Detecting Causality in the Frequency Domain with Cross-Mapping Coherence
This work addresses the challenge of causal discovery in complex, nonlinear systems for scientific and engineering fields, representing an incremental advancement by extending existing methods to the frequency domain.
The study tackled the problem of detecting causal relationships in the frequency domain between time series by introducing the Cross-Mapping Coherence (CMC) method, which accurately identified causal directions in simulations of logistic maps, Lorenz systems, Kuramoto oscillators, and the Wilson-Cowan model, showing high sensitivity, sample efficiency, and noise robustness.
Understanding causal relationships within a system is crucial for uncovering its underlying mechanisms. Causal discovery methods, which facilitate the construction of such models from time-series data, hold the potential to significantly advance scientific and engineering fields. This study introduces the Cross-Mapping Coherence (CMC) method, designed to reveal causal connections in the frequency domain between time series. CMC builds upon nonlinear state-space reconstruction and extends the Convergent Cross-Mapping algorithm to the frequency domain by utilizing coherence metrics for evaluation. We tested the Cross-Mapping Coherence method using simulations of logistic maps, Lorenz systems, Kuramoto oscillators, and the Wilson-Cowan model of the visual cortex. CMC accurately identified the direction of causal connections in all simulated scenarios. When applied to the Wilson-Cowan model, CMC yielded consistent results similar to spectral Granger causality. Furthermore, CMC exhibits high sensitivity in detecting weak connections, demonstrates sample efficiency, and maintains robustness in the presence of noise. In conclusion, the capability to determine directed causal influences across different frequency bands allows CMC to provide valuable insights into the dynamics of complex, nonlinear systems.