Delving into Non-Exchangeability for Conformal Prediction in Graph-Structured Multivariate Time Series

TL;DR

This paper introduces a spectral domain conformal prediction method for graph-structured multivariate time series, addressing exchangeability violations by leveraging spectral decomposition to improve uncertainty quantification.

Contribution

It proposes Spectral Graph Conditional Exchangeability (SGCE) and SCALE, a novel spectral conformal prediction method that enhances coverage validity and efficiency in graph time series.

Findings

SCALE achieves valid coverage on real-world traffic data.

SCALE improves coverage-efficiency trade-off over existing methods.

Spectral decomposition enables effective conformal prediction despite exchangeability violations.

Abstract

Point forecasting for graph-structured multivariate time series is a fundamental problem, but rigorous uncertainty quantification for such predictions is still underexplored. Conformal prediction (CP) offers uncertainty estimation with a solid coverage guarantee under the exchangeability assumption, which requires the joint data distribution to be unchanged under permutation. However, in graph-structured time series, inherent cross-node coupling can violate the exchangeability condition, making direct application of CP unreliable. Inspired by the spectral graph theory, such coupling resides in global trends and can be characterized by the low-frequency components, while high-frequency components are nearly exchangeable. Therefore, we propose a novel concept named Spectral Graph Conditional Exchangeability (SGCE), which conditions exchangeable high-frequency components on low-frequency ones to preserve global trends and enable effective CP in the spectral domain. Based on SGCE, we further propose Spectral Conformal prediction via wAveLEt transform (SCALE). SCALE uses graph wavelets to decompose low/high-frequency components and conformalizes high-frequency residuals via adaptive gating over a low-frequency embedding. Experimental results on real-world traffic datasets show that SCALE not only achieves valid coverage but also consistently improves the coverage-efficiency trade-off over the state-of-the-art CP methods.