# Mutual Information in Frequency and its Application to Measure Cross-Frequency Coupling in Epilepsy

arXiv: https://arxiv.org/abs/1711.01629 · HTML: https://mlsanity.com/paper/1711.01629/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Nov 2017.

## Built on by (most cited first, 2 of 2)

- [Deep Neural Imputation: A Framework for Recovering Incomplete Brain Recordings](https://mlsanity.com/paper/2206.08094/) (2022)
- [Fourier Preconditioning for Neural Feature Learning](https://mlsanity.com/paper/2607.02199/) (2026)

## Abstract (arXiv)

We define a metric, mutual information in frequency (MI-in-frequency), to detect and quantify the statistical dependence between different frequency components in the data, referred to as cross-frequency coupling and apply it to electrophysiological recordings from the brain to infer cross-frequency coupling. The current metrics used to quantify the cross-frequency coupling in neuroscience cannot detect if two frequency components in non-Gaussian brain recordings are statistically independent or not. Our MI-in-frequency metric, based on Shannon's mutual information between the Cramer's representation of stochastic processes, overcomes this shortcoming and can detect statistical dependence in frequency between non-Gaussian signals. We then describe two data-driven estimators of MI-in-frequency: one based on kernel density estimation and the other based on the nearest neighbor algorithm and validate their performance on simulated data. We then use MI-in-frequency to estimate mutual information between two data streams that are dependent across time, without making any parametric model assumptions. Finally, we use the MI-in- frequency metric to investigate the cross-frequency coupling in seizure onset zone from electrocorticographic recordings during seizures. The inferred cross-frequency coupling characteristics are essential to optimize the spatial and spectral parameters of electrical stimulation based treatments of epilepsy.