Heterogeneous Multiscale Multivariate Autoregressive Model: existence, sparse estimation and application to...

Area of Science:

• Neuroscience
• Computational Neuroscience
• Graph Theory

Background:

• Functional connectivity in neuroscience models brain interactions as graphs.
• Existing models lack methods to assess directed interactions within and across brain oscillations and neuronal activity.
• Understanding cognitive processes like learning requires analyzing these directed interactions.

Purpose of the Study:

• To propose a novel model, HM-MVAR (Heterogeneous Multiscale Multivariate Autoregressive), for assessing directed neural interactions.
• To introduce a data-driven weighted LASSO estimator for analyzing these interactions.
• To apply the model and method to real-world electrophysiological data.

Main Methods:

• Developed the HM-MVAR model representing linear combinations of neural interaction patterns (phase-locking, power-triggered phenomena).
• Utilized a block version of stationarity for multiscale structure analysis.
• Proposed a data-driven weighted LASSO estimator based on martingale exponential deviation inequalities.

Main Results:

• Proved the existence and stationarity conditions for the HM-MVAR model.
• Demonstrated the estimator's oracle inequality property and strong performance in simulations.
• Successfully applied the model to a public dataset, recovering known interactions and identifying novel phenomena.

Conclusions:

• The HM-MVAR model provides a robust framework for analyzing directed functional connectivity in the brain.
• The proposed estimator is statistically sound and performs well on complex data.
• This approach advances the understanding of neural dynamics and cognitive processes.