Regularized partial correlation provides reliable functional connectivity estimates while correcting for widespread confounding.

Functional connectivity (FC) has been invaluable for understanding the brain's communication network, with strong potential for enhanced FC approaches to yield additional insights. Unlike with the fMRI field-standard method of pairwise correlation, theory suggests that partial correlation can estimate FC without confounded and indirect connections. However, partial correlation FC can also display low repeat reliability, impairing the accuracy of individual estimates. We hypothesized that reliability would be increased by adding regularization, which can reduce overfitting to noise in regression-based approaches like partial correlation. We therefore tested several regularized alternatives - graphical lasso, graphical ridge, and principal component regression - against unregularized partial and pairwise correlation, applying them to empirical resting-state fMRI and simulated data. As hypothesized, regularization vastly improved reliability, quantified using between-session similarity and intraclass correlation. This enhanced reliability then granted substantially more accurate individual FC estimates when validated against structural connectivity (empirical data) and ground truth networks (simulations). Graphical lasso showed especially high accuracy among regularized approaches, seemingly by maintaining more valid underlying network structures. We additionally found graphical lasso to be robust to noise levels, data quantity, and subject motion - common fMRI error sources. Lastly, we demonstrated that resting-state graphical lasso FC can effectively predict fMRI task activations and individual differences in behavior, further establishing its reliability, external validity, and ability to characterize task-related functionality. We recommend graphical lasso or similar regularized methods for calculating FC, as they can yield more valid estimates of unconfounded connectivity than field-standard pairwise correlation, while overcoming the poor reliability of unregularized partial correlation.