Sparse low-dimensional causal modeling for the analysis of brain function.

Resting-state fMRI (rs-fMRI) provides a means to study how the information is processed in the brain. This modality has been increasingly used to estimate dynamical interactions between brain regions. However, the noise and the limited temporal resolution obtained from typical rs-fMRI scans make the extraction of reliable dynamical interactions challenging. In this work, we propose a new approach to tackle these issues. We estimate Granger Causality in full resolution rs-fMRI data by fitting sparse low-dimensional multivariate autoregressive models. We elaborate an efficient optimization strategy by combining spatial and temporal dimensionality reduction, extrapolation and stochastic gradient descent. We demonstrate by processing the rs-fMRI scans of the hundred unrelated Human Connectome Project subjects that our method captures interpretable brain interactions, in particular when a differentiable sparsity-inducing regularization is introduced in our framework.