mlsanityData to 7 Oct 2026

Conformal Prediction Bands for Multivariate Functional Data

arXiv 2106.01792 ↗First posted 3 Jun 2021stat.MEcited by 28

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Abstract (arXiv)

Motivated by the pressing request of methods able to create prediction sets in a general regression framework for a multivariate functional response and pushed by new methodological advancements in non-parametric prediction for functional data, we propose a set of conformal predictors that produce finite-sample either valid or exact multivariate simultaneous prediction bands under the mild assumption of exchangeable regression pairs. The fact that the prediction bands can be built around any regression estimator and that can be easily found in closed form yields a very widely usable method, which is fairly straightforward to implement. In addition, we first introduce and then describe a specific conformal predictor that guarantees an asymptotic result in terms of efficiency and inducing prediction bands able to modulate their width based on the local behavior and magnitude of the functional data. The method is investigated and analyzed through a simulation study and a real-world application in the field of urban mobility.

Key facts. Cited by 28 papers in the map (data through 7 Oct 2026). First posted on arXiv 3 Jun 2021.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 2; 2024: 7; 2025: 11; 2026: 5.

28 papers.

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  1. 2024Conformal prediction for multi-dimensional time series by ellipsoidal setscited by 37
  2. 2022A review of predictive uncertainty estimation with machine learningcited by 29
  3. 2024Calibrated Uncertainty Quantification for Operator Learning via Conformal Predictioncited by 25
  4. 2024Conformal Prediction: A Data Perspectivecited by 25
  5. 2025Minimum Volume Conformal Sets for Multivariate Regressioncited by 25
  6. 2024Using Uncertainty Quantification to Characterize and Improve Out-of-Domain Learning for PDEscited by 14
  7. 2022Conformal Prediction Intervals for Markov Decision Process Trajectoriescited by 12
  8. 2024Conformal Thresholded Intervals for Efficient Regressioncited by 11
  9. 2024Uncertainty Quantification of Surrogate Models using Conformal Predictioncited by 11
  10. 2025Calibrated Physics-Informed Uncertainty Quantificationcited by 8
  11. 2022Exact and Approximate Conformal Inference for Multi-Output Regressioncited by 7
  12. 2025Guaranteed prediction sets for functional surrogate modelscited by 7
16 more
  1. 2025Volume-Sorted Prediction Set: Efficient Conformal Prediction for Multi-Target Regressioncited by 6
  2. 2025Flow-based Conformal Prediction for Multi-dimensional Time Seriescited by 5
  3. 2023Conformal Loss-Controlling Predictioncited by 3
  4. 2024Uncertainty quantification in metric spacescited by 3
  5. 2025Reliable uncertainty quantification for 2D/3D anatomical landmark localization using multi-output conformal predictioncited by 2
  6. 2025Conformal and kNN Predictive Uncertainty Quantification Algorithms in Metric Spacescited by 2
  7. 2025Locally Adaptive Conformal Inference for Operator Modelscited by 2
  8. 2026Flow-Based Conformal Predictive Distributionscited by 2
  9. 2023Conformal inference for regression on Riemannian Manifoldscited by 1
  10. 2025Joint Registration and Conformal Prediction for Partially Observed Functional Datacited by 0
  11. 2025Minimax Multi-Target Conformal Prediction with Applications to Imaging Inverse Problemscited by 0
  12. 2025Multi-fidelity aerodynamic data fusion by autoencoder transfer learningcited by 0
  13. 2026Contrastive Conformal Setscited by 0
  14. 2026Conformal Robust Set Estimationcited by 0
  15. 2026Manifold Constrained Conformal Prediction for Spatial Eventscited by 0
  16. 2026SPARC: Single-Pass Scaling for Motion Forecasting with Conformal Bayesian Last Layerscited by 0