# Detecting Causality in the Frequency Domain with Cross-Mapping Coherence

arXiv: https://arxiv.org/abs/2407.20694 · HTML: https://mlsanity.com/paper/2407.20694/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 67 references that are in the map.
- First posted on arXiv 30 Jul 2024.

## Builds on (most cited first, 6 of 6)

- [Interpretable Models for Granger Causality Using Self-explaining Neural Networks](https://mlsanity.com/paper/2101.07600/) (2021)
- [Complete Inference of Causal Relations between Dynamical Systems](https://mlsanity.com/paper/1808.10806/) (2018)
- [Shadow-Mapping for Unsupervised Neural Causal Discovery](https://mlsanity.com/paper/2104.08183/) (2021)
- [Manifold-adaptive dimension estimation revisited](https://mlsanity.com/paper/2008.03221/) (2020)
- [Inferring Parsimonious Coupling Statistics in Nonlinear Dynamics with Variational Gaussian Processes](https://mlsanity.com/paper/2203.03868/) (2022)
- [Continuity scaling: A rigorous framework for detecting and quantifying causality accurately](https://mlsanity.com/paper/2203.14006/) (2022)

## Built on by (most cited first, 1 of 1)

- [Inference of hidden common driver dynamics by anisotropic self-organizing neural networks](https://mlsanity.com/paper/2504.01811/) (2025)

## Abstract (arXiv)

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.