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Bellman Conformal Inference: Calibrating Prediction Intervals For Time Series

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arxiv 2402.05203 v2 pith:R6AKCZOG submitted 2024-02-07 cs.LG stat.ML

Zitong Yang , Emmanuel Candès , Lihua Lei This is my paper · ORCID
classification cs.LGstat.ML
keywords intervalspredictiontimeaheadbellmanconformalexistingfind
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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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Parameter-Free and Group Conditional Online Conformal Prediction

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    POGO uses multi-portfolio wealth maximization to produce a single sequence of radii that achieve the strongest known finite-time group-conditional coverage without any learning-rate hyperparameter.

  2. Error-quantified Conformal Inference for Time Series

    stat.ML 2025-02 conditional novelty 5.0 of 10

    ECI adds a smoothed error-quantification term to the online conformal update rule and proves distribution-free long-run coverage bounds, yielding tighter prediction sets on real time-series benchmarks.

  3. Predictive Inference With Fast Feature Conformal Prediction

    cs.LG 2024-12 conditional novelty 5.0 of 10

    FFCP approximates feature conformal prediction with a gradient-normalized score, cutting runtime about 50x while maintaining coverage guarantees.

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