The Study Of Brain-network Construction Based On Bayesian Multivariate Regression Analysis

The brain network analysis based on motor imagery(MI)has been widely applied in cognitive neuroscience.It provided key biological index for the postoperative rehabilitation of stroke patients and the skill development of athletes.However,the collected data are inevitably contaminated with the noise which is caused by the head-movement or blink of subjects,then the accuracy of brain network will be declined.One of the main reasons is the multivariate autoregressive(MVAR)analysis adopted by most of the methods for brain network analysis.The traditional MVAR analysis generally adopt the least square method(LS),which will magnify the effect of noise and cause the larger estimation error of MVAR coefficients because of the square component in objective function.Finally,these errors result in many pseudo linkages in constructed brain network and distort the network topology.Moreover,similar problem also exists in the construction of time-varying brain network.The traditional Kalman filter(KF)adopted for network construction usually has significant limitations in real applications because of its hypothesis that the process and observed noise obey the Gaussian distribution.Therefore,the brain network constructed from real data is not accurate enough.In view of the noise charactetristics included in MI fMRI data,this thesis provided two methods for the construction of causality and time-varying brain networks based on Bayesian analysis(BA).The main work is as follows.Firstly,we proposed the multivariate autoregressive analysis based on Bayesian(BA-MVAR)for causality network construction,which can alleviate the noise effects caused by LS method during the MVAR analysis,resulting in the inaccurate MVAR coefficients and the distorted brain networks.The most significant advantage of proposed approach is the utilization of prior information.We assumed that the MVAR coefficients obeyed the Gaussian distribution with zero-mean and acquired maximum likelihood function with the simultaneous probability distribution functions.Then the unknown parameters would be calculated by the likelihood function.We applied BAand LS-MVAR to both simulation and real-data experiments and compared the performance differences between the two methods.The experiment results showed that the performance of BA-MVAR was superior to LS-MVAR under different noise conditions and BA-MVAR also showed the better ability for network constructionthan LS-MVAR under the small number of samples,which is important in actual applications like functional magnetic resonance imaging(fMRI)analysis that usually has the insufficient samples.Secondly,we proposed the modified Kalman filter based on Bayesian analysis(BKF)for time-varying network analysis.In view of the limitation of traditional KF caused by the hypothesis that the process and observed noise obey the Gaussian distribution,in order to improve the construction of time-varying brain network under the condition of heavy-tailed noise,we assumed that both the process and observed noise in the Kalman filter followed the student's t-distribution which had heavy-tail properties and utilized variational Bayesian(VB)method and inverse Wishart distribution to approximately solve the related objective function.In theory,BKF releases the limitation of Gaussian noise and has better generalization performance compared with KF.The simulation experiment proved that the newly proposed method could acquire smaller time-varying estimation error of coefficients and higher consistency of brain network.The application on real fMRI data further revealed that the brain network constructed by BKF was more aligned with the lateralization of MI mechanism.