arXiv:2605.04957cs.LG2026-05

针对图结构时间序列,提出基于频谱的置信预测方法,解决传统方法因节点关联失效的问题。

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

论文配图:Delving into Non-Exchangeability for Conformal Prediction in Graph-Structured Multivariate Time Series
图 1 · 摘自论文原文
  • 将图信号分解为低频(全局趋势)与高频(近似可交换)分量,构建频谱条件交换性
  • 在真实交通数据上实现100%覆盖率,且效率优于现有最优方法
  • 适合需要可靠不确定性估计的时空数据分析场景

图结构多变量时间序列的点预测是基础问题,但其严格不确定性量化仍不充分。分位数预测(CP)在交换性假设下提供有保证的覆盖率,但图中固有的跨节点耦合会破坏该假设,导致直接应用不可靠。受谱图理论启发,我们发现这种耦合体现在全局趋势,可由低频分量刻画,而高频分量近似满足交换性。为此,提出新概念——谱图条件交换性(SGCE),即以低频分量为条件,使高频分量保持交换性,从而在频域实现有效CP。基于此,提出基于小波变换的谱置信预测(SCALE):利用图小波分解高低频分量,通过低频嵌入自适应门控对高频残差进行分位数化。在真实交通数据集上的实验表明,SCALE不仅达到100%覆盖率,且持续提升覆盖-效率权衡,优于当前最优方法。

原文摘要 · Abstract (English)

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.

图神经网络置信预测时间序列频谱分析

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