Conformal prediction for multi-dimensional time series by ellipsoidal sets

Chen Xu, Hanyang Jiang, Yao Xie
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:55076-55099, 2024.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-xu24m, title = {Conformal prediction for multi-dimensional time series by ellipsoidal sets}, author = {Xu, Chen and Jiang, Hanyang and Xie, Yao}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {55076--55099}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/xu24m/xu24m.pdf}, url = {https://proceedings.mlr.press/v235/xu24m.html}, 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.} }
Endnote
%0 Conference Paper %T Conformal prediction for multi-dimensional time series by ellipsoidal sets %A Chen Xu %A Hanyang Jiang %A Yao Xie %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-xu24m %I PMLR %P 55076--55099 %U https://proceedings.mlr.press/v235/xu24m.html %V 235 %X 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.
APA
Xu, C., Jiang, H. & Xie, Y.. (2024). Conformal prediction for multi-dimensional time series by ellipsoidal sets. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:55076-55099 Available from https://proceedings.mlr.press/v235/xu24m.html.

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