mlsanityData to 7 Oct 2026

Conformal Uncertainty Sets for Robust Optimization

arXiv 2105.14957 ↗First posted 31 May 2021stat.ME math.OC stat.MLcited by 49

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Abstract (arXiv)

Decision-making under uncertainty is hugely important for any decisions sensitive to perturbations in observed data. One method of incorporating uncertainty into making optimal decisions is through robust optimization, which minimizes the worst-case scenario over some uncertainty set. We connect conformal prediction regions to robust optimization, providing finite sample valid and conservative ellipsoidal uncertainty sets, aptly named conformal uncertainty sets. In pursuit of this connection we explicitly define Mahalanobis distance as a potential conformity score in full conformal prediction. We also compare the coverage and optimization performance of conformal uncertainty sets, specifically generated with Mahalanobis distance, to traditional ellipsoidal uncertainty sets on a collection of simulated robust optimization examples.

Key facts. Cited by 49 papers in the map (data through 7 Oct 2026). Builds on 13 of its 54 references that are in the map. First posted on arXiv 31 May 2021.

Builds on

13 of 54 references.

References · 13

  1. 2016Distribution-Free Predictive Inference For Regressioncited by 657
  2. 2019Predictive inference with the jackknife+cited by 206
  3. 2013Learning by Transductioncited by 120
  4. 2020Conformal Prediction: a Unified Review of Theory and New Challengescited by 118
  5. 2019Distributional conformal predictioncited by 104
  6. 2013A Conformal Prediction Approach to Explore Functional Datacited by 85
  7. 2013Data-Driven Robust Optimizationcited by 84
  8. 2018Exact and Robust Conformal Inference Methods for Predictive Machine Learning With Dependent Datacited by 64
  9. 2021Copula-based conformal prediction for Multi-Target Regressioncited by 53
  10. 2020Exchangeability, Conformal Prediction, and Rank Testscited by 40
  11. 2019Conformal prediction with localizationcited by 22
  12. 2017Inductive Conformal Martingales for Change-Point Detectioncited by 17
1 more
  1. 2015A Practical Guide to Robust Optimizationcited by 16

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 3; 2023: 1; 2024: 10; 2025: 18; 2026: 16.

49 papers.

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  1. 2025Decision Theoretic Foundations for Conformal Prediction: Optimal Uncertainty Quantification for Risk-Averse Agentscited by 37
  2. 2022Copula Conformal Prediction for Multi-step Time Series Forecastingcited by 28
  3. 2023Conformal Contextual Robust Optimizationcited by 25
  4. 2024Conformal Prediction: A Data Perspectivecited by 25
  5. 2025Minimum Volume Conformal Sets for Multivariate Regressioncited by 25
  6. 2025Multivariate Conformal Prediction using Optimal Transportcited by 21
  7. 2021Stable Conformal Prediction Setscited by 19
  8. 2025Optimal Transport-based Conformal Predictioncited by 19
  9. 2024End-to-end Conditional Robust Optimizationcited by 17
  10. 2024End-to-End Conformal Calibration for Optimization Under Uncertaintycited by 14
  11. 2024Semiparametric conformal predictioncited by 13
  12. 2022Conformal Methods for Quantifying Uncertainty in Spatiotemporal Data: A Surveycited by 11
37 more
  1. 2024Conformal Prediction for Stochastic Decision-Making of PV Power in Electricity Marketscited by 8
  2. 2024Conformalized Interval Arithmetic with Symmetric Calibrationcited by 8
  3. 2025Multivariate Conformal Selectioncited by 8
  4. 2022Exact and Approximate Conformal Inference for Multi-Output Regressioncited by 7
  5. 2025Volume-Sorted Prediction Set: Efficient Conformal Prediction for Multi-Target Regressioncited by 6
  6. 2025Multivariate Standardized Residuals for Conformal Predictioncited by 6
  7. 2024Powerful batch conformal prediction for classificationcited by 4
  8. 2024Conformal Prediction for Hierarchical Datacited by 4
  9. 2025JAPAN: Joint Adaptive Prediction Areas with Normalising-Flowscited by 4
  10. 2025Adaptive Coverage Policies in Conformal Predictioncited by 4
  11. 2025Calibrating Decision Robustness via Inverse Conformal Risk Controlcited by 4
  12. 2026Optimal Decision-Making Based on Prediction Setscited by 4
  13. 2024Uncertainty quantification in metric spacescited by 3
  14. 2025Beyond Uncertainty Sets: Leveraging Optimal Transport to Extend Conformal Predictive Distributions to Multivariate Settingscited by 3
  15. 2024Learning minimal volume uncertainty ellipsoidscited by 2
  16. 2025Reliable uncertainty quantification for 2D/3D anatomical landmark localization using multi-output conformal predictioncited by 2
  17. 2025Smart Surrogate Losses for Contextual Stochastic Linear Optimization with Robust Constraintscited by 2
  18. 2025Conformal and kNN Predictive Uncertainty Quantification Algorithms in Metric Spacescited by 2
  19. 2025Neural Optimal Transport Meets Multivariate Conformal Predictioncited by 2
  20. 2025Interpretable Multivariate Conformal Prediction with Fast Transductive Standardizationcited by 2
  21. 2026Conformal Prediction for Generative Models via Adaptive Cluster-Based Density Estimationcited by 2
  22. 2026Decision-calibrated prediction sets for robust power system operationscited by 2
  23. 2025Self-supervised conformal prediction for uncertainty quantification in Poisson imaging problemscited by 1
  24. 2026Bulk-Calibrated Credal Ambiguity Sets: Fast, Tractable Decision Making under Out-of-Sample Contaminationcited by 1
  25. 2026A Kernel Nonconformity Score for Multivariate Conformal Predictioncited by 1
  26. 2026Risk-Controlled Post-Processing of Decision Policiescited by 1
  27. 2026Learning Polyhedral Conformal Sets for Robust Optimizationcited by 1
  28. 2026CONTRA: Conformal Prediction Region via Normalizing Flow Transformationcited by 1
  29. 2026Conformal Risk-Averse Decision Making with Action Conditional Guaranteecited by 1
  30. 2025Conformal Mixed-Integer Constraint Learning with Feasibility Guaranteescited by 0
  31. 2026Contrastive Conformal Setscited by 0
  32. 2026TRACE: Transport Alignment Conformal Prediction via Diffusion and Flow Matching Modelscited by 0
  33. 2026Multi-Variable Conformal Prediction: Optimizing Prediction Sets without Data Splittingcited by 0
  34. 2026Conformal Risk Sharing: Certified Cost Allocation with Participation Guaranteescited by 0
  35. 2026Decision-Calibrated Conformal Uncertainty for Pacing Decisions in Streaming Advertisingcited by 0
  36. 2026Coordinate Singularities Break Conformal Coverage for Gaze and Head Posecited by 0
  37. 2026Multivariate conformal uncertainty propagation in multitask atomistic simulation: Successes and pitfallscited by 0