A regularized and smoothed General Linear Kalman Filter for more accurate estimation of time-varying directed connectivity*

Adaptive algorithms based on the Kalman filter are valuable tools to model the dynamic and directed Granger causal interactions between neurophysiological signals simultaneously recorded from multiple cortical regions. Among these algorithms, the General Linear Kalman Filter (GLKF) has proven to be the most accurate and reliable. Here we propose a regularized and smoothed GLKF (spsm-GLKF) with ℓ1 norm penalties based on lasso or group lasso and a fixedinterval smoother. We show that the group lasso penalty promotes sparse solutions by shrinking spurious connections to zero, while the smoothing increases the robustness of the estimates. Overall, our results demonstrate that spsm-GLKF outperforms the original GLKF, and represents a more accurate tool for the characterization of dynamical and sparse functional brain networks.

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