{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/conformal-prediction-for-multi-dimensional","title":"Conformal prediction for multi-dimensional time series by ellipsoidal sets","arxiv_id":"2403.03850","date":"2024-03-06","proceeding":null,"authors":["Chen Xu","Hanyang Jiang","Yao Xie"],"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. 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