Brain connectivity plays an important role in determining the brain region’s function. Previous researchers proposed that the brain region’s function is characterized by that region’s input and output connectivity profiles. Following this proposal, numerous studies have investigated the relationship between connectivity and function. However, this proposal only utilizes direct connectivity profiles and thus is deficient in explaining individual differences in the brain region’s function. To overcome this problem, we proposed that a brain region’s function is characterized by that region’s multi-hops connectivity profile. To test this proposal, we used multi-hops functional connectivity to predict the individual face activation of the right fusiform face area (rFFA) via a multi-layer graph neural network and showed that the prediction performance is essentially improved. Results also indicated that the two-layer graph neural network is the best in characterizing rFFA’s face activation and revealed a hierarchical network for the face processing of rFFA.

In this paper, the high-dimensional linear regression model is considered, where the covariates are measured with additive noise. Different from most of the other methods, which are based on the assumption that the true covariates are fully obtained, results in this paper only require that the corrupted covariate matrix is observed. Then, by the application of information theory, the minimax rates of convergence for estimation are investigated in terms of the ${\ell }_p(1\le p<\infty )$-losses under the general sparsity assumption on the underlying regression parameter and some regularity conditions on the observed covariate matrix. The established lower and upper bounds on minimax risks agree up to constant factors when $p=2$, which together provide the information-theoretic limits of estimating a sparse vector in the high-dimensional linear errors-in-variables model. An estimator for the underlying parameter is also proposed and shown to be minimax optimal in the ${\ell }_2$-loss.

Functional connectivity (FC) network characterizes the functional interactions between brain regions and is considered to root in the underlying structural connectivity (SC) network. If this is the case, individual variations in SC should cause corresponding individual variations in FC. However, divergences exist in the correspondence between direct SC and FC and researchers still cannot capture individual differences in FC via direct SC. As brain regions may interact through multi‐hop indirect SC pathways, we conceived that one can capture the individual specific SC–FC relationship via incorporating indirect SC pathways appropriately. In this study, we designed graph propagation network (GPN) that models the information propagation between brain regions based on the SC network. Effects of interactions through multi‐hop SC pathways naturally emerge from the multilayer information propagation in GPN. We predicted the individual differences in FC network based on SC network via multilayer GPN and results indicate that multilayer GPN incorporating effects of multi‐hop indirect SCs greatly enhances the ability to predict individual FC network. Furthermore, the SC–FC relationship evaluated via the prediction accuracy is negatively correlated with the functional gradient, suggesting that the SC–FC relationship gradually uncouples along the functional hierarchy spanning from unimodal to transmodal cortex. We also revealed important intermediate brain regions along multi‐hop SC pathways involving in the individual SC–FC relationship. These results suggest that multilayer GPN can serve as a method to establish individual SC–FC relationship at the macroneuroimaging level.