Learning multiple granger graphical models via group fused lasso

Granger graphical models explain Granger causality between variables in time series through an estimation of zero pattern of coefficients in multivariate autoregressive (AR) models. In this paper, we consider a problem of estimating multiple Granger graphical models simultaneously that share similar topology structures from a set of time series data belonging to distinct classes. This is achieved by estimating a group of AR models and employing group fused lasso penalties to promote sparsity in AR coefficients of each model and sparsity in the difference between AR coefficients from two adjacent models. The resulting problem is in a class of group fused lasso formulation which fits nicely in a convex framework and then can be solved by a fast alternating directions method of multipliers (ADMM) algorithm. Advantages of the proposed method and the performance of the algorithm are illustrated through randomly generated data in a high-dimensional setting.