提出跨变量损失函数,提升多变量时序预测一致性
Multivariate Time Series Forecasting needs Cross Variable Loss

- 设计跨变量损失,约束未来值间的结构关系
- 在多个模型上验证,显著提升预测精度
- 适合需要强变量协同的时序预测场景
多变量时间序列预测面临独特挑战:未来变量常受共同系统动态驱动。现有研究多关注历史观测中的变量依赖,对未来的变量间依赖关注不足。现代预测模型普遍采用直接预测范式(DF),以逐点目标生成多步预测,未显式约束跨变量结构。本文揭示了在存在跨变量与滞后依赖时,DF目标存在不匹配问题,导致目标偏差。为此,提出可插拔的跨变量损失(CvLoss),通过在跨变量图上约束预测残差,惩罚预测片段中边级残差差异,促进同步与异步交互的一致性。实验表明,CvLoss能持续改进主流预测模型,优于代表性学习目标,且兼容多种预测主干网络。
原文摘要 · Abstract (English)
Multivariate time series forecasting presents unique challenges because future variables often co-evolve under shared system dynamics. While existing studies mainly focus on cross-variable dependencies in historical observations, dependencies among future values are much less explored. Specifically, modern forecasting models largely follow the Direct Forecasting (DF) paradigm, generating multi-step forecasts with point-wise objectives that do not explicitly constrain cross-variable structure. In this work, we show that the DF objective is mismatched in the presence of cross-variable and lagged dependencies, revealing an objective gap. To address this issue, we propose \textbf{C}ross-\textbf{V}ariable \textbf{Loss} (CvLoss), a plug-in structural regularizer that constrains forecast residuals on a cross-variable graph. CvLoss penalizes inconsistent edge-wise residual differences over forecast patches, encouraging consistency across both synchronous and asynchronous interactions. Our experiments show that CvLoss consistently improves competitive forecasting models, outperforms representative learning objectives, and is compatible with a variety of forecasting backbones.
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