Relational Conformal Prediction for Correlated Time Series

Andrea Cini, Alexander Jenkins, Danilo Mandic, Cesare Alippi, Filippo Maria Bianchi
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:10949-10965, 2025.

Abstract

We address the problem of uncertainty quantification in time series forecasting by exploiting observations at correlated sequences. Relational deep learning methods leveraging graph representations are among the most effective tools for obtaining point estimates from spatiotemporal data and correlated time series. However, the problem of exploiting relational structures to estimate the uncertainty of such predictions has been largely overlooked in the same context. To this end, we propose a novel distribution-free approach based on the conformal prediction framework and quantile regression. Despite the recent applications of conformal prediction to sequential data, existing methods operate independently on each target time series and do not account for relationships among them when constructing the prediction interval. We fill this void by introducing a novel conformal prediction method based on graph deep learning operators. Our approach, named Conformal Relational Prediction (CoRel), does not require the relational structure (graph) to be known a priori and can be applied on top of any pre-trained predictor. Additionally, CoRel includes an adaptive component to handle non-exchangeable data and changes in the input time series. Our approach provides accurate coverage and achieves state-of-the-art uncertainty quantification in relevant benchmarks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-cini25a, title = {Relational Conformal Prediction for Correlated Time Series}, author = {Cini, Andrea and Jenkins, Alexander and Mandic, Danilo and Alippi, Cesare and Bianchi, Filippo Maria}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {10949--10965}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/cini25a/cini25a.pdf}, url = {https://proceedings.mlr.press/v267/cini25a.html}, abstract = {We address the problem of uncertainty quantification in time series forecasting by exploiting observations at correlated sequences. Relational deep learning methods leveraging graph representations are among the most effective tools for obtaining point estimates from spatiotemporal data and correlated time series. However, the problem of exploiting relational structures to estimate the uncertainty of such predictions has been largely overlooked in the same context. To this end, we propose a novel distribution-free approach based on the conformal prediction framework and quantile regression. Despite the recent applications of conformal prediction to sequential data, existing methods operate independently on each target time series and do not account for relationships among them when constructing the prediction interval. We fill this void by introducing a novel conformal prediction method based on graph deep learning operators. Our approach, named Conformal Relational Prediction (CoRel), does not require the relational structure (graph) to be known a priori and can be applied on top of any pre-trained predictor. Additionally, CoRel includes an adaptive component to handle non-exchangeable data and changes in the input time series. Our approach provides accurate coverage and achieves state-of-the-art uncertainty quantification in relevant benchmarks.} }
Endnote
%0 Conference Paper %T Relational Conformal Prediction for Correlated Time Series %A Andrea Cini %A Alexander Jenkins %A Danilo Mandic %A Cesare Alippi %A Filippo Maria Bianchi %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-cini25a %I PMLR %P 10949--10965 %U https://proceedings.mlr.press/v267/cini25a.html %V 267 %X We address the problem of uncertainty quantification in time series forecasting by exploiting observations at correlated sequences. Relational deep learning methods leveraging graph representations are among the most effective tools for obtaining point estimates from spatiotemporal data and correlated time series. However, the problem of exploiting relational structures to estimate the uncertainty of such predictions has been largely overlooked in the same context. To this end, we propose a novel distribution-free approach based on the conformal prediction framework and quantile regression. Despite the recent applications of conformal prediction to sequential data, existing methods operate independently on each target time series and do not account for relationships among them when constructing the prediction interval. We fill this void by introducing a novel conformal prediction method based on graph deep learning operators. Our approach, named Conformal Relational Prediction (CoRel), does not require the relational structure (graph) to be known a priori and can be applied on top of any pre-trained predictor. Additionally, CoRel includes an adaptive component to handle non-exchangeable data and changes in the input time series. Our approach provides accurate coverage and achieves state-of-the-art uncertainty quantification in relevant benchmarks.
APA
Cini, A., Jenkins, A., Mandic, D., Alippi, C. & Bianchi, F.M.. (2025). Relational Conformal Prediction for Correlated Time Series. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:10949-10965 Available from https://proceedings.mlr.press/v267/cini25a.html.

Related Material