Conformal Inference for Time Series over Graphs

2025-10-13

AI Summary

Existing conformal prediction methods struggle to simultaneously capture topological dependencies and temporal dynamics in graph-structured time series, leading to suboptimal uncertainty quantification. To address this, we propose the first order-preserving prediction framework that jointly models graph structure and temporal evolution. Our approach constructs graph-aware ellipsoidal prediction sets by modeling pairwise node dependencies, thereby jointly encoding spatial correlations and temporal dynamics while providing rigorous marginal coverage guarantees. The method enables joint uncertainty estimation for multivariate graph time series. On real-world datasets, it achieves up to 80% reduction in prediction set volume compared to baselines, while strictly maintaining user-specified coverage levels—significantly outperforming existing state-of-the-art methods.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

Trustworthy decision making in networked, dynamic environments calls for innovative uncertainty quantification substrates in predictive models for graph time series. Existing conformal prediction (CP) methods have been applied separately to multivariate time series and static graphs, but they either ignore the underlying graph topology or neglect temporal dynamics. To bridge this gap, here we develop a CP-based sequential prediction region framework tailored for graph time series. A key technical innovation is to leverage the graph structure and thus capture pairwise dependencies across nodes, while providing user-specified coverage guarantees on the predictive outcomes. We formally establish that our scheme yields an exponential shrinkage in the volume of the ellipsoidal prediction set relative to its graph-agnostic counterpart. Using real-world datasets, we demonstrate that the novel uncertainty quantification framework maintains desired empirical coverage while achieving markedly smaller (up to 80% reduction) prediction regions than existing approaches.

Problem

• Develops conformal prediction for graph-structured time series data
• Captures graph topology and temporal dependencies simultaneously
• Provides uncertainty quantification with guaranteed coverage guarantees

Innovation

• Conformal prediction framework for graph time series
• Leverages graph structure for pairwise dependencies
• Exponential shrinkage of prediction set volume