mlsanityData to 7 Oct 2026

Bellman Conformal Inference: Calibrating Prediction Intervals For Time Series

arXiv 2402.05203 ↗First posted 7 Feb 2024cs.LG stat.MLcited by 12

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Abstract (arXiv)

We introduce Bellman Conformal Inference (BCI), a framework that wraps around any time series forecasting models and provides approximately calibrated prediction intervals. Unlike existing methods, BCI is able to leverage multi-step ahead forecasts and explicitly optimize the average interval lengths by solving a one-dimensional stochastic control problem (SCP) at each time step. In particular, we use the dynamic programming algorithm to find the optimal policy for the SCP. We prove that BCI achieves long-term coverage under arbitrary distribution shifts and temporal dependence, even with poor multi-step ahead forecasts. We find empirically that BCI avoids uninformative intervals that have infinite lengths and generates substantially shorter prediction intervals in multiple applications when compared with existing methods.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). Builds on 24 of its 45 references that are in the map. First posted on arXiv 7 Feb 2024.

Builds on

24 of 45 references.

References · 24

  1. 2017Attention Is All You Needcited by 59,932
  2. 2017DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networkscited by 1,004
  3. 2021A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantificationcited by 777
  4. 2016Distribution-Free Predictive Inference For Regressioncited by 657
  5. 2019Conformal Prediction Under Covariate Shiftcited by 511
  6. 2021Adaptive Conformal Inference Under Distribution Shiftcited by 360
  7. 2022Conformal prediction beyond exchangeabilitycited by 348
  8. 2022Conformal Risk Controlcited by 290
  9. 2021Distribution-Free, Risk-Controlling Prediction Setscited by 278
  10. 2021Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Controlcited by 256
  11. 2022Adaptive Conformal Predictions for Time Seriescited by 155
  12. 2020Conformal Inference of Counterfactuals and Individual Treatment Effectscited by 150
12 more
  1. 2022Conformal Inference for Online Prediction with Arbitrary Distribution Shiftscited by 123
  2. 2021Darts: User-Friendly Modern Machine Learning for Time Seriescited by 90
  3. 2019Nested conformal prediction and quantile out-of-bag ensemble methodscited by 88
  4. 2013A Conformal Prediction Approach to Explore Functional Datacited by 85
  5. 2023Conformal PID Control for Time Series Predictioncited by 85
  6. 2022Sequential Predictive Conformal Inference for Time Seriescited by 71
  7. 2018Exact and Robust Conformal Inference Methods for Predictive Machine Learning With Dependent Datacited by 64
  8. 2021Conformalized Survival Analysiscited by 53
  9. 2022Achieving Risk Control in Online Learning Settingscited by 38
  10. 2022Copula Conformal Prediction for Multi-step Time Series Forecastingcited by 28
  11. 2022Conformal Prediction Intervals for Markov Decision Process Trajectoriescited by 12
  12. 2023Multi-step ahead prediction intervals for non-parametric autoregressions via bootstrap: consistency, debiasing and pertinencecited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 3; 2025: 7; 2026: 2.

12 papers.

  1. 2024Conformal Prediction: A Data Perspectivecited by 25
  2. 2024Kernel-based Optimally Weighted Conformal Time-Series Predictioncited by 12
  3. 2025Error-quantified Conformal Inference for Time Seriescited by 11
  4. 2025Topology-Aware Conformal Prediction for Stream Networkscited by 3
  5. 2025Calibrated Multi-Level Quantile Forecastingcited by 2
  6. 2025Bellman Calibration for V-Learning in Offline Reinforcement Learningcited by 2
  7. 2026Spectral Adaptive Conformal Prediction for Structured Non-Exchangeable Datacited by 1
  8. 2024Distribution-Free Predictive Inference under Unknown Temporal Driftcited by 0
  9. 2025Feature Fitted Online Conformal Prediction for Deep Time Series Forecasting Modelcited by 0
  10. 2025Online Conformal Model Selection for Nonstationary Time Seriescited by 0
  11. 2025Optimization-based Online Conformal Prediction for Multi-step Forecastingcited by 0
  12. 2026Parameter-Free and Group Conditional Online Conformal Predictioncited by 0