mlsanityData to 7 Oct 2026

Least Ambiguous Set-Valued Classifiers with Bounded Error Levels

arXiv 1609.00451 ↗First posted 2 Sep 2016stat.ME cs.LG stat.MLcited by 270

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Abstract (arXiv)

In most classification tasks there are observations that are ambiguous and therefore difficult to correctly label. Set-valued classifiers output sets of plausible labels rather than a single label, thereby giving a more appropriate and informative treatment to the labeling of ambiguous instances. We introduce a framework for multiclass set-valued classification, where the classifiers guarantee user-defined levels of coverage or confidence (the probability that the true label is contained in the set) while minimizing the ambiguity (the expected size of the output). We first derive oracle classifiers assuming the true distribution to be known. We show that the oracle classifiers are obtained from level sets of the functions that define the conditional probability of each class. Then we develop estimators with good asymptotic and finite sample properties. The proposed estimators build on existing single-label classifiers. The optimal classifier can sometimes output the empty set, but we provide two solutions to fix this issue that are suitable for various practical needs.

Key facts. Cited by 270 papers in the map (data through 7 Oct 2026). First posted on arXiv 2 Sep 2016.

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Citing papers per year: 2021: 14; 2022: 25; 2023: 24; 2024: 61; 2025: 83; 2026: 63.

270 papers.

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  1. 2021A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantificationcited by 777
  2. 2021Adaptive Conformal Inference Under Distribution Shiftcited by 360
  3. 2023Robots That Ask For Help: Uncertainty Alignment for Large Language Model Plannerscited by 298
  4. 2021Distribution-Free, Risk-Controlling Prediction Setscited by 278
  5. 2021Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Controlcited by 256
  6. 2023Conformal Prediction with Large Language Models for Multi-Choice Question Answeringcited by 131
  7. 2024Benchmarking LLMs via Uncertainty Quantificationcited by 124
  8. 2022Conformal Inference for Online Prediction with Arbitrary Distribution Shiftscited by 123
  9. 2024A Survey on Uncertainty Quantification of Large Language Models: Taxonomy, Open Research Challenges, and Future Directionscited by 115
  10. 2023Class-Conditional Conformal Prediction with Many Classescited by 109
  11. 2021Learning Optimal Conformal Classifierscited by 108
  12. 2022Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imagingcited by 107
38 more
  1. 2021Distribution-free uncertainty quantification for classification under label shiftcited by 99
  2. 2021Fair Conformal Predictors for Applications in Medical Imagingcited by 74
  3. 2024API Is Enough: Conformal Prediction for Large Language Models Without Logit-Accesscited by 68
  4. 2021Conformalized Survival Analysiscited by 53
  5. 2023Conformal Prediction for Deep Classifier via Label Rankingcited by 52
  6. 2023Federated Conformal Predictors for Distributed Uncertainty Quantificationcited by 46
  7. 2024Length Optimization in Conformal Predictioncited by 39
  8. 2022Improving Trustworthiness of AI Disease Severity Rating in Medical Imaging with Ordinal Conformal Prediction Setscited by 38
  9. 2025Decision Theoretic Foundations for Conformal Prediction: Optimal Uncertainty Quantification for Risk-Averse Agentscited by 37
  10. 2022On the Utility of Prediction Sets in Human-AI Teamscited by 34
  11. 2023Conformal prediction under ambiguous ground truthcited by 31
  12. 2022Conformal Prediction Sets with Limited False Positivescited by 28
  13. 2022Distribution Free Prediction Sets for Node Classificationcited by 28
  14. 2024Uncertainty-Aware Evaluation for Vision-Language Modelscited by 28
  15. 2021Set-valued classification -- overview via a unified frameworkcited by 27
  16. 2024Provably Robust Conformal Prediction with Improved Efficiencycited by 27
  17. 2023Designing Decision Support Systems Using Counterfactual Prediction Setscited by 26
  18. 2024Introspective Planning: Aligning Robots' Uncertainty with Inherent Task Ambiguitycited by 26
  19. 2022Efficient and Differentiable Conformal Prediction with General Function Classescited by 25
  20. 2023Probabilistically robust conformal predictioncited by 25
  21. 2024Towards Human-AI Complementarity with Prediction Setscited by 25
  22. 2024Conformal Prediction: A Data Perspectivecited by 25
  23. 2025Minimum Volume Conformal Sets for Multivariate Regressioncited by 25
  24. 2023Adaptive conformal classification with noisy labelscited by 24
  25. 2024Adaptive Bounding Box Uncertainties via Two-Step Conformal Predictioncited by 23
  26. 2025E-Values Expand the Scope of Conformal Predictioncited by 23
  27. 2022Prediction Sets Adaptive to Unknown Covariate Shiftcited by 22
  28. 2024Conformalized Credal Set Predictorscited by 21
  29. 2024An Information Theoretic Perspective on Conformal Predictioncited by 21
  30. 2024Trustworthy Classification through Rank-Based Conformal Prediction Setscited by 20
  31. 2022Integrative conformal p-values for powerful out-of-distribution testing with labeled outlierscited by 19
  32. 2023PAC Prediction Sets Under Label Shiftcited by 19
  33. 2024Conformal Semantic Image Segmentation: Post-hoc Quantification of Predictive Uncertaintycited by 19
  34. 2025CP-Router: An Uncertainty-Aware Router Between LLM and LRMcited by 19
  35. 2024Probabilistically Correct Language-based Multi-Robot Planning using Conformal Predictioncited by 18
  36. 2024Conformal Prediction for Class-wise Coverage via Augmented Label Rank Calibrationcited by 18
  37. 2024Sample then Identify: A General Framework for Risk Control and Assessment in Multimodal Large Language Modelscited by 18
  38. 2022MAPIE: an open-source library for distribution-free uncertainty quantificationcited by 17

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