An efficient algorithm for estimating brain covariance networks.

Often derived from partial correlations or many pairwise analyses, covariance networks represent the inter-relationships among regions and can reveal important topological structures in brain measures from healthy and pathological subjects. However both approaches are not consistent network estimators and are sensitive to the value of the tuning parameters. Here, we propose a consistent covariance network estimator by maximising the network likelihood (MNL) which is robust to the tuning parameter. We validate the consistency of our algorithm theoretically and via a simulation study, and contrast these results against two well-known approaches: the graphical LASSO (gLASSO) and Pearson pairwise correlations (PPC) over a range of tuning parameters. The MNL algorithm had a specificity equal to and greater than 0.94 for all sample sizes in the simulation study, and the sensitivity was shown to increase as the sample size increased. The gLASSO and PPC demonstrated a specificity-sensitivity trade-off over a range of values of tuning parameters highlighting the discrepancy in the results for misspecified values. Application of the MNL algorithm to the case study data showed a loss of connections between healthy and impaired groups, and improved ability to identify between lobe connectivity in contrast to gLASSO networks. In this work, we propose the MNL algorithm as an effective approach to find covariance brain networks, which can inform the organisational features in brain-wide analyses, particularly for large sample sizes.