标题： 多频段可变滞后格兰杰因果关系：跨频率的因果时间序列推断统一框架 显示英文标题

标题： Multi-Band Variable-Lag Granger Causality: A Unified Framework for Causal Time Series Inference across Frequencies

摘要： 理解时间序列中的因果关系对于许多领域都是基础性的，包括神经科学、经济学和行为科学。 格兰杰因果关系是用于推断时间序列因果关系的一种著名技术。 通常，格兰杰因果关系框架在原因和结果之间有一个强固定的滞后假设，这在复杂系统中往往不现实。 尽管最近关于可变滞后格兰杰因果关系（VLGC）的工作通过允许原因在每个时间点以不同的时间滞后影响结果来解决这一限制，但它未能考虑到因果互动不仅可能在时间延迟上变化，也可能在频率带之间变化。 例如，在脑信号中，α波活动可能比较慢的δ波振荡以更短的延迟影响另一个区域。 在本工作中，我们形式化了多频段可变滞后格兰杰因果关系（MB-VLGC），并提出了一种新框架，通过显式建模频率依赖的因果延迟来推广传统的VLGC。 我们提供了MB-VLGC的正式定义，展示了其理论合理性，并提出了一个高效的推理流程。 在多个领域的广泛实验表明，我们的框架在合成和现实世界数据集上显著优于现有方法，证实了其对任何类型时间序列数据的广泛应用性。 代码和数据集已公开。 显示英文摘要

摘要： Understanding causal relationships in time series is fundamental to many domains, including neuroscience, economics, and behavioral science. Granger causality is one of the well-known techniques for inferring causality in time series. Typically, Granger causality frameworks have a strong fix-lag assumption between cause and effect, which is often unrealistic in complex systems. While recent work on variable-lag Granger causality (VLGC) addresses this limitation by allowing a cause to influence an effect with different time lags at each time point, it fails to account for the fact that causal interactions may vary not only in time delay but also across frequency bands. For example, in brain signals, alpha-band activity may influence another region with a shorter delay than slower delta-band oscillations. In this work, we formalize Multi-Band Variable-Lag Granger Causality (MB-VLGC) and propose a novel framework that generalizes traditional VLGC by explicitly modeling frequency-dependent causal delays. We provide a formal definition of MB-VLGC, demonstrate its theoretical soundness, and propose an efficient inference pipeline. Extensive experiments across multiple domains demonstrate that our framework significantly outperforms existing methods on both synthetic and real-world datasets, confirming its broad applicability to any type of time series data. Code and datasets are publicly available.