Sparse and shrunken estimates of MRI networks in the brain and their influence on network properties

Estimation of morphometric relationships between cortical regions is a widely used approach to identify and characterize structural connectivity. The elevated number of regions that can be considered in a whole-brain correlation analysis might lead to overfitted models. However, the overfitting can be avoided by using regularization methods. We found that, as expected, non-regularized correlations had low variability when a scarce number of variables were considered.
However, a slight increase of variables led to an increase of variance of several magnitude orders. On the other hand, the regularized approaches showed more stable results with a relative low variance at the expense of a little bias. Interestingly, topological properties as local and global efficiency estimated in networks constructed from traditional non-regularized correlations also showed higher variability when compared to those from regularized networks. Our findings suggest that a population-based connectivity study can achieve a more robust description of cortical topology through regularization of the correlation estimates. Four regularization methods were examined: Two with shrinkage (Ridge and Schäfer’s shrinkage), one with sparsity (Lasso) and one with both shrinkage and sparsity (Elastic net). Furthermore, the different regularizations resulted in different correlation estimates as well as network properties. The shrunken estimates resulted in lower variance of the estimates than the sparse estimates.