Quantifying relationships between components of a complex system is critical to understanding the rich network of interactions that characterize the behavior of the system. Traditional methods for detecting pairwise dependence of time series, such as Pearson correlation, Granger causality, and mutual information, are computed directly in the space of measured time-series values. But for systems in which interactions are mediated by statistical properties of the time series (`time-series features') over longer timescales, this approach can fail to capture the underlying dependence from limited and noisy time-series data, and can be challenging to interpret. Addressing these issues, here we introduce an information-theoretic method for detecting dependence between time series mediated by time-series features that provides interpretable insights into the nature of the interactions. Our method extracts a candidate set of time-series features from sliding windows of the source time series and assesses their role in mediating a relationship to values of the target process. Across simulations of three different generative processes, we demonstrate that our feature-based approach can outperform a traditional inference approach based on raw time-series values, especially in challenging scenarios characterized by short time-series lengths, high noise levels, and long interaction timescales. Our work introduces a new tool for inferring and interpreting feature-mediated interactions from time-series data, contributing to the broader landscape of quantitative analysis in complex systems research, with potential applications in various domains including but not limited to neuroscience, finance, climate science, and engineering.

翻译：量化复杂系统中各组成部分之间的关系，对于理解表征系统行为特征的丰富交互网络至关重要。传统的检测时间序列成对依赖关系的方法（如皮尔逊相关性、格兰杰因果关系和互信息）直接在测量到的时间序列值的空间中进行计算。然而，当系统内相互作用通过更长时标上的时间序列统计性质（即“时间序列特征”）进行中介时，这种方法可能无法从有限且有噪声的时间序列数据中捕捉到潜在的依赖关系，并且难以解释。为解决这些问题，本文引入了一种信息论方法，用于检测由时间序列特征中介的时间序列之间的依赖关系，从而提供关于相互作用性质的可解释性洞见。我们的方法从源时间序列的滑动窗口中提取候选时间序列特征集，并评估它们在调节目标过程值关系中的作用。通过三种不同生成过程的模拟，我们证明了基于特征的方法能够优于基于原始时间序列值的传统推断方法，尤其是在短时间序列长度、高噪声水平和长相互作用时标的挑战性场景中。我们的工作引入了一种从时间序列数据中推断和解释特征中介相互作用的新工具，为复杂系统研究中更广泛的定量分析领域做出了贡献，并具有包括但不限于神经科学、金融、气候科学和工程等多个领域的潜在应用前景。