A Modular State Space Model for the Brain’s Directional Connectivity
We introduce a new high-dimensional state-space model based on multivariate autoregressive models for the brain’s directional connectivity. The new model features modules of functionally independent sub-networks and is referred to as the modular state-space model (MSS). An expectation-maximization (EM) algorithm based on Kalman filtering is developed to estimate the MSS and to identify clusters of densely connectivity brain regions. We compare the MSS with existing high-dimensional ordinary differential equation models for the brain’s directional network, and show that the former is more robust to data noise and can identify connected brain regions with a higher true positive rate and lower false positive rate. We apply the developed MMS and EM algorithm to intracranial EEG data collected from a patient with medically intractable epilepsy in mapping the brain networks around the seizure onset times.