Conformal Inference for Time Series over Graphs

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.