Gaussian Processes Spectral Kernels Recover Brain Metastable Oscillatory Modes

Gaussian processes (GPs) are a powerful machine learning tool to reveal hidden patterns in data. GPs hyperparameters are estimated from data, providing a framework for regression and classification tasks. We capitalize on the power of GPs to drive insights about the biophysical mechanisms underpinning metastable brain oscillations from observable data. Here, we used Multi-Output GPs (MOGPs) with Cross-Spectral Mixture (CSM) kernels to analyze the emergent oscillatory features from a whole-brain network model. The CSM kernel comprises a linear combination of oscillatory modes that represent the properties of characteristic fundamental frequencies. We simulate a network of phase-coupled oscillators comprising 90 brain regions connected according to the human connectome, with biophysical attributes that drive into three dynamic regimes: highly synchronized, low synchronized, and metastable synchrony. We trained MOGPs with the simulated time series. We show that the optimal number of oscillatory modes in each dynamical regime was correctly estimated in an unsupervised manner. The estimated hyperparameters after training the MOGPs described the oscillatory dynamics of each regime. Notably, in the metastable regime, 5 oscillatory modes were estimated, one corresponding to the fundamental frequency and four oscillatory modes that interchanged the magnitude of the covariance over time segments. We conclude that the MOGPs with CSM kernels were capable of recovering the metastable oscillatory modes and inferring attributes that are biophysically plausible and interpretable.