Relational Conformal Prediction for Correlated Time Series

2025-02-13

AI Summary

This work addresses uncertainty quantification in multivariate related time series forecasting, where existing methods neglect inter-series dependencies, yielding unreliable prediction intervals. To this end, we propose CoRel—the first graph-agnostic conformal prediction framework for relational time series—which jointly integrates graph neural networks with conformal prediction to learn implicit inter-series dependencies in a fully data-driven manner, without requiring prior graph structures. CoRel supports arbitrary pre-trained forecasters and introduces an adaptive calibration mechanism to handle non-exchangeability and temporal distribution shift. Evaluated on multiple benchmark datasets, CoRel significantly improves empirical coverage and statistical reliability of prediction intervals, achieving state-of-the-art performance in uncertainty quantification for multivariate time series forecasting.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

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 method, named Conformal Relational Prediction (CoRel), does not require the relational structure (graph) to be known as a prior and can be applied on top of any pre-trained time series 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 archives state-of-the-art uncertainty quantification in relevant benchmarks.

Problem

• Uncertainty quantification in time series forecasting
• Exploiting relational structures for prediction accuracy
• Handling non-exchangeable data in time series analysis

Innovation

• Graph deep learning operators
• Conformal prediction framework
• Adaptive non-exchangeable data handling