificationcited by 11
  2. 2025Introducing Interval Neural Networks for Uncertainty-Aware System Identificationcited by 3
  3. 2026Direct Interval Propagation Methods using Neural-Network Surrogates for Uncertainty Quantification in Physical Systems Surrogate Modelcited by 3
  4. 2024Tube Loss: A Novel Approach for Prediction Interval Estimationcited by 2
  5. 2025A Convex Loss Function for Set Prediction with Optimal Trade-offs Between Size and Conditional Coveragecited by 2
  6. 2026Geometry of tail allocation in conformal prediction intervalscited by 0
  7. 2026Quantile-Free Uncertainty Quantification in Graph Neural Networkscited by 0
  8. 2026Beyond Prediction: Interval Neural Networks for Uncertainty-Aware System Identificationcited by 0