Prediction of fMRI activity using vector autoregressive models: a comparison of sparse and low-rank approaches

Vector autoregressive (VAR) models have a history of being used to examine functional connectivity in the brain, as captured by functional MRI studies. Such models allow for an estimation of Granger-causal relationships between regions of interest across the brain. Unfortunately, since the number of parameters in the VAR model scales as the square of the number of regions, and this is typically large compared to the number of temporal observations, these parameter estimates will exhibit high variance. To address this challenge, we introduce a low-rank pre-smoothing method that applies a low-rank approximation to the observations before fitting a VAR model. We estimate these models using individual subject data from both task-based and resting-state conditions, tuning hyper-parameters at the population level. Our low-rank approach is directly compared against sparse and unconstrained estimation methods. Evaluations of predictive performance and model structure reveal that our pre-smoothing technique enables robust individual-level parameter estimation and significantly reduces prediction error, a finding further validated by synthetic experiments where the ground-truth parameters are known.