mlsanityData to 7 Oct 2026

Learning Prediction Intervals for Regression: Generalization and Calibration

arXiv 2102.13625 ↗First posted 26 Feb 2021stat.ML cs.LGcited by 16

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Abstract (arXiv)

We study the generation of prediction intervals in regression for uncertainty quantification. This task can be formalized as an empirical constrained optimization problem that minimizes the average interval width while maintaining the coverage accuracy across data. We strengthen the existing literature by studying two aspects of this empirical optimization. First is a general learning theory to characterize the optimality-feasibility tradeoff that encompasses Lipschitz continuity and VC-subgraph classes, which are exemplified in regression trees and neural networks. Second is a calibration machinery and the corresponding statistical theory to optimally select the regularization parameter that manages this tradeoff, which bypasses the overfitting issues in previous approaches in coverage attainment. We empirically demonstrate the strengths of our interval generation and calibration algorithms in terms of testing performances compared to existing benchmarks.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). Builds on 26 of its 67 references that are in the map. First posted on arXiv 26 Feb 2021.

Builds on

26 of 67 references.

References · 26

  1. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,416
  2. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,888
  3. 2017Spectrally-normalized margin bounds for neural networkscited by 681
  4. 2016Distribution-Free Predictive Inference For Regressioncited by 657
  5. 2019Conformalized Quantile Regressioncited by 620
  6. 2018Regularisation of Neural Networks by Enforcing Lipschitz Continuitycited by 311
  7. 2017Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networkscited by 304
  8. 2015Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networkscited by 295
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  12. 2018Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networkscited by 193
14 more
  1. 2017Formal Guarantees on the Robustness of a Classifier against Adversarial Manipulationcited by 182
  2. 2017Spectral Norm Regularization for Improving the Generalizability of Deep Learningcited by 178
  3. 2018High-Quality Prediction Intervals for Deep Learning: A Distribution-Free, Ensembled Approachcited by 117
  4. 2019Nested conformal prediction and quantile out-of-bag ensemble methodscited by 88
  5. 2013A Conformal Prediction Approach to Explore Functional Datacited by 85
  6. 2019Adaptive, Distribution-Free Prediction Intervals for Deep Networkscited by 56
  7. 2020Predictive Inference Is Free with the Jackknife+-after-Bootstrapcited by 55
  8. 2018Limitations of the Lipschitz constant as a defense against adversarial examplescited by 48
  9. 2020Discriminative Jackknife: Quantifying Uncertainty in Deep Learning via Higher-Order Influence Functionscited by 34
  10. 2020Decision trees as partitioning machines to characterize their generalization propertiescited by 12
  11. 2017liquidSVM: A Fast and Versatile SVM packagecited by 7
  12. 2017Discriminative Learning of Prediction Intervalscited by 5
  13. 2019HDI-Forest: Highest Density Interval Regression Forestcited by 2
  14. 2019Combating Conservativeness in Data-Driven Optimization under Uncertainty: A Solution Path Approachcited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 2; 2023: 6; 2024: 2; 2025: 2; 2026: 2.

16 papers.

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  1. 2021Adaptive Conformal Inference Under Distribution Shiftcited by 360
  2. 2023A Survey on Uncertainty Quantification Methods for Deep Learningcited by 78
  3. 2022Training Uncertainty-Aware Classifiers with Conformalized Deep Learningcited by 62
  4. 2023Conformal Prediction for Deep Classifier via Label Rankingcited by 52
  5. 2022Efficient and Differentiable Conformal Prediction with General Function Classescited by 25
  6. 2023Improving Uncertainty Quantification of Deep Classifiers via Neighborhood Conformal Prediction: Novel Algorithm and Theoretical Analysiscited by 16
  7. 2021Quantifying Epistemic Uncertainty in Deep Learningcited by 10
  8. 2023Efficient Uncertainty Quantification and Reduction for Over-Parameterized Neural Networkscited by 10
  9. 2023UTOPIA: Universally Trainable Optimal Prediction Intervals Aggregationcited by 8
  10. 2025Collaborative Bayesian Optimization via Wasserstein Barycenterscited by 7
  11. 2025Extreme Conformal Prediction: Reliable Intervals for High-Impact Eventscited by 5
  12. 2023Likelihood Annealing: Fast Calibrated Uncertainty for Regressioncited by 3
4 more
  1. 2024Adjusting Regression Models for Conditional Uncertainty Calibrationcited by 0
  2. 2024Data-light Uncertainty Set Merging with Admissibilitycited by 0
  3. 2026Softmax is not Enough (for Adaptive Conformal Classification)cited by 0
  4. 2026Bi-Level Chaotic Fusion Based Graph Convolutional Network for Stock Market Prediction Intervalcited by 0