The triple network model that consists of the default-mode network (DMN), central-executive network (CEN), and salience network (SN) has been suggested as a powerful paradigm for investigation of network mechanisms underlying various cognitive functions and brain disorders. A crucial hypothesis in this model is that the fronto-insular cortex (FIC) in the SN plays centrally in mediating interactions between the networks. Using a machine learning approach based on independent component analysis and Bayesian network (BN), this study characterizes the directed connectivity architecture of the triple network and examines the role of FIC in connectivity of the model. Data-driven exploration shows that the FIC initiates influential connections to all other regions to globally control the functional dynamics of the triple network. Moreover, stronger BN connectivity between the FIC and regions of the DMN and the CEN, as well as the increased outflow connections from the FIC are found to predict individual performance in memory and executive tasks. In addition, the posterior cingulate cortex in the DMN was also confirmed as an inflow hub that integrates information converging from other areas. Collectively, the results highlight the central role of FIC in mediating the activity of large-scale networks, which is crucial for individual cognitive function.