Conformal prediction for multi-dimensional time series by ellipsoidal sets
<|reference_start|>Conformal prediction for multi-dimensional time series by ellipsoidal sets: 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.<|reference_end|>
@article{xu2024conformal,
    title={Conformal prediction for multi-dimensional time series by ellipsoidal
  sets},
    author={Chen Xu, Hanyang Jiang, Yao Xie},
    journal={arXiv preprint arXiv:2403.03850},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.03850},
    primaryClass={stat.ML cs.LG}
}