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Conformal Inference for Online Prediction with Arbitrary Distribution Shifts

arXiv 2208.08401 ↗First posted 17 Aug 2022stat.ME cs.LGcited by 123

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Abstract (arXiv)

We consider the problem of forming prediction sets in an online setting where the distribution generating the data is allowed to vary over time. Previous approaches to this problem suffer from over-weighting historical data and thus may fail to quickly react to the underlying dynamics. Here we correct this issue and develop a novel procedure with provably small regret over all local time intervals of a given width. We achieve this by modifying the adaptive conformal inference (ACI) algorithm of Gibbs and Cand`es (2021) to contain an additional step in which the step-size parameter of ACI's gradient descent update is tuned over time. Crucially, this means that unlike ACI, which requires knowledge of the rate of change of the data-generating mechanism, our new procedure is adaptive to both the size and type of the distribution shift. Our methods are highly flexible and can be used in combination with any baseline predictive algorithm that produces point estimates or estimated quantiles of the target without the need for distributional assumptions. We test our techniques on two real-world datasets aimed at predicting stock market volatility and COVID-19 case counts and find that they are robust and adaptive to real-world distribution shifts.

Key facts. Cited by 123 papers in the map (data through 7 Oct 2026). Builds on 16 of its 30 references that are in the map. First posted on arXiv 17 Aug 2022.

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16 of 30 references.

References · 16

  1. 2020WILDS: A Benchmark of in-the-Wild Distribution Shiftscited by 1,366
  2. 2019Introduction to Online Convex Optimizationcited by 793
  3. 2019Conformalized Quantile Regressioncited by 620
  4. 2019Conformal Prediction Under Covariate Shiftcited by 511
  5. 2021Adaptive Conformal Inference Under Distribution Shiftcited by 360
  6. 2022Conformal prediction beyond exchangeabilitycited by 348
  7. 2016Least Ambiguous Set-Valued Classifiers with Bounded Error Levelscited by 270
  8. 2019Predictive inference with the jackknife+cited by 206
  9. 2022Adaptive Conformal Predictions for Time Seriescited by 155
  10. 2021Distribution-free uncertainty quantification for classification under label shiftcited by 99
  11. 2022Practical Adversarial Multivalid Conformal Predictioncited by 65
  12. 2018Exact and Robust Conformal Inference Methods for Predictive Machine Learning With Dependent Datacited by 64
4 more
  1. 2022Doubly Robust Calibration of Prediction Sets under Covariate Shiftcited by 40
  2. 2020Adaptive Regret for Control of Time-Varying Dynamicscited by 38
  3. 2014Optimal learning with Bernstein Online Aggregationcited by 35
  4. 2022Conformal Prediction with Temporal Quantile Adjustmentscited by 25

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 12; 2024: 38; 2025: 38; 2026: 34.

123 papers.

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  1. 2023Conformal PID Control for Time Series Predictioncited by 85
  2. 2023Improved Online Conformal Prediction via Strongly Adaptive Online Learningcited by 76
  3. 2024Online conformal prediction with decaying step sizescited by 53
  4. 2024Conformal Prediction for Natural Language Processing: A Surveycited by 52
  5. 2023High-Dimensional Prediction for Sequential Decision Makingcited by 41
  6. 2023Conformal Prediction Regions for Time Series using Linear Complementarity Programmingcited by 33
  7. 2023Non-Exchangeable Conformal Risk Controlcited by 29
  8. 2022Distribution Free Prediction Sets for Node Classificationcited by 28
  9. 2024Conformal Validity Guarantees Exist for Any Data Distribution (and How to Find Them)cited by 26
  10. 2024Conformal Prediction: A Data Perspectivecited by 25
  11. 2023Adaptive conformal classification with noisy labelscited by 24
  12. 2024Conformal Prediction for Class-wise Coverage via Augmented Label Rank Calibrationcited by 18
38 more
  1. 2025Out-of-Distribution Generalization in Time Series: A Surveycited by 15
  2. 2023Conformal inference is (almost) free for neural networks trained with early stoppingcited by 14
  3. 2024Active, anytime-valid risk controlling prediction setscited by 14
  4. 2025Wasserstein-regularized Conformal Prediction under General Distribution Shiftcited by 14
  5. 2025The Relationship between No-Regret Learning and Online Conformal Predictioncited by 13
  6. 2024Discounted Adaptive Online Learning: Towards Better Regularizationcited by 12
  7. 2024Bellman Conformal Inference: Calibrating Prediction Intervals For Time Seriescited by 12
  8. 2024Kernel-based Optimally Weighted Conformal Time-Series Predictioncited by 12
  9. 2024Split Conformal Prediction under Data Contaminationcited by 12
  10. 2024Conformal online model aggregationcited by 11
  11. 2024Conformalized Interactive Imitation Learning: Handling Expert Shift and Intermittent Feedbackcited by 11
  12. 2025Error-quantified Conformal Inference for Time Seriescited by 11
  13. 2025Conformal Prediction under Levy-Prokhorov Distribution Shifts: Robustness to Local and Global Perturbationscited by 11
  14. 2024Uncertainty quantification for probabilistic machine learning in earth observation using conformal predictioncited by 9
  15. 2025Predictive inference for time series: why is split conformal effective despite temporal dependence?cited by 9
  16. 2024SoNIC: Safe Social Navigation with Adaptive Conformal Inference and Constrained Reinforcement Learningcited by 8
  17. 2024Multi-model Ensemble Conformal Prediction in Dynamic Environmentscited by 8
  18. 2025Conformal Prediction and Human Decision Makingcited by 8
  19. 2025Direct Prediction Set Minimization via Bilevel Conformal Classifier Trainingcited by 8
  20. 2023Empirically Validating Conformal Prediction on Modern Vision Architectures Under Distribution Shift and Long-tailed Datacited by 7
  21. 2024Stochastic Online Conformal Prediction with Semi-Bandit Feedbackcited by 7
  22. 2025Conformal Information Pursuit for Interactively Guiding Large Language Modelscited by 7
  23. 2024Adapting Prediction Sets to Distribution Shifts Without Labelscited by 6
  24. 2023Post-selection Inference for Conformal Prediction: Trading off Coverage for Precisioncited by 5
  25. 2023Conformal Policy Learning for Sensorimotor Control Under Distribution Shiftscited by 5
  26. 2024Conformal Predictive Systems Under Covariate Shiftcited by 5
  27. 2024Conformal Distributed Remote Inference in Sensor Networks Under Reliability and Communication Constraintscited by 5
  28. 2025WQLCP: Weighted Adaptive Conformal Prediction for Robust Uncertainty Quantification Under Distribution Shiftscited by 5
  29. 2025Online Conformal Prediction with Efficiency Guaranteescited by 5
  30. 2025Towards Generalizable Safety in Crowd Navigation via Conformal Uncertainty Handlingcited by 5
  31. 2024Uncertainty Quantification for Neurosymbolic Programs via Compositional Conformal Predictioncited by 4
  32. 2024CHAMP: Conformalized 3D Human Multi-Hypothesis Pose Estimatorscited by 4
  33. 2024Adaptive Conformal Inference by Particle Filtering under Hidden Markov Modelscited by 4
  34. 2024Conformal Prediction for Hierarchical Datacited by 4
  35. 2025Exploring the Noise Robustness of Online Conformal Predictioncited by 4
  36. 2025Valid Selection among Conformal Setscited by 4
  37. 2025Non-exchangeable Conformal Prediction with Optimal Transport: Tackling Distribution Shifts with Unlabeled Datacited by 4
  38. 2025Conformal Prediction for Time-series Forecasting with Change Pointscited by 4

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