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

Abstract

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 reconstructin..