Sparse Graphical Models for Functional Connectivity Networks: Best Methods and the Autocorrelation Issue

Sparse graphical models are frequently used to explore both static and dynamic functional brain networks from neuroimaging data. However, the practical performance of the models has not been studied in detail for brain networks. In this work, we have two objectives. First, we compare several sparse graphical model estimation procedures and several selection criteria under various experimental settings, such as different dimensions, sample sizes, types of data, and sparsity levels of the true model structures. We discuss in detail the superiority and deficiency of each combination. Second, in the same simulation study, we show the impact of autocorrelation and whitening on the estimation of functional brain networks. We apply the methods to a resting-state functional magnetic resonance imaging (fMRI) data set. Our results show that the best sparse graphical model, in terms of detection of true connections and having few false-positive connections, is the smoothly clipped absolute deviation (SCAD) estimating method in combination with the Bayesian information criterion (BIC) and cross-validation (CV) selection method. In addition, the presence of autocorrelation in the data adversely affects the estimation of networks but can be helped by using the CV selection method. These results question the validity of a number of fMRI studies where inferior graphical model techniques have been used to estimate brain networks.