Estimation of high-dimensional connectivity in FMRI data via subspace autoregressive models

We consider the challenge in estimating effective connectivity of brain networks with a large number of nodes from fMRI data. The classical vector autoregressive (VAR) modeling tends to produce unreliable estimates for large dimensions due to the huge number of parameters. We propose a subspace estimator for large-dimensional VAR model based on a latent variable model. We derive a subspace VAR model with the observational and noise process driven by a few latent variables, which allows for a lower-dimensional subspace of the dependence structure. We introduce a fitting procedure by first estimating the latent space by principal component analysis (PCA) of the residuals and then reconstructing the subspace estimators from the PCs. Simulation results show superiority of the subspace VAR estimator over the conventional least squares (LS) under high-dimensional settings, with improved accuracy and consistency. Application to estimating large-scale effective connectivity from resting-state fMRI shows the ability of our method in identifying interesting modular structure of human brain networks during rest.