Study On Multivariate Autoregressive Model Baced On Lasso Penalty

In order to overcome the limitation of Autoregressive?AR?only for single channel signals,Multivariate Autoregressive?MVAR?has become a basic tool for processing multichannel time series.However,as the number of sequences increases,the MVAR model becomes overparameterized.At present,many methods,including regularization,have been proposed to reduce the dimension of multichannel signals.In this paper,the penalty function is added to the MVAR model to achieve this goal.This paper firstly introduces the basic principle of Lasso-MVAR and Group Lasso MVAR.At the same time,the method of combining gradient descent and block coordinate descent is used to estimate the model parameters,as well as the extracted features are classified with the traditional support vector machine.Besides,the Group Lasso MVAR is applied to the EEG signals collated by Keirn et al.The experimental results show that the classification accuracy based on Own/Other Group Lasso MVAR is the highest,and when the parameter space is larger,the structural sparse regularization method is more stable than the MVAR model and the Lasso-MVAR model.Furthermore,the basic principle of Hierarchical Vector Autoregressive and the proximal gradient descent algorithm are analyzed in detail,which is applied to the first and third groups of experimental data of International BCI Competition IV.The experimental results show that the HVAR method is superior to the traditional MVAR method and Lasso-MVAR method to some extent,and hierarchical structure achieves high computation efficiency.Finally,this paper describes the basic principle of Sparse Group Lasso Multivariate Autoregressive with Exogenous Variables and the solution of model parameters,and its application to the concentration prediction of air pollutants of Beijing-Tianjin-Hebei region.The results show that the normalized mean square error of PM₁₀ based on Sparse Own/Other Group Lasso Multivariate Autoregressive with Exogenous Variables is relatively low,and the prediction accuracy is higher than that of MVAR method,Sparse Group MVAR method and HVAR method.In addition,by analyzing the parameters of sparse group MVARX,we can know that Beijing,Tianjin and Hebei have different influences on Beijing's air quality.