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Conformal Inference for Time Series over Graphs

Sonakshi Dua, Gonzalo Mateos, Sundeep Prabhakar Chepuri

TL;DR

This paper extends conformal prediction to graph time series by introducing graph-filtered residuals and a graph-aware Mahalanobis nonconformity score to form ellipsoidal prediction sets with guaranteed coverage. By exploiting homophily through a first-order graph diffusion filter, the method achieves exponential shrinkage of the prediction-set volume compared with graph-agnostic CP, while maintaining the prescribed coverage. Theoretical guarantees include a finite-sample conditional coverage bound and an explicit volume reduction tied to the graph spectrum and filter strength, and empirical validation across three real-world datasets shows substantial efficiency gains (up to 80% smaller regions) with preserved coverage. These results enable more trustworthy and efficient uncertainty quantification for forecasted graph time series in dynamic networked environments.

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.

Conformal Inference for Time Series over Graphs

TL;DR

This paper extends conformal prediction to graph time series by introducing graph-filtered residuals and a graph-aware Mahalanobis nonconformity score to form ellipsoidal prediction sets with guaranteed coverage. By exploiting homophily through a first-order graph diffusion filter, the method achieves exponential shrinkage of the prediction-set volume compared with graph-agnostic CP, while maintaining the prescribed coverage. Theoretical guarantees include a finite-sample conditional coverage bound and an explicit volume reduction tied to the graph spectrum and filter strength, and empirical validation across three real-world datasets shows substantial efficiency gains (up to 80% smaller regions) with preserved coverage. These results enable more trustworthy and efficient uncertainty quantification for forecasted graph time series in dynamic networked environments.

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.

Paper Structure

This paper contains 11 sections, 2 theorems, 10 equations, 1 figure, 5 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem Statement
  4. Graph-aware Ellipsoidal Prediction Sets
  5. Graph-aware Nonconformity Score
  6. Ellipsoidal Uncertainty Sets
  7. Theoretical Analysis
  8. Conditional Coverage
  9. Ellipsoid Volume Shrinkage
  10. Numerical Experiments
  11. Conclusions

Key Result

Theorem 1

Ellipsoidal_SPCI. Assume the true covariance matrix $\boldsymbol{\Sigma}_{\mathcal{G}}$ is known and positive definite with minimum eigenvalue at least $\lambda>0$, the filtered residuals $\{{{\mathbf{e}}}_t\}$ are i.i.d. over time, and the CDF of the true nonconformity score is Lipschitz. Then, we where $T$ is the training data size, $\delta_T$ is the bound on the residual error, and $L$ depends

Figures (1)

  • Figure 1: Residuals are smooth over the graph. Connected nodes have a smaller gap in the residuals than unconnected nodes. The plot is generated using prediction residuals from a model ${\mathcal{M}}$ on the Wiki Maths dataset (see also Section \ref{['sec:num_exp']}), averaged across all timesteps.

Theorems & Definitions (3)

  • Theorem 1
  • Theorem 2
  • proof