mlsanityData to 7 Oct 2026

Prediction and outlier detection in classification problems

arXiv 1905.04396 ↗First posted 10 May 2019stat.ME math.ST stat.APcited by 44

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Abstract (arXiv)

We consider the multi-class classification problem when the training data and the out-of-sample test data may have different distributions and propose a method called BCOPS (balanced and conformal optimized prediction sets). BCOPS constructs a prediction set C(x) as a subset of class labels, possibly empty. It tries to optimize the out-of-sample performance, aiming to include the correct class as often as possible, but also detecting outliers x, for which the method returns no prediction (corresponding to C(x) equal to the empty set). The proposed method combines supervised-learning algorithms with the method of conformal prediction to minimize a misclassification loss averaged over the out-of-sample distribution. The constructed prediction sets have a finite-sample coverage guarantee without distributional assumptions. We also propose a method to estimate the outlier detection rate of a given method. We prove asymptotic consistency and optimality of our proposals under suitable assumptions and illustrate our methods on real data examples.

Key facts. Cited by 44 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 May 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 6; 2022: 5; 2023: 9; 2024: 8; 2025: 12; 2026: 4.

44 papers.

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  1. 2021A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantificationcited by 777
  2. 2021Distribution-Free, Risk-Controlling Prediction Setscited by 278
  3. 2021Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Controlcited by 256
  4. 2021Testing for Outliers with Conformal p-valuescited by 133
  5. 2023Class-Conditional Conformal Prediction with Many Classescited by 109
  6. 2021Distribution-free uncertainty quantification for classification under label shiftcited by 99
  7. 2022Training Uncertainty-Aware Classifiers with Conformalized Deep Learningcited by 62
  8. 2023Conformal Prediction for Deep Classifier via Label Rankingcited by 52
  9. 2022iDECODe: In-distribution Equivariance for Conformal Out-of-distribution Detectioncited by 27
  10. 2023Probabilistically robust conformal predictioncited by 25
  11. 2024Conformal Prediction: A Data Perspectivecited by 25
  12. 2023Adaptive conformal classification with noisy labelscited by 24
32 more
  1. 2022Integrative conformal p-values for powerful out-of-distribution testing with labeled outlierscited by 19
  2. 2021Private Prediction Setscited by 16
  3. 2023Derandomized Novelty Detection with FDR Control via Conformal E-valuescited by 15
  4. 2023Conformal inference is (almost) free for neural networks trained with early stoppingcited by 14
  5. 2025Backward Conformal Predictioncited by 13
  6. 2024Does confidence calibration improve conformal prediction?cited by 12
  7. 2025Conformal Inference under High-Dimensional Covariate Shifts via Likelihood-Ratio Regularizationcited by 11
  8. 2025Synthetic-Powered Predictive Inferencecited by 9
  9. 2023SymmPI: Predictive Inference for Data with Group Symmetriescited by 8
  10. 2024Out-of-Distribution Detection Should Use Conformal Prediction (and Vice-versa?)cited by 7
  11. 2025Conformal Information Pursuit for Interactively Guiding Large Language Modelscited by 7
  12. 2024Conformal Predictive Programming for Chance Constrained Optimizationcited by 6
  13. 2025Conformal Prediction Meets Long-tail Classificationcited by 5
  14. 2022Distribution-Free Finite-Sample Guarantees and Split Conformal Predictioncited by 4
  15. 2024Leave-One-Out-, Bootstrap- and Cross-Conformal Anomaly Detectorscited by 4
  16. 2025Exploring the Noise Robustness of Online Conformal Predictioncited by 4
  17. 2024Efficient Online Set-valued Classification with Bandit Feedbackcited by 3
  18. 2025Conformal Inference for Open-Set and Imbalanced Classificationcited by 3
  19. 2023Conformalized Semi-supervised Random Forest for Classification and Abnormality Detectioncited by 2
  20. 2025Adapting Rule Representation With Four-Parameter Beta Distribution for Learning Classifier Systemscited by 1
  21. 2025Set Valued Predictions For Robust Domain Generalizationcited by 1
  22. 2022Learning Acceptance Regions for Many Classes with Anomaly Detectioncited by 0
  23. 2023A Saliency-based Clustering Framework for Identifying Aberrant Predictionscited by 0
  24. 2024Adjusting Regression Models for Conditional Uncertainty Calibrationcited by 0
  25. 2024Conjunction Subspaces Test for Conformal and Selective Classificationcited by 0
  26. 2025Semiparametric Learning from Open-Set Label Shift Datacited by 0
  27. 2025On the Adversarial Robustness of Learning-based Conformal Novelty Detectioncited by 0
  28. 2025MMDCP: A Distribution-free Approach to Outlier Detection and Classification with Coverage Guarantees and SCW-FDR Controlcited by 0
  29. 2026Softmax is not Enough (for Adaptive Conformal Classification)cited by 0
  30. 2026ConformalHDC: Uncertainty-Aware Hyperdimensional Computing with Application to Neural Decodingcited by 0
  31. 2026Conformal Robust Set Estimationcited by 0
  32. 2026Mitigating Class-Tail Undercoverage in Medical Vision-Language Models under Clinical Shiftcited by 0