mlsanityData to 7 Oct 2026

Calibrated Multiple-Output Quantile Regression with Representation Learning

arXiv 2110.00816 ↗First posted 2 Oct 2021cs.LGcited by 49

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Abstract (arXiv)

We develop a method to generate predictive regions that cover a multivariate response variable with a user-specified probability. Our work is composed of two components. First, we use a deep generative model to learn a representation of the response that has a unimodal distribution. Existing multiple-output quantile regression approaches are effective in such cases, so we apply them on the learned representation, and then transform the solution to the original space of the response. This process results in a flexible and informative region that can have an arbitrary shape, a property that existing methods lack. Second, we propose an extension of conformal prediction to the multivariate response setting that modifies any method to return sets with a pre-specified coverage level. The desired coverage is theoretically guaranteed in the finite-sample case for any distribution. Experiments conducted on both real and synthetic data show that our method constructs regions that are significantly smaller compared to existing techniques.

Key facts. Cited by 49 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 2 Oct 2021.

Builds on

18 of 55 references.

References · 18

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2017Neural Discrete Representation Learningcited by 4,650
  3. 2015Variational Inference with Normalizing Flowscited by 2,161
  4. 2021A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantificationcited by 777
  5. 2019Conformalized Quantile Regressioncited by 620
  6. 2021Distribution-Free, Risk-Controlling Prediction Setscited by 278
  7. 2019Predictive inference with the jackknife+cited by 206
  8. 2019Distributional conformal predictioncited by 104
  9. 2019Nested conformal prediction and quantile out-of-bag ensemble methodscited by 88
  10. 2020Beyond Pinball Loss: Quantile Methods for Calibrated Uncertainty Quantificationcited by 77
  11. 2019A comparison of some conformal quantile regression methodscited by 76
  12. 2020CD-split and HPD-split: efficient conformal regions in high dimensionscited by 74
6 more
  1. 2019Flexible distribution-free conditional predictive bands using density estimatorscited by 64
  2. 2016Learning Features of Music from Scratchcited by 57
  3. 2019Adaptive, Distribution-Free Prediction Intervals for Deep Networkscited by 56
  4. 2021Improving Conditional Coverage via Orthogonal Quantile Regressioncited by 48
  5. 2019Conformal prediction with localizationcited by 22
  6. 2021Representation Learning Beyond Linear Prediction Functionscited by 21

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 6; 2024: 11; 2025: 20; 2026: 10.

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  1. 2024Conformal prediction for multi-dimensional time series by ellipsoidal setscited by 37
  2. 2023Conformal Contextual Robust Optimizationcited by 25
  3. 2024Conformal Prediction: A Data Perspectivecited by 25
  4. 2025Minimum Volume Conformal Sets for Multivariate Regressioncited by 25
  5. 2025Multivariate Conformal Prediction using Optimal Transportcited by 21
  6. 2025Optimal Transport-based Conformal Predictioncited by 19
  7. 2024Conformal Prediction for Class-wise Coverage via Augmented Label Rank Calibrationcited by 18
  8. 2025Rectifying Conformity Scores for Better Conditional Coveragecited by 17
  9. 2023Lightweight, Uncertainty-Aware Conformalized Visual Odometrycited by 13
  10. 2024Semiparametric conformal predictioncited by 13
  11. 2022Deep Non-Crossing Quantiles through the Partial Derivativecited by 12
  12. 2022Fast Nonlinear Vector Quantile Regressioncited by 11
37 more
  1. 2024Conformal Thresholded Intervals for Efficient Regressioncited by 11
  2. 2025Relational Conformal Prediction for Correlated Time Seriescited by 11
  3. 2024Conformal Prediction for Ensembles: Improving Efficiency via Score-Based Aggregationcited by 9
  4. 2025Multivariate Conformal Selectioncited by 8
  5. 2025Conditional Coverage Diagnostics for Conformal Predictioncited by 8
  6. 2024Distribution-Free Conformal Joint Prediction Regions for Neural Marked Temporal Point Processescited by 7
  7. 2023Max-Rank: Efficient Multiple Testing for Conformal Predictioncited by 6
  8. 2025Volume-Sorted Prediction Set: Efficient Conformal Prediction for Multi-Target Regressioncited by 6
  9. 2025Multivariate Standardized Residuals for Conformal Predictioncited by 6
  10. 2023Multi-Modal Conformal Prediction Regions with Simple Structures by Optimizing Convex Shape Templatescited by 4
  11. 2024Deep Ensemble Shape Calibration: Multi-Field Post-hoc Calibration in Online Advertisingcited by 4
  12. 2024Conformal Prediction for Hierarchical Datacited by 4
  13. 2025JAPAN: Joint Adaptive Prediction Areas with Normalising-Flowscited by 4
  14. 2025Multivariate Latent Recalibration for Conditional Normalizing Flowscited by 3
  15. 2025ResCP: Reservoir Conformal Prediction for Time Series Forecastingcited by 3
  16. 2025Beyond Uncertainty Sets: Leveraging Optimal Transport to Extend Conformal Predictive Distributions to Multivariate Settingscited by 3
  17. 2024Learning minimal volume uncertainty ellipsoidscited by 2
  18. 2025Reliable uncertainty quantification for 2D/3D anatomical landmark localization using multi-output conformal predictioncited by 2
  19. 2025Zono-Conformal Prediction: Zonotope-Based Uncertainty Quantification for Regression and Classification Taskscited by 2
  20. 2025Neural Optimal Transport Meets Multivariate Conformal Predictioncited by 2
  21. 2026Conformal Prediction for Generative Models via Adaptive Cluster-Based Density Estimationcited by 2
  22. 2023QuantProb: Generalizing Probabilities along with Predictions for a Pre-trained Classifiercited by 1
  23. 2025Multivariate Uncertainty Quantification with Tomographic Quantile Forestscited by 1
  24. 2026CONTRA: Conformal Prediction Region via Normalizing Flow Transformationcited by 1
  25. 2023Balanced Marginal and Joint Distributional Learning via Mixture Cramer-Wold Distancecited by 0
  26. 2024Conformalized High-Density Quantile Regression via Dynamic Prototypes-based Probability Density Estimationcited by 0
  27. 2025Feature Fitted Online Conformal Prediction for Deep Time Series Forecasting Modelcited by 0
  28. 2025Enforcing Calibration in Multi-Output Probabilistic Regression with Pre-rank Regularizationcited by 0
  29. 2025Minimax Multi-Target Conformal Prediction with Applications to Imaging Inverse Problemscited by 0
  30. 2026Super-Level-Set Regression: Conditional Quantiles via Volume Minimizationcited by 0
  31. 2026TRACE: Transport Alignment Conformal Prediction via Diffusion and Flow Matching Modelscited by 0
  32. 2026Multi-Variable Conformal Prediction: Optimizing Prediction Sets without Data Splittingcited by 0
  33. 2026Conformal Reliability: A New Evaluation Metric for Conditional Generationcited by 0
  34. 2026SPACE: Sample-cloud Predictive Adaptive Conformal Ellipsoids for Multivariate Time-Series Forecastingcited by 0
  35. 2026Scaling-Score Conformal Prediction for Multi-Target Regressioncited by 0
  36. 2026Tail-Aware Geometry Learning for Conformal Ellipsoidscited by 0
  37. 2026Multivariate conformal uncertainty propagation in multitask atomistic simulation: Successes and pitfallscited by 0