Tensor-on-Tensor Time Series Regression for Integrated One-step Analysis of fMRI Data

Music City Center 

Data acquisition in a functional Magnetic Resonance Imaging (fMRI) activation detection experiment yields a massively structured array- or tensor-variate dataset that needs to be analyzed with respect to a set of time-varying stimuli and possibly other covariates. The conventional approach employs a two-stage analysis: The first stage fits an univariate regression on the time series data at each individual voxel and reduces the voxel-wise data to a single statistic. The statistical parametric map formed from these voxel-wise test statistics is then fed into a second-stage analysis that potentially incorporates spatial context between the voxels and identifies activation within them. We develop a holistic yet practical tensor-variate methodology that provides one-stage tensor-variate regression modeling of the entire time series array-variate dataset. Low-rank specifications on the tensor-variate regression parameters and Kronecker separable error covariance tensors make our innovation feasible. A block relaxation algorithm provides maximum likelihood estimates of the model parameters. An R package, with C backends for computational feasibility, operationalizes our methods. Performance on different real-data-imitating simulation studies and a functional MRI study about Major Depressive Disorder demonstrate the stability of our approach and that it can reliably identify cerebral regions that are significantly activated.

functional MRI

Kronecker separable models

tensor decomposition

tensor variate statistics