Conformal prediction for multi-dimensional time series by ellipsoidal sets

• URL: http://arxiv.org/abs/2403.03850v2
• Date: Thu, 23 May 2024 16:51:43 GMT
• Title: Conformal prediction for multi-dimensional time series by ellipsoidal sets
• Authors: Chen Xu, Hanyang Jiang, Yao Xie,
• Abstract summary: Conformal prediction (CP) has been a popular method for uncertainty quantification because it is distribution-free, model-agnostic, and theoretically sound. We develop a sequential CP method called $textttMultiDimS PCI$ that builds prediction $textitregions$ for a multivariate response.
• Score: 9.44133696606093
• License: http://creativecommons.org/licenses/by/4.0/
• 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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