Estimation of high-dimensional brain connectivity from FMRI data using factor modeling

We consider identifying effective connectivity of brain networks from fMRI time series. The standard vector autoregressive (VAR) models fail to give reliable network estimates, typically involving very large number of nodes. This paper adopts a dimensionality reduction approach based on factor modeling, to enable effective and efficient high-dimensional VAR analysis of large network connectivity. We derive a subspace VAR (SVAR) model from the factor model (FM) in which the observations are driven by a lower dimensional subspace of common latent factors, following an autoregressive dynamics. We consider the principal components (PC) method which can produce consistent estimators for the FM, and the resulting SVAR model, even when the dimension is large. This leads to robust large network analysis. Besides, estimates based on the main principal subspace can reveal global connectivity structure. Evaluation on a realistic simulated fMRI dataset shows that the proposed SVAR model with PC estimation can accurately detect the presence of connections and reasonably identify their causal directions, even for a large network.