Conformal prediction for multi-dimensional time series by ellipsoidal sets

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 $\text{MultiDimSPCI}$ that builds prediction $\text{regions}$ for a multivariate response, especially in the context of multivariate time series, which are not exchangeable. Theoretically, we estimate $\text{finite-sample}$ high-probability bounds on the conditional coverage gap. Empirically, we demonstrate that $\text{MultiDimSPCI}$ maintains valid coverage on a wide range of multivariate time series while producing smaller prediction regions than CP and non-CP baselines.

Accepted by the Forty-first International Conference on Machine Learning (ICML 2024)