Objective: The multivariate autoregression (MVAR) model is an effective model to construct brain causality networks. However, the accuracy of MVAR parameter estimation is considerably affected by outliers such as head movements and eye blinks contained in EEG signals, especially in short time windows.
Methods: We proposed a robust MVAR parameter estimation method based on a Bayesian probabilistic framework and Laplace fitting error known as Lap-SBL. With the Bayesian inference framework, we can accurately estimate the MVAR parameters under short time windows. Additionally, to alleviate the influence of outliers, we model the fitting error using the Laplace distribution instead of the typical Gaussian distribution. We employ convex analysis to model the inference task by approximating the Laplace noise prior with a maximum over Gaussian functions with varying scales. The variational inference approach was used to efficiently estimate the MVAR parameters.
Results: The numerical results suggest that the proposed method obtains less parameter estimation bias and more consistent linkages than existing benchmark methods, i.e., LS, LASSO, LAPPS and SBL. The motor imagery experimental data analysis shows that Lap-SBL can better describe the lateralization characteristics of brain network. This lateralization is less apparent in a subject with poor MI classification accuracy.
Conclusion and significance: Lap-SBL effectively suppresses the influence of outliers and recovers reliable networks in the presence of outliers and short time windows.