mlsanityData to 7 Oct 2026

High-Quality Prediction Intervals for Deep Learning: A Distribution-Free, Ensembled Approach

arXiv 1802.07167 ↗First posted 20 Feb 2018stat.MLcited by 117

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Abstract (arXiv)

This paper considers the generation of prediction intervals (PIs) by neural networks for quantifying uncertainty in regression tasks. It is axiomatic that high-quality PIs should be as narrow as possible, whilst capturing a specified portion of data. We derive a loss function directly from this axiom that requires no distributional assumption. We show how its form derives from a likelihood principle, that it can be used with gradient descent, and that model uncertainty is accounted for in ensembled form. Benchmark experiments show the method outperforms current state-of-the-art uncertainty quantification methods, reducing average PI width by over 10%.

Key facts. Cited by 117 papers in the map (data through 7 Oct 2026). First posted on arXiv 20 Feb 2018.

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Citing papers per year: 2021: 27; 2022: 12; 2023: 34; 2024: 19; 2025: 15; 2026: 10.

117 papers.

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  1. 2021A Survey of Uncertainty in Deep Neural Networkscited by 675
  2. 2023A Survey on Uncertainty Quantification Methods for Deep Learningcited by 78
  3. 2023Improved Online Conformal Prediction via Strongly Adaptive Online Learningcited by 76
  4. 2024Estimating Epistemic and Aleatoric Uncertainty with a Single Modelcited by 52
  5. 2021Quantifying Uncertainty in Deep Spatiotemporal Forecastingcited by 48
  6. 2021AutoDEUQ: Automated Deep Ensemble with Uncertainty Quantificationcited by 31
  7. 2021Valid prediction intervals for regression problemscited by 28
  8. 2021Optimized conformal classification using gradient descent approximationcited by 27
  9. 2023A Large-Scale Study of Probabilistic Calibration in Neural Network Regressioncited by 26
  10. 2024CreINNs: Credal-Set Interval Neural Networks for Uncertainty Estimation in Classification Taskscited by 26
  11. 2022Efficient and Differentiable Conformal Prediction with General Function Classescited by 25
  12. 2023Optimal Training of Mean Variance Estimation Neural Networkscited by 17
38 more
  1. 2021Learning Prediction Intervals for Regression: Generalization and Calibrationcited by 16
  2. 2021NOMU: Neural Optimization-based Model Uncertaintycited by 16
  3. 2023Improving Uncertainty Quantification of Deep Classifiers via Neighborhood Conformal Prediction: Novel Algorithm and Theoretical Analysiscited by 16
  4. 2021How to Evaluate Uncertainty Estimates in Machine Learning for Regression?cited by 15
  5. 2023Quantifying Deep Learning Model Uncertainty in Conformal Predictioncited by 13
  6. 2023Calibration in Machine Learning Uncertainty Quantification: beyond consistency to target adaptivitycited by 13
  7. 2023Uncertainty Quantification of Spatiotemporal Travel Demand with Probabilistic Graph Neural Networkscited by 12
  8. 2023Distributionally Robust Statistical Verification with Imprecise Neural Networkscited by 12
  9. 2024Looks Too Good To Be True: An Information-Theoretic Analysis of Hallucinations in Generative Restoration Modelscited by 12
  10. 2026BAGEN: Are LLM Agents Budget-Aware?cited by 12
  11. 2021DeepGLEAM: A hybrid mechanistic and deep learning model for COVID-19 forecastingcited by 11
  12. 2022Conformal Methods for Quantifying Uncertainty in Spatiotemporal Data: A Surveycited by 11
  13. 2021Quantifying Epistemic Uncertainty in Deep Learningcited by 10
  14. 2023Efficient Uncertainty Quantification and Reduction for Over-Parameterized Neural Networkscited by 10
  15. 2021Deep Classifiers with Label Noise Modeling and Distance Awarenesscited by 8
  16. 2022Evaluating Aleatoric Uncertainty via Conditional Generative Modelscited by 8
  17. 2023ST-GIN: An Uncertainty Quantification Approach in Traffic Data Imputation with Spatio-temporal Graph Attention and Bidirectional Recurrent United Neural Networkscited by 8
  18. 2024Relaxed Quantile Regression: Prediction Intervals for Asymmetric Noisecited by 8
  19. 2023Retrospective Uncertainties for Deep Models using Vine Copulascited by 7
  20. 2023Ensembled Prediction Intervals for Causal Outcomes Under Hidden Confoundingcited by 7
  21. 2024Probabilistic Calibration by Design for Neural Network Regressioncited by 6
  22. 2025CLEAR: Calibrated Learning for Epistemic and Aleatoric Riskcited by 6
  23. 2021PI3NN: Out-of-distribution-aware prediction intervals from three neural networkscited by 5
  24. 2021Bayesian Confidence Calibration for Epistemic Uncertainty Modellingcited by 5
  25. 2022Structure and Distribution Metric for Quantifying the Quality of Uncertainty: Assessing Gaussian Processes, Deep Neural Nets, and Deep Neural Operators for Regressioncited by 5
  26. 2022What's Behind the Mask: Estimating Uncertainty in Image-to-Image Problemscited by 5
  27. 2022Dual Accuracy-Quality-Driven Neural Network for Prediction Interval Generationcited by 5
  28. 2023Validation of uncertainty quantification metrics: a primer based on the consistency and adaptivity conceptscited by 5
  29. 2023Adaptive Modeling of Uncertainties for Traffic Forecastingcited by 5
  30. 2023Deep Evidential Learning for Bayesian Quantile Regressioncited by 5
  31. 2023Uncertainty-aware Traffic Prediction under Missing Datacited by 5
  32. 2025Extreme Conformal Prediction: Reliable Intervals for High-Impact Eventscited by 5
  33. 2021Uncertainty-Aware Boosted Ensembling in Multi-Modal Settingscited by 4
  34. 2023Reliable Prediction Intervals with Directly Optimized Inductive Conformal Regression for Deep Learningcited by 4
  35. 2024SAUC: Sparsity-Aware Uncertainty Calibration for Spatiotemporal Prediction with Graph Neural Networkscited by 4
  36. 2025E-PINNs: Epistemic Physics-Informed Neural Networkscited by 4
  37. 2021Exploring Uncertainty in Deep Learning for Construction of Prediction Intervalscited by 3
  38. 2021Bayesian Neural Hawkes Process for Event Uncertainty Predictioncited by 3

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