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Conformal prediction for multi-dimensional time series by ellipsoidal sets

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arxiv 2403.03850 v2 pith:FJQSTR6L submitted 2024-03-06 stat.ML cs.LG

Chen Xu , Hanyang Jiang , Yao Xie This is my paper · ORCID
classification stat.MLcs.LG
keywords predictionmultivariateseriestimeconformalcoveragemethodmultidimspci
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abstract

Conformal prediction (CP) has been a popular method for uncertainty quantification because it is distribution-free, model-agnostic, and theoretically sound. For forecasting problems in supervised learning, most CP methods focus on building prediction intervals for univariate responses. In this work, we develop a sequential CP method called $\texttt{MultiDimSPCI}$ that builds prediction $\textit{regions}$ for a multivariate response, especially in the context of multivariate time series, which are not exchangeable. Theoretically, we estimate $\textit{finite-sample}$ high-probability bounds on the conditional coverage gap. Empirically, we demonstrate that $\texttt{MultiDimSPCI}$ maintains valid coverage on a wide range of multivariate time series while producing smaller prediction regions than CP and non-CP baselines.

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Cited by 6 Pith papers

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

  1. Conformal Prediction for Hierarchical Data

    stat.ML 2024-11 conditional novelty 7.0 of 10

    Projecting non-conformity scores onto the coherent subspace of a hierarchy makes split-conformal prediction regions smaller while preserving finite-sample coverage, under i.i.d. data and, for the efficiency results, e...

  2. SpeedCP: Fast Kernel-based Conditional Conformal Prediction

    stat.ME 2025-09 conditional novelty 6.0 of 10

    SpeedCP traces the regularization and score solution paths of RKHS quantile regression, making RKHS-based conditional conformal prediction fast and adaptable to low-rank latent embeddings.

  3. Relational Conformal Prediction for Correlated Time Series

    cs.LG 2025-02 conditional novelty 6.0 of 10

    CoRel trains a graph neural network on prediction residuals to estimate quantile intervals for correlated time series, reporting narrower intervals than per-series conformal baselines on three benchmarks.

  4. Spatial Conformal Inference through Localized Quantile Regression

    stat.ML 2024-12 reject novelty 6.0 of 10

    LSCP uses quantile regression to learn local weights for spatial conformal prediction, but its finite-sample coverage theorem rests on a flawed proof step.

  5. Conformal Prediction for Electricity Price Forecasting in the Day-Ahead and Real-Time Balancing Market

    cs.LG 2025-02 conditional novelty 5.0 of 10

    An equal-weight ensemble of quantile regression, EnbPI, and SPCI yields competitive prediction intervals and the highest simulated battery-trading profits against individual forecasting methods on Irish electricity ma...

  6. Spatio-Temporal Conformal Prediction for Power Outage Data

    stat.ML 2024-11 reject novelty 5.0 of 10

    A graph conformal prediction method using quantile random forests on neighbor residuals reaches nominal marginal coverage for power outage counts, but non-zero outage coverage is poor and no theoretical guarantee is provided.

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