Characterizing interactions between multiple brain regions is important for understanding brain function. Functional connectivity measures based on partial correlation provide an estimate of the linear conditional dependence between brain regions after removing the linear influence of other regions. Estimation of partial correlations is, however, difficult when the number of regions is large, as is now increasingly the case with a growing number of large-scale brain connectivity studies. To address this problem, we develop novel methods for estimating sparse partial correlations between multiple regions in fMRI data using elastic net penalty (SPC-EN), which combines L1- and L2-norm regularization We show that L1-norm regularization in SPC-EN provides sparse interpretable solutions while L2-norm regularization improves the sensitivity of the method when the number of possible connections between regions is larger than the number of time points, and when pair-wise correlations between brain regions are high. An issue with regularization-based methods is choosing the regularization parameters which in turn determine the selection of connections between brain regions. To address this problem, we deploy novel stability selection methods to infer significant connections between brain regions. We also compare the performance of SPC-EN with existing methods which use only L1-norm regularization (SPC-L1) on simulated and experimental datasets. Detailed simulations show that the performance of SPC-EN, measured in terms of sensitivity and accuracy is superior to SPC-L1, especially at higher rates of feature prevalence. Application of our methods to resting-state fMRI data obtained from 22 healthy adults shows that SPC-EN reveals a modular architecture characterized by strong inter-hemispheric links, distinct ventral and dorsal stream pathways, and a major hub in the posterior medial cortex - features that were missed by conventional methods. Taken together, our findings suggest that SPC-EN provides a powerful tool for characterizing connectivity involving a large number of correlated regions that span the entire brain.
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