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Copula-based conformal prediction for Multi-Target Regression

arXiv 2101.12002 ↗First posted 28 Jan 2021cs.LG cs.AI stat.MLcited by 53

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Abstract (arXiv)

There are relatively few works dealing with conformal prediction for multi-task learning issues, and this is particularly true for multi-target regression. This paper focuses on the problem of providing valid (i.e., frequency calibrated) multi-variate predictions. To do so, we propose to use copula functions applied to deep neural networks for inductive conformal prediction. We show that the proposed method ensures efficiency and validity for multi-target regression problems on various data sets.

Key facts. Cited by 53 papers in the map (data through 7 Oct 2026). Builds on 6 of its 51 references that are in the map. First posted on arXiv 28 Jan 2021.

Builds on

6 of 51 references.

References · 6

  1. 2017An Overview of Multi-Task Learning in Deep Neural Networkscited by 791
  2. 2017Self-Normalizing Neural Networkscited by 591
  3. 2013Learning by Transductioncited by 120
  4. 2014Regression Conformal Prediction with Nearest Neighbourscited by 59
  5. 2017CLTune: A Generic Auto-Tuner for OpenCL Kernelscited by 25
  6. 2020Training conformal predictorscited by 20

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 5; 2023: 4; 2024: 11; 2025: 20; 2026: 12.

53 papers.

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  1. 2021Conformal Uncertainty Sets for Robust Optimizationcited by 49
  2. 2022Probabilistic Conformal Prediction Using Conditional Random Samplescited by 47
  3. 2024Conformal prediction for multi-dimensional time series by ellipsoidal setscited by 37
  4. 2022Copula Conformal Prediction for Multi-step Time Series Forecastingcited by 28
  5. 2024Conformal Prediction: A Data Perspectivecited by 25
  6. 2025Minimum Volume Conformal Sets for Multivariate Regressioncited by 25
  7. 2024Adaptive Bounding Box Uncertainties via Two-Step Conformal Predictioncited by 23
  8. 2025Multivariate Conformal Prediction using Optimal Transportcited by 21
  9. 2025Optimal Transport-based Conformal Predictioncited by 19
  10. 2022MAPIE: an open-source library for distribution-free uncertainty quantificationcited by 17
  11. 2025Rectifying Conformity Scores for Better Conditional Coveragecited by 17
  12. 2024Semiparametric conformal predictioncited by 13
38 more
  1. 2022Conformal Methods for Quantifying Uncertainty in Spatiotemporal Data: A Surveycited by 11
  2. 2024Uncertainty Quantification of Surrogate Models using Conformal Predictioncited by 11
  3. 2024Your copula is a classifier in disguise: classification-based copula density estimationcited by 8
  4. 2025Conditional Coverage Diagnostics for Conformal Predictioncited by 8
  5. 2022Exact and Approximate Conformal Inference for Multi-Output Regressioncited by 7
  6. 2025Guaranteed prediction sets for functional surrogate modelscited by 7
  7. 2023Max-Rank: Efficient Multiple Testing for Conformal Predictioncited by 6
  8. 2025Volume-Sorted Prediction Set: Efficient Conformal Prediction for Multi-Target Regressioncited by 6
  9. 2025Document Summarization with Conformal Importance Guaranteescited by 6
  10. 2025Flow-based Conformal Prediction for Multi-dimensional Time Seriescited by 5
  11. 2024Powerful batch conformal prediction for classificationcited by 4
  12. 2024Conformal Prediction for Hierarchical Datacited by 4
  13. 2025JAPAN: Joint Adaptive Prediction Areas with Normalising-Flowscited by 4
  14. 2025Calibrating Decision Robustness via Inverse Conformal Risk Controlcited by 4
  15. 2023Conformal Loss-Controlling Predictioncited by 3
  16. 2023Uncertainty quantification in automated valuation models with spatially weighted conformal predictioncited by 3
  17. 2024JANET: Joint Adaptive predictioN-region Estimation for Time-seriescited by 3
  18. 2025Topology-Aware Conformal Prediction for Stream Networkscited by 3
  19. 2025Beyond Uncertainty Sets: Leveraging Optimal Transport to Extend Conformal Predictive Distributions to Multivariate Settingscited by 3
  20. 2024Learning minimal volume uncertainty ellipsoidscited by 2
  21. 2025Reliable uncertainty quantification for 2D/3D anatomical landmark localization using multi-output conformal predictioncited by 2
  22. 2025Zono-Conformal Prediction: Zonotope-Based Uncertainty Quantification for Regression and Classification Taskscited by 2
  23. 2025Neural Optimal Transport Meets Multivariate Conformal Predictioncited by 2
  24. 2025Interpretable Multivariate Conformal Prediction with Fast Transductive Standardizationcited by 2
  25. 2026Conformal Prediction for Generative Models via Adaptive Cluster-Based Density Estimationcited by 2
  26. 2026Geometry-Aware Uncertainty Quantification via Conformal Prediction on Manifoldscited by 2
  27. 2024Conformalised Conditional Normalising Flows for Joint Prediction Regions in time seriescited by 1
  28. 2025SpeedCP: Fast Kernel-based Conditional Conformal Predictioncited by 1
  29. 2026A Kernel Nonconformity Score for Multivariate Conformal Predictioncited by 1
  30. 2023Learning Nonparametric High-Dimensional Generative Models: The Empirical-Beta-Copula Autoencodercited by 0
  31. 2025Assumption-free fidelity bounds for hardware noise characterizationcited by 0
  32. 2025Minimax Multi-Target Conformal Prediction with Applications to Imaging Inverse Problemscited by 0
  33. 2026Elements of Conformal Predictioncited by 0
  34. 2026TRACE: Transport Alignment Conformal Prediction via Diffusion and Flow Matching Modelscited by 0
  35. 2026Multi-Variable Conformal Prediction: Optimizing Prediction Sets without Data Splittingcited by 0
  36. 2026When Is a Conformal Guarantee Fair? Auditing Silent Subgroup Under-Coverage in Alzheimer's Disease Longitudinal Predictioncited by 0
  37. 2026SPACE: Sample-cloud Predictive Adaptive Conformal Ellipsoids for Multivariate Time-Series Forecastingcited by 0
  38. 2026Scaling-Score Conformal Prediction for Multi-Target Regressioncited by 0

50 most cited of 53 All 53 (JSON)