Learning A Common Granger Causality Network Using A Non-Convex Regularization

This paper proposes an estimation for learning a common Granger network of panel data. When vector time series are collected from several subjects belonging to a homogeneous group, a relationship structure of variables can be assumed to share the same topology, while the model parameters of individual subjects could be varied. The formulation is a regularized least-squares estimation of multiple vector autoregressive (VAR) models with a non-convex $\ell_{2,1/2}$-norm penalty. The common sparsity pattern of VAR coefficients from all models can reveal a consistent network in a group level. Simulation results show that the proposed formulation achieves better accuracy of learning Granger networks than the convex group lasso formulation. Preliminary results of discovering brain connectivities from ABIDE fMRI data sets showed that sparse common networks among subjects from normal and autism groups are distinctive in some brain regions.