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 regions for a multivariate response, especially in the context of multivariate time series, which are not exchangeable. Theoretically, we estimate 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.

翻译：共形预测（Conformal Prediction, CP）因其无需分布假设、模型无关且理论严谨的特点，已成为不确定性量化领域的主流方法。在监督学习的预测问题中，大多数CP方法聚焦于构建单变量响应的预测区间。本文提出一种名为$\texttt{MultiDimSPCI}$的序列共形预测方法，该方法可构建多变量响应的预测区域，尤其适用于非可交换的多元时间序列场景。理论上，我们给出了条件覆盖间隙的有限样本高概率界估计。实证结果表明，$\texttt{MultiDimSPCI}$在保持有效覆盖率的条件下，相较于CP及非CP基线方法，能在更广泛的多元时间序列数据上产生更紧凑的预测区域。