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Distribution Calibration for Regression

arXiv 1905.06023 ↗First posted 15 May 2019stat.ML cs.AI cs.LGcited by 89

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Abstract (arXiv)

We are concerned with obtaining well-calibrated output distributions from regression models. Such distributions allow us to quantify the uncertainty that the model has regarding the predicted target value. We introduce the novel concept of distribution calibration, and demonstrate its advantages over the existing definition of quantile calibration. We further propose a post-hoc approach to improving the predictions from previously trained regression models, using multi-output Gaussian Processes with a novel Beta link function. The proposed method is experimentally verified on a set of common regression models and shows improvements for both distribution-level and quantile-level calibration.

Key facts. Cited by 89 papers in the map (data through 14 Oct 2026). First posted on arXiv 15 May 2019.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 18; 2022: 12; 2023: 22; 2024: 9; 2025: 15; 2026: 13.

89 papers.

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  1. 2021Calibrating Predictions to Decisions: A Novel Approach to Multi-Class Calibrationcited by 79
  2. 2021Classifier Calibration: A survey on how to assess and improve predicted class probabilitiescited by 73
  3. 2022Better Uncertainty Calibration via Proper Scores for Classification and Beyondcited by 65
  4. 2021Uncertainty Toolbox: an Open-Source Library for Assessing, Visualizing, and Improving Uncertainty Quantificationcited by 57
  5. 2022Low-Degree Multicalibrationcited by 45
  6. 2021Inspect, Understand, Overcome: A Survey of Practical Methods for AI Safetycited by 35
  7. 2021Calibrated and Sharp Uncertainties in Deep Learning via Density Estimationcited by 33
  8. 2021X-CAL: Explicit Calibration for Survival Analysiscited by 30
  9. 2021Valid prediction intervals for regression problemscited by 29
  10. 2023A Large-Scale Study of Probabilistic Calibration in Neural Network Regressioncited by 27
  11. 2021Estimating Expected Calibration Errorscited by 24
  12. 2021Flexible Model Aggregation for Quantile Regressioncited by 22
38 more
  1. 2022COLD Fusion: Calibrated and Ordinal Latent Distribution Fusion for Uncertainty-Aware Multimodal Emotion Recognitioncited by 22
  2. 2021Calibrated Uncertainty for Molecular Property Prediction using Ensembles of Message Passing Neural Networkscited by 21
  3. 2022Calibration tests beyond classificationcited by 20
  4. 2023Calibration by Distribution Matching: Trainable Kernel Calibration Metricscited by 20
  5. 2023Towards Building Self-Aware Object Detectors via Reliable Uncertainty Quantification and Calibrationcited by 19
  6. 2021CAMul: Calibrated and Accurate Multi-view Time-Series Forecastingcited by 17
  7. 2021When in Doubt: Neural Non-Parametric Uncertainty Quantification for Epidemic Forecastingcited by 16
  8. 2021Natural Posterior Network: Deep Bayesian Uncertainty for Exponential Family Distributionscited by 13
  9. 2022A review of machine learning concepts and methods for addressing challenges in probabilistic hydrological post-processing and forecastingcited by 12
  10. 2023Density-Softmax: Efficient Test-time Model for Uncertainty Estimation and Robustness under Distribution Shiftscited by 12
  11. 2023Guaranteed Coverage Prediction Intervals with Gaussian Process Regressioncited by 12
  12. 2023Resilient Multiple Choice Learning: A learned scoring scheme with application to audio scene analysiscited by 12
  13. 2023MUBen: Benchmarking the Uncertainty of Molecular Representation Modelscited by 11
  14. 2023Uncertainty Estimation for Molecules: Desiderata and Methodscited by 11
  15. 2021Online Calibrated and Conformal Prediction Improves Bayesian Optimizationcited by 10
  16. 2022Evaluating Aleatoric Uncertainty via Conditional Generative Modelscited by 10
  17. 2023On the Calibration of Human Pose Estimationcited by 10
  18. 2022Parametric and Multivariate Uncertainty Calibration for Regression and Object Detectioncited by 9
  19. 2023On the role of Model Uncertainties in Bayesian Optimizationcited by 8
  20. 2024Density-Regression: Efficient and Distance-Aware Deep Regressor for Uncertainty Estimation under Distribution Shiftscited by 7
  21. 2024Calibrating Expressions of Certaintycited by 7
  22. 2022Multi-hypothesis 3D human pose estimation metrics favor miscalibrated distributionscited by 6
  23. 2024Orthogonal Causal Calibrationcited by 6
  24. 2021Bayesian Confidence Calibration for Epistemic Uncertainty Modellingcited by 5
  25. 2023Sharp Calibrated Gaussian Processescited by 5
  26. 2023Leveraging Locality and Robustness to Achieve Massively Scalable Gaussian Process Regressioncited by 5
  27. 2023Tailoring Mixup to Data for Calibrationcited by 5
  28. 2024SAUC: Sparsity-Aware Uncertainty Calibration for Spatiotemporal Prediction with Graph Neural Networkscited by 5
  29. 2025Three Types of Calibration with Properties and their Semantic and Formal Relationshipscited by 5
  30. 2022Remember to correct the bias when using deep learning for regression!cited by 4
  31. 2022Quantile-constrained Wasserstein projections for robust interpretability of numerical and machine learning modelscited by 4
  32. 2024Multi-fidelity Gaussian process surrogate modeling for regression problems in physicscited by 4
  33. 2024Calibrated Probabilistic Forecasts for Arbitrary Sequencescited by 4
  34. 2021Uncertainty Characteristics Curves: A Systematic Assessment of Prediction Intervalscited by 3
  35. 2021f-Cal: Calibrated aleatoric uncertainty estimation from neural networks for robot perceptioncited by 3
  36. 2022Exploring Effective Knowledge Transfer for Few-shot Object Detectioncited by 3
  37. 2023Likelihood Annealing: Fast Calibrated Uncertainty for Regressioncited by 3
  38. 2023Distribution-Free Model-Agnostic Regression Calibration via Nonparametric Methodscited by 3

50 most cited of 89 All 89 (JSON)