ICML 2025

Relational Conformal Prediction for Correlated Time Series
Andrea Cini 1 2 Alexander Jenkins 1 3 Danilo Mandic 3 Cesare Alippi 1 4 Filippo Maria Bianchi 5 6
Abstract
We address the problem of uncertainty quantifi-
cation in time series forecasting by exploiting
observations at correlated sequences. Relational
deep learning methods leveraging graph repre-
sentations 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 es-
timate the uncertainty of such predictions has
been largely overlooked in the same context. To
this end, we propose a novel distribution-free ap-
proach based on the conformal prediction frame-
work and quantile regression. Despite the recent
applications of conformal prediction to sequen-
tial 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 in-
troducing a novel conformal prediction method
based on graph deep learning operators.
Our
approach, named Conformal Relational Predic-
tion (COREL), does not require the relational
structure (graph) to be known a priori and can be
applied on top of any pre-trained predictor. Addi-
tionally, COREL includes an adaptive component
to handle non-exchangeable data and changes in
the input time series. Our approach provides ac-
curate coverage and achieves state-of-the-art un-
certainty quantification in relevant benchmarks.
1. Introduction
Many recent advancements in deep learning methods for
time series forecasting rely on learning from large collec-
tions of (related) time series (Benidis et al., 2022; Liang
1IDSIA USI-SUPSI, Universit`a della Svizzera italiana 2Swiss
National Science Foundation Postdoc Fellow 3Imperial College
London 4Politecnico di Milano 5UiT The Arctic University of Nor-
way 6NORCE Norwegian Research Centre AS. Correspondence
to: Andre...