Sparse plus low-rank autoregressive identification in neuroimaging time series

This paper considers the problem of identifying multivariate autoregressive (AR) sparse plus low-rank graphical models. Based on a recent problem formulation, we use the alternating direction method of multipliers (ADMM) to solve it efficiently as a convex program for sizes encountered in neuroimaging applications. We apply this algorithm on synthetic and real neuroimaging datasets with a specific focus on the information encoded in the low-rank structure of our model. In particular, we illustrate that this information captures the spatio-temporal structure of the original data, generalizing classical component analysis approaches.