Inferring interpretable pairwise interactions from time-series data using time-series features

Abstract

Quantifying relationships between components of a complex system is critical to understanding the system's behaviours. Traditional methods for detecting pairwise dependence of time series, such as Pearson correlation and mutual information, are computed directly in the space of measured time-series values. But for systems where interactions between components 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, 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 set of candidate 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 generative processes, we demonstrate that our feature-based approach can outperform a traditional inference approach, especially in challenging scenarios characterized by high noise levels and long interaction timescales. Applied to whole-brain calcium imaging of Caenorhabditis elegans, our method detects higher dependence rates among structurally connected neuron pairs and reveals dominant interactions mediated by non-linear and auto-correlation features. These results underscore the potential of our method to both detect and provide valuable insights into the nature of pairwise interactions in a system. Our work introduces a new tool for inferring and interpreting long-timescale interactions from dynamical systems, contributing to the broader landscape of quantitative analysis in complex systems research.