Oliver M. Cliff, Annie G. Bryant, Joseph T. Lizier et al.
Scientists have developed hundreds of techniques to measure the interactions between pairs of processes in complex systems. But these computational methods, from correlation coefficients to causal inference, rely on distinct quantitative theories that remain largely disconnected. Here we introduce a library of 237 statistics of pairwise interactions and assess their behavior on 1053 multivariate time series from a wide range of real-world and model-generated systems. Our analysis highlights new commonalities between different mathematical formulations, providing a unified picture of a rich interdisciplinary literature. Using three real-world case studies, we then show that simultaneously leveraging diverse methods from across science can uncover those most suitable for addressing a given problem, yielding interpretable understanding of the conceptual formulations of pairwise dependence that drive successful performance. Our framework is provided in extendable open software, enabling comprehensive data-driven analysis by integrating decades of methodological advances.
In this work, we are interested in structure learning for a set of spatially distributed dynamical systems, where individual subsystems are coupled via latent variables and observed through a filter. We represent this model as a directed acyclic graph (DAG) that characterises the unidirectional coupling between subsystems. Standard approaches to structure learning are not applicable in this framework due to the hidden variables, however we can exploit the properties of certain dynamical systems to formulate exact methods based on state space reconstruction. We approach the problem by using reconstruction theorems to analytically derive a tractable expression for the KL-divergence of a candidate DAG from the observed dataset. We show this measure can be decomposed as a function of two information-theoretic measures, transfer entropy and stochastic interaction. We then present two mathematically robust scoring functions based on transfer entropy and statistical independence tests. These results support the previously held conjecture that transfer entropy can be used to infer effective connectivity in complex networks.