mlsanityData to 7 Oct 2026

Copula Conformal Prediction for Multi-step Time Series Forecasting

arXiv 2212.03281 ↗First posted 6 Dec 2022cs.LG stat.APcited by 28

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Abstract (arXiv)

Accurate uncertainty measurement is a key step to building robust and reliable machine learning systems. Conformal prediction is a distribution-free uncertainty quantification algorithm popular for its ease of implementation, statistical coverage guarantees, and versatility for underlying forecasters. However, existing conformal prediction algorithms for time series are limited to single-step prediction without considering the temporal dependency. In this paper, we propose a Copula Conformal Prediction algorithm for multivariate, multi-step Time Series forecasting, CopulaCPTS. We prove that CopulaCPTS has finite sample validity guarantee. On several synthetic and real-world multivariate time series datasets, we show that CopulaCPTS produces more calibrated and sharp confidence intervals for multi-step prediction tasks than existing techniques.

Key facts. Cited by 28 papers in the map (data through 7 Oct 2026). Builds on 28 of its 57 references that are in the map. First posted on arXiv 6 Dec 2022.

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28 of 57 references.

References · 28

  1. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,416
  2. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,888
  3. 2021A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantificationcited by 777
  4. 2019Argoverse: 3D Tracking and Forecasting with Rich Mapscited by 728
  5. 2016Distribution-Free Predictive Inference For Regressioncited by 657
  6. 2019Conformalized Quantile Regressioncited by 620
  7. 2015Variational Dropout and the Local Reparameterization Trickcited by 489
  8. 2020Learning Lane Graph Representations for Motion Forecastingcited by 380
  9. 2021Adaptive Conformal Inference Under Distribution Shiftcited by 360
  10. 2014Stochastic Gradient Hamiltonian Monte Carlocited by 341
  11. 2017Concrete Dropoutcited by 227
  12. 2015A Theoretically Grounded Application of Dropout in Recurrent Neural Networkscited by 161
16 more
  1. 2017Multiplicative Normalizing Flows for Variational Bayesian Neural Networkscited by 157
  2. 2022Adaptive Conformal Predictions for Time Seriescited by 155
  3. 2019High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processescited by 147
  4. 2019Distributional conformal predictioncited by 104
  5. 2019Adaptive, Distribution-Free Prediction Intervals for Deep Networkscited by 56
  6. 2020Predictive Inference Is Free with the Jackknife+-after-Bootstrapcited by 55
  7. 2021Copula-based conformal prediction for Multi-Target Regressioncited by 53
  8. 2021Conformal Uncertainty Sets for Robust Optimizationcited by 49
  9. 2021Quantifying Uncertainty in Deep Spatiotemporal Forecastingcited by 48
  10. 2021Sample-Efficient Safety Assurances using Conformal Predictioncited by 41
  11. 2022TACTiS: Transformer-Attentional Copulas for Time Seriescited by 38
  12. 2021Learning Quantile Functions without Quantile Crossing for Distribution-free Time Series Forecastingcited by 32
  13. 2021Conditional Neural Relational Inference for Interacting Systemscited by 28
  14. 2022Multivariate Quantile Function Forecastercited by 19
  15. 2020Frequentist Uncertainty in Recurrent Neural Networks via Blockwise Influence Functionscited by 18
  16. 2018PythonRobotics: a Python code collection of robotics algorithmscited by 12

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Citing papers per year: 2023: 6; 2024: 6; 2025: 8; 2026: 8.

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  1. 2023Improved Online Conformal Prediction via Strongly Adaptive Online Learningcited by 76
  2. 2023Conformal Prediction for Time Series with Modern Hopfield Networkscited by 40
  3. 2023Conformal Prediction Regions for Time Series using Linear Complementarity Programmingcited by 33
  4. 2023Non-Exchangeable Conformal Risk Controlcited by 29
  5. 2025Minimum Volume Conformal Sets for Multivariate Regressioncited by 25
  6. 2023Forking Uncertainties: Reliable Prediction and Model Predictive Control with Sequence Models via Conformal Risk Controlcited by 19
  7. 2024Bellman Conformal Inference: Calibrating Prediction Intervals For Time Seriescited by 12
  8. 2025Conditional Coverage Diagnostics for Conformal Predictioncited by 8
  9. 2024Distribution-Free Conformal Joint Prediction Regions for Neural Marked Temporal Point Processescited by 7
  10. 2024Conformal confidence sets for biomedical image segmentationcited by 6
  11. 2025Flow-based Conformal Prediction for Multi-dimensional Time Seriescited by 5
  12. 2024Conformal Off-Policy Prediction for Multi-Agent Systemscited by 3
16 more
  1. 2024Conformal Trajectory Prediction with Multi-View Data Integration in Cooperative Drivingcited by 3
  2. 2025Beyond Uncertainty Sets: Leveraging Optimal Transport to Extend Conformal Predictive Distributions to Multivariate Settingscited by 3
  3. 2026CAWI: Copula-Aligned Weight Initialization for Randomized Neural Networkscited by 3
  4. 2025Reliable uncertainty quantification for 2D/3D anatomical landmark localization using multi-output conformal predictioncited by 2
  5. 2026When Environments Shift: Safe Planning with Generative Priors and Robust Conformal Predictioncited by 2
  6. 2024Adaptive Conformal Inference for Multi-Step Ahead Time-Series Forecasting Onlinecited by 1
  7. 2025Dual-Splitting Conformal Prediction for Multi-Step Time Series Forecastingcited by 1
  8. 2025Uncertainty-Calibrated Prediction of Randomly-Timed Biomarker Trajectories with Conformal Bandscited by 1
  9. 2026Spectral Adaptive Conformal Prediction for Structured Non-Exchangeable Datacited by 1
  10. 2023Continuous Time Evidential Distributions for Irregular Time Seriescited by 0
  11. 2025Feature Fitted Online Conformal Prediction for Deep Time Series Forecasting Modelcited by 0
  12. 2026Calibrated uncertainty quantification for prosumer flexibility aggregation in ancillary service marketscited by 0
  13. 2026Conformal Prediction Algorithms for Time Series Forecasting: Methods and Benchmarkingcited by 0
  14. 2026Simulation-Augmented Multi-Step Split Conformal Prediction for Aggregated Forecastscited by 0
  15. 2026TRACE-CRC: Trajectory-Adaptive Conformal Risk Control for Multi-Step Channel State Information Predictioncited by 0
  16. 2026Multivariate conformal uncertainty propagation in multitask atomistic simulation: Successes and pitfallscited by 0