High-Dimensional MVAR Model Identification Based on Structured Sparsity Penalization

Multivariate autoregressive modeling is widely considered in neuroscience, especially when effective connectivity is concerned. In high-dimensional space, the conventional least-squares estimation of the autoregressive coefficients is no more consistent, hence the interest in regularizing the solution. Therefore, regularized approaches have been developed such as the Least Absolute Shrinkage Selection Operator (LASSO) promoting sparsity, which performs well provided that it is combined with the extended Bayesian Information Criterion (eBIC) to jointly estimate the MVAR model order and penalty parameter. Unfortunately, this need for eBIC requires much more computation time, making such approaches unsuitable for identifying high-dimensional MVAR models. The method proposed in this letter, named SOCAR (Simultaneous identification of the Order and the Coefficients of multivariate AutoRegressive models), estimates both the order and the coefficients of the model by combining mixed-norm regularization with classical sparse priors (e.g. LASSO). Weighted penalties are minimized in order to drive more easily sparsity to the right place. Experiments carried out on simulated signals show that SOCAR offers a good compromise between performance and numerical complexity.