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A Conformal Prediction Approach to Explore Functional Data

arXiv 1302.6452 ↗First posted 26 Feb 2013stat.ML cs.LGcited by 85

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Abstract (arXiv)

This paper applies conformal prediction techniques to compute simultaneous prediction bands and clustering trees for functional data. These tools can be used to detect outliers and clusters. Both our prediction bands and clustering trees provide prediction sets for the underlying stochastic process with a guaranteed finite sample behavior, under no distributional assumptions. The prediction sets are also informative in that they correspond to the high density region of the underlying process. While ordinary conformal prediction has high computational cost for functional data, we use the inductive conformal predictor, together with several novel choices of conformity scores, to simplify the computation. Our methods are illustrated on some real data examples.

Key facts. Cited by 85 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 Feb 2013.

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Citing papers per year: 2021: 11; 2022: 16; 2023: 13; 2024: 16; 2025: 14; 2026: 15.

85 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. 2021Learning Optimal Conformal Classifierscited by 108
  6. 2022Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imagingcited by 107
  7. 2023Conformal Prediction for Deep Classifier via Label Rankingcited by 52
  8. 2021Conformal Uncertainty Sets for Robust Optimizationcited by 49
  9. 2022Probabilistic Conformal Prediction Using Conditional Random Samplescited by 47
  10. 2021PAC Prediction Sets Under Covariate Shiftcited by 42
  11. 2022Improving Trustworthiness of AI Disease Severity Rating in Medical Imaging with Ordinal Conformal Prediction Setscited by 38
  12. 2022Predictive Inference with Feature Conformal Predictioncited by 33
38 more
  1. 2022Conformal Prediction with Temporal Quantile Adjustmentscited by 25
  2. 2024Calibrated Uncertainty Quantification for Operator Learning via Conformal Predictioncited by 25
  3. 2024Conformal Prediction: A Data Perspectivecited by 25
  4. 2025Minimum Volume Conformal Sets for Multivariate Regressioncited by 25
  5. 2022Prediction Sets Adaptive to Unknown Covariate Shiftcited by 22
  6. 2022Semantic uncertainty intervals for disentangled latent spacescited by 22
  7. 2024An Information Theoretic Perspective on Conformal Predictioncited by 21
  8. 2022Split Localized Conformal Predictioncited by 20
  9. 2023PAC Prediction Sets Under Label Shiftcited by 19
  10. 2021Private Prediction Setscited by 16
  11. 2021Learning Prediction Intervals for Regression: Generalization and Calibrationcited by 16
  12. 2022Conformal Off-policy Predictioncited by 14
  13. 2023Conformal Prediction for Network-Assisted Regressioncited by 14
  14. 2023On the Expected Size of Conformal Prediction Setscited by 13
  15. 2024Semiparametric conformal predictioncited by 13
  16. 2022Conformal Prediction Intervals for Markov Decision Process Trajectoriescited by 12
  17. 2022Posterior-Variance-Based Error Quantification for Inverse Problems in Imagingcited by 12
  18. 2024Bellman Conformal Inference: Calibrating Prediction Intervals For Time Seriescited by 12
  19. 2025Conformal Inference under High-Dimensional Covariate Shifts via Likelihood-Ratio Regularizationcited by 11
  20. 2021Quantifying Epistemic Uncertainty in Deep Learningcited by 10
  21. 2023Efficient Uncertainty Quantification and Reduction for Over-Parameterized Neural Networkscited by 10
  22. 2024Conformal Generative Modeling with Improved Sample Efficiency through Sequential Greedy Filteringcited by 10
  23. 2022Conformal Prediction Intervals with Temporal Dependencecited by 9
  24. 2025Synthetic-Powered Predictive Inferencecited by 9
  25. 2023Adaptive Conformal Regression with Jackknife+ Rescaled Scorescited by 8
  26. 2023SymmPI: Predictive Inference for Data with Group Symmetriescited by 8
  27. 2024Conformal Risk Control for Ordinal Classificationcited by 8
  28. 2022Conformal Prediction Bands for Two-Dimensional Functional Time Seriescited by 7
  29. 2022Exact and Approximate Conformal Inference for Multi-Output Regressioncited by 7
  30. 2025Conformal Information Pursuit for Interactively Guiding Large Language Modelscited by 7
  31. 2023Distribution-free risk assessment of regression-based machine learning algorithmscited by 6
  32. 2024Conformal Predictive Programming for Chance Constrained Optimizationcited by 6
  33. 2024Selecting informative conformal prediction sets with false coverage rate controlcited by 6
  34. 2024Two-stage Risk Control with Application to Ranked Retrievalcited by 6
  35. 2025Enhancing Trustworthiness of Graph Neural Networks with Rank-Based Conformal Trainingcited by 6
  36. 2023Efficient and Multiply Robust Risk Estimation under General Forms of Dataset Shiftcited by 5
  37. 2023Conformalized Deep Splines for Optimal and Efficient Prediction Setscited by 5
  38. 2024Conformalized Answer Set Prediction for Knowledge Graph Embeddingcited by 5

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